When it comes to reporting on Indian gaming deals in Florida, white man speaks (writes?) with forked tongue!

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I have been watching developments on the gambling front in Florida with some interest lately, not because I plan to waste money on a trip down there but because the fuss and palaver provides clues about the way state legislators think.

After much self-righteous huffing and puffing, lawmakers basically caved to all the Seminole tribe's demands, swallowing whole the bait that 45,000 new jobs will be created and $4 billion will be added to state revenues by game expansions at the tribe's seven casinos.

Today's news item reflects the immediate impact of Florida's concessions to its Native Americans: a blatant attempt by the Indian casinos to gouge players at their blackjack tables.

The deal's publicity push promised $5 blackjack and baccarat, plus no-limit poker and sundry other gambling options, but when it came down to it, low-limit blackjack tables were nowhere to be found.

Worse than that, $25 players suddenly found their tables being switched up to a $100 minimum.

And unlike in Nevada, where low-limit players are allowed to keep playing at low stakes when the table minimum is hiked, anyone attempting to bet below the new limits was told to take a hike.

What amazes me is that none of the stories I have read makes any attempt to address the question of what table limits are all about.

Or why state pols invariably cave to casinos' demands, sucked in by promises of huge revenues that save them from the politically dangerous responsibility of funding services from legitimate sources untainted by moral murk.

Countless studies have shown that wherever it gets the nod (including in Nevada and New Jersey) legalized gambling costs more jobs than it creates and more money than it generates.

But somehow legislators never read those things, or are persuaded not to believe them.

Back to table limits: We can all guess that minimums are bumped up on weekends when demand increases because casinos are crowded, and we can grudgingly accept it as good business.

But the reality is that higher minimums reduce player's spreads, and that's where extra house profits lie.

A $5 player might spread all the way up to (gasp) $50, and even if he chooses his bet values more or less randomly, his 1-10 spread gives him a marginally better shot at staying ahead of the game than if he were to flat-bet at $5.

If the same player with the same limited budget is coerced into opening at $25, his spread will likely still cap out at or near $50, making him a more likely loser.

Of course higher minimums mean more moolah in the house's coffers, but tighter spreads make player losses that much more certain.

There's no good news about spreads in any of my models, that's for sure.

It is absolutely possible to win for a while with a spread as tight as 1-5 or 1-10, and if that were not so, no one would play table games and folks like the Florida Seminoles would lose their Native American shirts.

But the longer you play with a limited spread, the more likely it is that the prevailing house edge will gobble up your bankroll, especially if, like most gamblers, you are challenging the negative odds with inadequate funding.

Whatever your maximum, you will need many multiples of that amount in the bank to enable you to ride out rough spots and come out the other side ahead of the game.

And the narrower the spread, the larger the multiple, with a decreasing chance of success proportionate to the value of the "max." That's because the sooner you hit that green ceiling, the more you will be at the mercy of the house edge.

Overall, with a mere half-million or so mixed-game outcomes in my data set, a spread tighter than 1-2,500 will always lose in the end. It will do nicely for very long stretches, but will ultimately fail.

That assumes, of course, that you follow the dictates of computer simulations and take no defensive action whatsoever when a house spike hits and suddenly you can't win a bet to save your life.

A spread that wide is out of the reach of almost everyone, I realize.

But the harsh truth about gambling games is that they cannot be beaten without a disciplined plan with big bucks behind it.

Then again, a fat bankroll alone won't win in the end, so money is not everything.

Spread is the key, and evidently, those wily Florida Seminoles (whose casinos are actually being run by even wilier pros from Las Vegas and Atlantic City) know it.

Blackjack is far and away the best table game for target betting, because of its doubles, splits and naturals.

But variations on the traditional game, especially Royal Match, should always be avoided like the plague, along with layouts where the pay-out on a natural has been cut from 3-2 to 6-5.

Baccarat lags behind blackjack because wins never pay more than 1-1 (forget Ties and other distractions...they're a rip-off!), and the only sensible way to bet is to back Player only.

I know, I know, Banker wins more often than Player by an infinitesimal percentage. But the tiny edge it offers is blown to bits and then some by the 5% commission on Banker payouts.

The great advantage of baccarat is that it's a high rollers' game offering table limits that are generally far higher than for blackjack.

So when a recovery series drags on and bet values are weighed down with multiple zeroes, baccarat may be the best option for target betting.

Camouflage is a critical element in target betting, and full size baccarat layouts with all manner of high-value chips in play can provide it like no other game.

There are several target betting options that can be profitable when bet values in a new series are relatively low, but because the house edge is much higher (five times higher or more) you should figure to head back to blackjack or baccarat the moment the going gets tough.

Personally, I enjoy field bets at craps in spite of a house edge that ranges from around 2.6% to above 5.0%, depending on the payout for 6,6 (go for 3x tables whenever possible).

As in blackjack, a turnaround bet on the field can hit an x2 or x3 payout, greatly adding to the EOS profit.

I like 3-card poker for the same reason, although target betting has to be modified to accommodate the ante/raise procedure.

An important rule: never, ever bet on "Pair Plus"!

It is very rare indeed to see a player who doesn't put money in that innocent-looking drain-hole, and it is the reason most 3-card poker players are losers.

Bet only the ante, raise only on a Q,6 or better, and when figuring your LTD+ values, you should HALVE your current loss to date, rounding up in appropriate increments (-$275 calls for an ante bet of $150, for example).

The house edge for the game is around 4.0%, or at least 4x that for blackjack. But as long as bet values are at the low end of your sliding scale, the game's ante bonuses (up to 6x!) can make for profitable play for a while.

Again, never waste money on Pair-plus and ignore whatever sales pitches you may hear from dealers and even other players.

Pair-plus makes about as much sense as a Tie bet in baccarat, and in effect it requires you to constantly bet against yourself!

Roulette has its charms when seats at blackjack and baccarat layouts are hard to find, but the house edge of 5.26% makes it a short-term option at best.

Put your money on 1-1 options only (black/red, odd/even, first/last), although I confess that often I do well picking a 2-1 column (usually the first on the left), sticking with it every time, and applying the same LTD/2 rule as for 3-card poker.

Those are the only table games I will ever play in a casino.

My ranking: blackjack, baccarat, craps field, 3-card poker, roulette.

And when the going gets tough, blackjack is always #1, backed up by baccarat when table limits become a problem.

Table limits are, of course, much lower at craps, 3CP and roulette than at blackjack and baccarat, so that is another solid reason to limit your play against games with higher (or should that be lower?) negative expectation.

Follow the target betting rules consistently and you will win consistently too, which always becomes a problem after a while.

Losers get nothing from casino personnel other than forced sympathy and encouragement to lose some more.

Winners are welcome, as long as they eventually become losers - if they keep on winning, they are assumed to be cheats, and hell hath no fury like pit boss who suspects illegal shenanigans.

As a frequent winner, expect to be scrutinized and sometimes even gently harassed.

But don't expect the treatment to let up even after you have been proved honest and upright...winning is itself a sin in the house's book.

Your best allies are the dealers. Treat them well, and they will be less inclined to clue in their bosses on how you are managing to reverse the expected direction of the "chip flow."

Dealers who know you and can rely on you for steady tokes will usually tip you off when they are on a hot streak, a concept that academic mathematicians insist can have no bearing on overall odds but every player knows to be a very real part of gambling life.

You will win steadily and reliably, sometimes attracting the attention of other players even before the dealer takes notice (although dealers are mostly much quicker and smarter than they are given credit for!).

In spite of that, never run away with the idea that you are invincible. You have standard negative expectation whacked, for sure, but sometimes the house edge can go dangerously haywire before it settles back to the norm, and you need to be ready for that.

Pit staff will want to get to know you, but never be flattered by their attention.

Winners attract "comps" because the house wants them to stay where the money was won until it gets lost again, which is how the script plays out for most punters.

Never angle for comps. You don't need them, and their price is too high.

(Losers are sometimes "comped" too, but only the ones who keep returning for more punishment, demonstrating that they have money to burn and are looking for a light!).

You will be tracked during play once the spotlight is on you, but you do not have to make the house's job easier by giving them your name.

If you can, shrug off overtures from glad-handing pit personnel and say you are just passing through and no thanks, you don't want a Privileged Player's Premium card, or whatever.

Anonymity is a much better way to go, although it gets harder to achieve the longer you keep winning.

Play quietly and politely, keep your head down, and resist the temptation to tell wayward players how to improve their game, even if they ask for your advice (and they will).

Just remember that losers make the games possible. You need them as much as the house does.

In spite of negative expectation, you really do have the math on your side.

Although each bet theoretically faces the same negative odds, there are other numbers at work in a gambling game that work in your favor.

Among them is the demonstrable fact that for both sides in a game, more wins are isolated than are followed by a second win.

That's bad for you when you are bumping your NB value in response to a mid-recovery win. But, more often, you are betting (with the OL, 2L, 3L and MSL target betting rules) that the house will comply with expectation and lose on the heels of a win.

It is a fact that you will lose more potential turnaround bets than you win, thanks to the house edge.

It is also a fact that because you keep adjusting your NB values to match and exceed the loss to date right after a mid-series win, that small disadvantage will only very rarely be a problem.

You know you are going to lose more bets than you win.

It follows both logically and mathematically that in that case, you must ensure that over the long haul, you win more when you win than you lose when you lose.

Have I said that before?

Blackjack players will often tell you that the house advantage lies in the fact that you, the player, have to decide the fate of your hand before the dealer does. So if you draw a "stiff" (two cards that have to be hit) and then bust, the dealer wins even if he turns out to have had a worse starter hand than yours.

The "bust first" rule is a factor, certainly, and it bolsters the house edge significantly. But not nearly as substantively as the simple fact that the dealer has a lot more money to back him than you do.

The house can take a licking for an awfully long time, and will probably be rescued by its flimsy numerical edge long before it has to cry Uncle.

All a flat or random bettor can do is soldier on when times are tough, and pray for a miracle.

The target player needs neither prayers nor miracles.

As a target strategist, your best weapon lies in the fact that you set bet values, not the house.

The house will always, in the end, win more often than you. But you get to determine how much it wins when it wins and how much it loses when it loses.

That is true for every player, but it consistently makes the difference between winning and losing only when target betting is part of the picture.

Target betting shows you how and when to exploit control that most players don't know they have.

Random players hit their personal limits very quickly, and from then on will usually need to win more often than they lose because the odds are that that is the only way they can hope to win more money than they lose.

Your bets freeze in a downturn but will, when appropriate, keep rising to stay one step ahead of the LTD.

And that makes it really difficult for the house to beat you in the end.

In the good old days, pit bosses often used index cards on a chest-level desktop to track the activity of players who were either regulars requesting a rating, or of special interest for some other reason (an excess of "luck" for example).

One column of cards would track losers, and the column beside it would be for winners.

Usually, a card moved into the losers column would never move out of it, making it easy for the pit staffer to mentally tally one set of cards against the other and guess the current state of the house's bottom line.

What they would rather not do was move a card from lose to win, then lose, then win, which is what will happen again and again to a target player who stays in the same blackjack pit for too long.

Keyboard clicks have mostly taken over from squiggles on index cards, but either way, the moral of this tale is: Keep moving.

Most of the time, recoveries will come in six bets or fewer, and profits will accrue at a gentle pace that does not attract much attention.

Paired wins are less frequent than isolated wins, for sure, but on average they are rarely more than a handful of bets apart.

However, when a series drags on for ten or more rounds and the bets begin to look like real money, never be tempted to show the pit how clever you are by achieving EOS under the watchful eyes of the same crew that saw you place your piddling opening bet.

Betting from $5 to $500 in the same general vicinity is a bad idea.

I did that several times too often before I determined that profits and a low profile mattered more than demonstrating how deep a hole I could get out of.

Cash, not kudos...that's the rule!

If you really want empathy (especially when alternate layouts are temporarily hard to find) it is best to suspend play against a challenging series that would usually require a move, keep the LTD/NB numbers in your head, and drop back to a minimum bet.

You can accumulate several "deferred" series if you choose, saving them for another casino or another day, and your (temporary) losses will keep at least one pit crew happy for a while.

The folks in the next pit you visit will likely have a lot less to smile about.


The screenshot composite above is from the current BST blackjack session, which as I type this is a little over half done (I don't play as often or as long as I used to, on the grounds that my point was made long ago!). The numbers you see are not "proof" of anything, just an example of what can be achieved with target betting. Three of the four sessions had more losses than wins, and the other was a virtual break-even. In each case, the state of the bankroll after the last hand belies those numbers (and unlike many no-dough apps, BST does not permit players to alter their bankrolls!). I suppose it's possible that similar results might be seen if a simple Martingale were used against Ken Smith's elegant little app, but I have my doubts. I also suppose that cheating is an option. But it isn't for me. As I always say: What for? Target betting is easier and more reliable than cheating could ever be!

An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you.
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Occasional losses are inevitable as long as there is a house advantage (and there always is). Target betting makes those losses very rare indeed.

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Sims tell lies. We all know that. But when they say things you want to hear, they're so cool.

Opponents of any and all betting methods that challenge the supremacy of the house advantage in casino games of chance are crystal clear in their interpretation of the "laws" of mathematics.

If the actual value (AV) or house advantage (HA) applicable to a representative sample of outcomes is a negative percentage, then a player's losses against those outcomes will closely approximate his total action multiplied by the HA.

So 1,000 bets against a negative HA of 2.0% with an average bet value (ABV) of $10 will result in a loss of $200, give or take a chip or two.

There is no room for equivocation here: "Any amount bet against a negative expectation must have a negative result."

Luck can upset the house's applecart for a while, but it is a temporary phenomenon according to the law(s) of large numbers, and the axiom can be boiled down to three little words...you can't win.

That means that the following sim-generated results could not have happened:




They did happen, against outcomes supplied by a random number generator (RNG), with all five indicated progressive betting methods showing a profit after 1,000 rounds in spite of a very substantial house edge.

Last time, I posted a summary from 150,000 RNG outcomes that showed target betting well ahead of the game in defiance of the "laws" of arithmetic as interpreted by the gambling industry and its very smart experts.

And to be fair, their pessimistic view of a gambler's long-term prospects is logical as long as the punter bets fixed amounts or bets randomly.

If he bets progressively with a very specific target in sight, negative expectation will be thwarted at least 99.99% of the time, making results like those above and elsewhere on this blog commonplace.

The methods summarized here include the standard Small Martingale, which doubles the bet after any loss until a win is achieved, delivering a profit equal to the value of the opening bet, and a souped-up Martingale (-5, -10, -25, -50, -100, -250, +500) that gooses win values in proportion to an increase in overall risk.

Target betting heads the list, of course, with OG referring to a version of Oscar's Grind that departs from the rules laid out by Tom Ainslie in his book.

Mr. Ainslie claims that "Oscar" has been a steady winner for him year after year and is endorsed by one of gambling's premier mathematicians. But I have been far less lucky whenever I have applied it against one of those sims that systems debunkers love so much.

The OG shown above doubles the bet after a win, to a maximum value of the loss to date (LTD) plus one unit.

The Ainslie version adds one unit after a win, ensuring that recovery after a prolonged downturn will be long and arduous indeed.

Mr. Ainslie recommends abandoning a recovery attempt and starting over if the LTD hits 20 units (-$100 at a layout with a $5 minimum). That rule makes getting ahead a very iffy proposition.

OGT spices things up a little by making the win target not one measly unit, but 10% of the maximum loss in the current series. So if the method is $500 "in the hole" at one point, the win target is $50, and so on.

In each of the above summaries, EXP shows the amount each method "should have" lost in compliance with the HA x Action formula promoted by the gambling biz.

As you can see, it didn't happen, which is not to say that it never will.

The estimable Wizard of Odds, by far the most eloquent of all the casino shills plying their trade on the Internet, describes his decisive debunking of a betting strategy devised by a challenger with the lyrical name of Daniel Rainsong.

I have no knowledge of Mr. Rainsong's method and have been unable to track him down, but my guess is he wuz robbed.

The sim that beat him imposed a spread limit of 1,024 to 1, which might not have stymied Mr. Rainsong's strategy but would be a big problem for mine.

Mike "Wiz" Shackleford, self-billed as an international casino consultant, was able to offer Mr. Rainsong a seemingly generous house edge in his "billion bet sim" because he well knows that it is a deficiency in the critical combination of spread and bankroll, not the value of the HA below double digits, that seals a player's negative fate.

Hell's bells, he could have set the runaway sim's HA at zero and still have "beaten" the Rainsong method. But that, of course, would have given his game away.

Like many gambling industry insiders, the Wiz is well aware that inadequate bankrolls and tight spreads are the stuff that fat house wins are made of.

An even-money game (the sort that does not exist in any casino) would draw out the house's winning process a little longer, it's true. But it is short-term negative spikes against the player that put the wind up inexperienced players and wipe out piddling bankrolls, not gouge-level HAs.

The great joke in gambling is that most punters would be defeated by a game that actually gives them the edge!

That is why casinos routinely report game win percentages that far exceed the known HA for blackjack, baccarat, craps, roulette and the rest.

Think of the billboard slogan that suckers could be reading as they pedal-to-the-metal towards their certain doom in Las vegas: "We'll give you a player edge, but we'll STILL kick your ass."

Spread is the whole ball of wax for progressive betting or for ANY winning method, and a 1,024-1 limit is a deliberately deceptive gift to anyone claiming that the house edge is unbeatable.

It is a non-issue for most gamblers, for whom a 1-10 spread is too much excitement, as well as a guarantee that they will lose unless they get very, very lucky.

Casino operators have known since the beginning of time that capping the bet spread is the most effective way to protect the house edge.

That is why table limits ($5 to $500 at a blackjack layout, for example) exist, and why pit personnel are on the lookout for players who gradually escalate their bets until they achieve a turnaround win and then start over.

"The math" demands that the sooner you hit your upper limit, whether it is house-imposed or your choice, the more likely you are to fall victim to negative expectation.

Conversely, the more wiggle room you are permitted, the greater is the probability that you will be able to win more when you win than you lose when you lose, thereby overcoming the otherwise inexorable ill effect of losing more often than you win.

It is a challenge to work a casino with target betting, and it can only be done by keeping as low a profile as possible.

My policy has always been to spread no wider than 1 to 50 at a bottom tier casino (say, $5 to $250), and no wider than 1-5 at any one layout once the bet has reached $100.

Above the bottom level, the rule of thumb remains 1-5 at the current layout, and drops to 1-10 in any one casino.

The theoretical effect of this sliding scale is a whole lot of to and fro between layouts and casinos, but theory has a habit of evaporating when real life takes over.

Because the odds against you do not change much from deck to deck or game to game, a recovery series made problematic by "local" limits can be suspended until better conditions are available. But that will not happen often.

As your bankroll grows, it becomes easier to stay calm and confident when the pressure is on, and respond appropriately.

In spite of all of the Wiz's claims to the contrary, computer simulations are not a substitute for real play because they exclude the most critical component of gambling, the human element.

They also eliminate cards, dice, wheels, dealers and real time.

I have on occasion been accused of being an agent of the casinos because I offer players an alternative to losing that cannot possibly help them in the long run.

All I can say to that is that anyone claiming that games of chance cannot be beaten is a far more effective shill for the casinos than I could ever be.

Bet flat or bet randomly and you will lose.

Bet progressively according to the rules that I have been providing free of charge for more than a decade, and the odds will be dramatically in your favor rather than fractionally against you.

Either way, the arithmetic is very simple.

Against a game with a 2.0% house edge, you have a 49% chance of winning any bet and a 51% chance of losing it, whether you use target betting or not.

That means that each and every time you place an LTD+ bet in the hope of turning a losing series around, you will probably lose it.

But because your bet values keep changing to match the LTD (and because you either win or lose 100% of your bet, not some cockamamie amount in between) you can be confident that eventually, you will beat those negative odds.

On average, target betting with optimum parameters applied will turn a recovery series around in just over five rounds.

Both versions of the Martingale will do the job a little faster, but their greatest drawback is that they are unplayable in most casinos (pit staff will interfere with their use because they know they represent a real threat).

Tom Ainslie's inch-by-inch version of Oscar's Grind needs an average of 30 rounds to get out of the hole with the 20-unit bust limit omitted. It cuts that number by more than half with the limit in place, but struggles to make a profit, obliterating its gains with a succession of $100 bailouts.

Oscar's Grind could easily be a creation of the casino industry because the limits Mr. Ainslie advocates guarantee that it will fail while deluding the player into thinking that he is in control.

It is a progression, to be sure, but a halfhearted and nervous one that is no threat to the house advantage.

Capping the bet at $100 (assuming a $5 opener) will accelerate the bankroll's downfall and might even be more dangerous than betting random amounts within the same range and hoping for a little luck.

A veteran dealer at Caesars Palace in Las Vegas once told me that Frank Sinatra, a blackjack enthusiast who liked to take over an entire table, would stuff his pockets full of chips and walk away when he won but was not required to pay off his marker when he lost.

That, I admit, may be the best betting strategy I ever heard of. Target betting is the next best thing, far superior to any version of Oscar's Grind!

It all comes down to the comparative frequency of wins and losses, or the win-loss pattern (WLP), and the demonstrable mathematical truth that for both sides in the game, isolated wins are more common than streaks.

For a random player, the WLP whisks his fortunes back and forth like a falling leaf in a gentle breeze, a win here, two losses there, a win, a loss, two wins, three losses.

In essence, the target player bets against the house being able to sustain a winning streak, which is subtly different from putting his money on his own luck.

Most gamblers backing what they hope is a player winning streak do so diffidently, often failing to recover the chips they lost when the WLP went against them.

Target betting's primary objective is to recover past losses in fewer bets than it took to lose the money in the first place.

It is "axiomatic" that if the house cannot take a bite out of your bankroll by winning more often than you do, than the house has a problem.

When all of target betting's rules are in play, the strategy will recover prior losses with a single win more than 70 percent of the time (not as impressive as a Martingale's 100 percent, but usually not as dangerous or as obvious, either!).

Until the strategy's top limit bet value is reached, two consecutive wins will do the job.

Once the "max" is on the table, target betting is as much at the mercy of the house advantage as any other method.

But in order to get into a hole that deep, the method must have been battered by a spike in the house edge that will at some point have to be at least partially offset in order for the known laws of math to hold true.

Let's say that the house edge went haywire for a while, putting you 12 bets "behind" in in 30 rounds, for a series HA of -12/30 = -40.0%. Ouch! All of a sudden, you are at your limit, and the only thing that can save you from certain death is the size of your bankroll (and your intestinal fortitude).

How likely is it that the house spike will continue, or that the next few dozen hands will not contain enough player wins to get you out of the hole? Not very.

Negative expectation for the game is, say, 2.0% (higher than blackjack, but easier to work with when it comes to arithmetic). We know that at some point in the future, the 12 bets you are now behind will be mixed in with upcoming wins and losses until the overall house edge for a sample beginning with the first bet in the current series drops from 40.0% to a number much closer to 2.0%.

In theory, the WLP could bounce gently to and fro without any significant streaks either way for the next 570 bets until the overall house edge settles at the level where it is "supposed" to be.

But that is very rarely the way things go in games of chance. Much more likely is a pattern resembling one of the three red-line charts shown above: more downs than ups, but enough ups to save the day for you and your bankroll.

For most players, falling just a handful of bets behind sets them on a slippery slope that cannot be escaped without a calculated exploitation of every potential winning streak.

Bumping the bet in response to every win will at times increase the speed of the downward slide. But it will also make a very rapid recovery possible.

I spend a lot of my casino time watching other players from a respectful distance, because seeing them succumb to a WLP that I know I could easily have beaten is almost as satisfying as winning myself.

Don't get me wrong, I get no pleasure at all from seeing strangers lose their money. But there is nothing I can do to help them, and monitoring their avoidable missteps at least provides one of us with a positive outcome!

If you want to win consistently, you first have to accept that over time, you are going to make more wrong bets than right ones, and decide what you are going to do about that.

If you are $50 behind and plan to stick with a bet value averaging $10, then you know you will need five more winning bets than losing ones in the near future just to break even again. How likely is that? Again...not very.

By freezing your bet after a loss, you are, in a sense, betting that the house will continue its winning streak for a while.

When you bump your bet value in response to a mid-recovery win, you are up against the same negative odds that apply to every bet but recognize that a ping-pong volley of bets of equal value is not going to get you out of the hole.

The great irony is that much of the time, betting as wide a spread as you can afford will put you at less risk than betting smaller amounts over and over again as you slowly slide deeper into the mire.

Along the way you have to set aside the standard gambler's dream of rich rewards for little risk, and think instead the way the house does.

Be happy to pocket a win that is just a few percentage points of your total action, remembering that that is how the bills get paid in the casino that surrounds you.

Don't be greedy, don't be noisy, don't get cocky and above all, keep your head down.

You will win far more money far more often than the average gambler. But that does not mean you are unbeatable.

An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you.
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An international math superstar's assessment of sims as models of human behavior: "Absolute rubbish!"

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Last week's edition of Newsweek includes an article which I interpret as vindication for my longstanding skepticism about the validity of computer simulations as predictors of human behavior.

Paul Wilmott is described as a leading quant, meaning that he specializes in developing new principles of quantitative finance that can be safely applied to the complex world of economics.

It seems he agrees with me that because mathematics cannot predict human behavior, mathematicians recklessly created models that ignored it entirely, with the disastrous results that we are all now living through.

Economics and gambling are alike only when it comes to the speculative nature of stock trading, but human nature has a powerful influence in both fields, and ignoring it is both deceptive and dangerous.

To celebrate Mr. Wilmott's dismissal of most financial models as "absolute rubbish" I decided to boost my database of blackjack and baccarat outcomes past the half-million mark by writing a new "sim" of my own to give me 150,000 new rounds.

That might seem foolish or hypocritical, but I had every reason to be confident that target betting would come out ahead this time, just as it always has.

I would love to be able to claim that there was not a loser among the 20 models of 7,500 rounds or 100 shoes apiece, but it didn't work out that way.

Here's the bottom line:


Given my dismissal of sims as proof of anything other than the disingenuous agenda of house-trained mythematicians, I can hardly trumpet the above summary as a victory for the principles of target betting.

But like my critics, I have to be grateful for the speed and convenience of computer game simulations while doubting their relevance to real play in real time by real people risking real money.

It would take me at least a month to record and collate 150,000 outcomes of baccarat, which has to be the most laborious table game ever devised, and even my soon-to-be-replaced laptop was able to come up with this data set in barely 15 minutes.

The first thing to notice is how similar most of these sets are to the baccarat data independently supplied by Messrs. Jones and Rodriguez.

As regular readers will know, my quarrel with sims is based on their requirement that the "player" they pretend to emulate must bet exactly the same way whatever the current conditions. Like a suicidal lunatic, in a word.

No defensive tactics or damage control can be applied in the otherworld of runaway sims. And perhaps the silliest conceit of all is that, in a sim, it must be possible to bet from the house minimum to the house limit in one place.

The defenders of the status quo insist that damage control is in the long run irrelevant, because the inexorable nature of the house advantage makes the probability of a beneficial effect slightly less than a 50-50 proposition in the same way that each bet is slightly more likely to lose than to win.

What this assumption willfully ignores is that progressive betting changes the odds from less than 50% to better than 90%, as shown throughout the earlier blackjack/baccarat data set and in the new outcomes summarized above.

That's an improvement from less than 1 chance in 2 to a much friendlier 10 chances in 11!

Target betting will always show a profit if a recovery series lasts for 10 rounds or fewer, even if more bets were lost than won in that series.

In the latest set, 91.4% of all series fell into that "easy win" category.

That's not to say that series lasting longer will lose - there was just ONE "bust" in 28,798 series in the new sample, indicating a win rate of 99.9965%.

My experience is that real play almost always offers better conditions than any simulation, even if that substitute for reality is based upon actual outcomes recorded in a casino.

The problem is, of course, that even "real" results become sim-like when they are plugged en masse into a model, with a betting strategy then strictly applied with no reliance on a human response to potential threats to the bankroll.

It is a classic rock-and-hard-place dilemma, confirming that the only truly relevant test of a betting strategy is real play by...etc.

The gambling industry knows that essential truth better than any mathematician!

Paul Wilmott happens to be the loudest and most visible among countless 20/20 visionaries who were either silent or unheard in the run-up to the economic tsunami that, according to an estimate I read on the Net today, has wiped out more than $1.3 trillion in Americans' personal wealth in less than a year.

The only good news is that a big chunk of that washed-away wealth was in the hands of casino moguls like Steve Wynn, Sheldon Adelson and Kirk Kerkorian after they had leeched it from the misguided fools who actually earned it before flushing it away in Las Vegas.

To the thousands of Wall Street wonks whose jobs were sucked away by the ebb tide, I can only suggest that target betting in a casino offers them a better shot at rebuilding their bankrolls than their former workplace ever will again!

And target betting is also a whole lot less complicated and dangerous than any of the fancy fiscal formulas that flew ever higher before succumbing to the force of gravity and falling to earth.

What sims ignore is that once a player recognizes that progressive betting is the only way to win consistently, a wide array of tactics become available to him or her.

And while a million-dollar bankroll may be ideal, it is not essential: the principles of target betting can be adapted to more modest resources, and will always offer the player better long-term odds of success than flying by the seat of his pants.

Luck might serve him better in the short term. But luck never lasts, for either side of the gambling equation.

The new RNG summary offers a wealth of useful insights that are not rendered totally meaningless by the unreliability of sims.

For instance, a standard Martingale and my souped-up versions of double-up and Oscar's Grind all did well against the new sample, each reversing the effect of the negative expectation that would have doomed a flat or random bettor challenging the same outcomes.

There may be skeptics out there who will say that 150,000 rounds is "not a representative sample" but they will be tooting a hollow tune: very few "recreational" gamblers will place that many bets in an entire lifetime.

The bottom line is that all of the results I have reported in this blog are impossible according to the conventional wisdom, meaning that either the conventional wisdom is wrong or I am a fraud.

In the new non-fraudulent sample summarized here, 14 of 20 sets of 7,500 outcomes ended with more bets lost than won, and more than 64% of all series "should have" ended with a negative or neutral result.

Instead, more than 73% of all series scored a profit after just one win, a minor miracle made possible by a combination of the OL, 2L, 3L and MSL rules of target betting (click on the rules link at the top of the blog for a refresher course).

The average end of series (EOS) win came in less than six bets.

As expected (and required by the overall house edge), more EOS attempts failed than succeeded. But because the win target is constantly updated to match the loss to date, that was not, in the end, a problem.

Target betting with the above parameters applied is an aggressive approach suited only to a large bankroll, but the actual exposure was barely 50% of the recommended $1 million.

The average win per 7,500 rounds was more than $110,000 or about $1,000 per shoe of baccarat.

Target betting turned a negative expectation of 0.97% (low for baccarat, but that can happen) into a positive result equal to +1.54% of total action.

SM, SM+ and OG (see below) all did better than target betting, in percentage terms, but delivered smaller funny-money profits.

Target betting is intended to win more when it wins than it loses when it loses in order to overcome the inescapable house advantage in casino games of chance, and against the new sample, the overall average win value exceeded the average loss value by 5%. That was more than enough to trump the house edge.

The AWV/ALV percentage for the 19 winning sets was 115%.

The average bet for target betting was $529, although only 5% of all bets (7,440 out of 150,000) exceeded $1,000.

The averages for SM, SM+ and OG were $51, $217 and $74 respectively.

The final target betting win against this irrelevant and unreliable sample of outcomes (it came from a sim, so how else can I describe it?) was equal to a little more than $800 per hour of play.

Exposure of the bankroll exceeded 10% in 9 of the 20 sets of baccarat outcomes. I will apply "bare bones" parameters against the same data sample sometime soon and post the results.

The "expected" result from this set, given a -0.97% actual value (AV) and target betting action of $79.35 million, was a LOSS of $773,000 in contrast to a WIN of $1.22m.

The overall win rate for target betting was 99.9965% or 1 loss in 29,798 series.

My critics will continue to insist that none of this could have happened without sleight of hand. That is because in many cases their livelihood depends on denial.

More about the alternatives to target betting featured in the above summary...

SM is the much-maligned standard Martingale (-1, -2, -4, -8, +16), which is very effective but almost always unplayable because of the vigilant paranoia of pit personnel.

SM+ is my adaptation of SM to deliver a little more than $5 in profit from a $5 opening bet: -$5, -$10, -$25, -$50, +$100). It is also virtually unplayable, although scrutiny can sometimes be dodged in a busy casino by betting no more than 3 wrong bets at any one location.

OG is for Oscar's Grind, which as far as I know is the only betting strategy ever endorsed in a mass-market "how to" book about gambling.

That alone makes the method suspect, since gambling books as a genre are intended to encourage people to play more while reinforcing the message that losing is ultimately inevitable.

I applaud OG for freezing the bet after a loss, thus helping to confound the enemy. But author Tom Ainslie's rules (NB=PB+1u after a win, bail out after a 20u loss, and do not apply a win progression) are in my view a prescription for certain failure.

Mr. Ainslie claims he has paid for countless Caribbean gambling trips with Oscar, which makes him a very lucky fellow. Whenever I model his rules, I drown in red ink!

My "OG" applies a win progression of PB+1u after an opening win, and as with target betting makes the streak-ending loss the LTD. After that, the mid-series win response is PBx2 to a max of LTD+1u rather than Mr. Ainslie's wimpy PB+1u.

As I said earlier, a player who embraces the unique efficacy of progressive betting as an antidote to the progressive (or regressive) process called losing has multiple options that range from mildly confident to supremely cocky.

Any one of them is better than playing and losing the way the gambling industry expects you to.

An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you.
_

"Proof of wins is meaningless. Anyone can win once in a while. All that matters is that when your system loses, it loses BIG!"

_
I cannot over emphasize how important it is that anyone interested in learning the principles of target betting should not take my word for anything.

Gamblers are too ready to believe whatever they are told, but this blog is not aimed at them.

My audience (I hope!) consists of smart people who enjoy playing casino table games but do not consider that losing at them is inevitable.

They are not gamblers. They are players. And believe me, there is a big difference.

I was asked some time ago about the viability of a $100,000 target betting bankroll against baccarat, and my response was that while it stands a pretty good chance of making a steady profit, I would not recommend it.

I said that because target betting is not about taking chances. Its objective is to win, and the likelihood of success depends not on luck but on optimal use of available resources.

The switches or settings - the rules - of target betting each play a vital role in helping us towards our long-term goal, but only one of them is absolutely indispensable, and that is the LTD+ response to a mid-recovery win.

Even that can be modified to lessen potential strain on a limited bankroll, but once we start doing that, we need to be aware that recovery may take longer and deliver a smaller profit.

Last time, I introduced the acronym WYNN for "watch your negative numbers," and while I intended to poke a little fun at the best-known casino operator on the planet, the message was absolutely serious.

Most of the models displayed in past posts show a bankroll of $1 million and a win capability of at least $1,000 an hour at blackjack (less at baccarat because James Bond's favorite game pays even money at best).

Trimming money-making tactics necessarily cuts into anticipated revenue while reducing risk somewhat, and that requires a significant reduction in the "bust" limit, from a cool million to $250,000 or less.

After all, a 75% drop in the rate of return is only acceptable if it also permits a proportionate cut in the risk, or "level of investment."

I am generally inclined to the "if it ain't broke, don't fix it" point of view, but I do recognize that it is easier to say (or type) the words one million dollars than it is to put the indicated sum into play in a casino.

All of the models in my database are available to anyone who asks nicely to see them, and very few indicate a level of exposure greater than 50% of the notional bankroll.

With all target betting's bells and whistles clanging and shrieking, an exposure of 10% or less is not uncommon, and the strategy wins at such a rapid clip that the initial investment quickly becomes a distant memory.

The whole idea of target betting is to build resources as efficiently as possible, because as the bankroll gets fatter, the chances of long-term failure diminish.

What my critics refuse to accept is that human beings do not play like the mindless robots that are at the heart of any computer game simulation.

An excess of caution can often be more dangerous than outright recklessness, but a skilled player develops intuition that becomes more reliable as time goes by.

Personally, I can never prove that the dealer who shakes his or her head as I approach a blackjack table, warning me away from a current "hot" streak, will have actually saved me any grief. But I certainly appreciate the friendly thought, and very rarely ignore it.

So it is with a negative trend that was not preceded by a red flag waving: If it feels right, I will move before I reach my predetermined spread limit, and I certainly will not stick around past that point.

The argument that in the long run, "damage control" stands less than a 50-50 chance of escaping potentially deadly playing conditions and leading to a quicker recovery is deliberately and cynically specious.

And the claim that improved conditions were just as likely to have come along if the player had stayed put and taken his punishment like a man is irrelevant: table limits are a reality, and where they are not a factor, a target bettor has his own rules to follow.

The arithmetic tells us that no one, however clever or lucky he may be, can escape the effects of the house advantage in the long run.

In terms of wins vs. losses, with the latter inevitably expressed by a larger number than the former, that is true and it is foolish to believe otherwise.

And it follows that anyone who bets fixed sums or determines the value of his wagers randomly must in the end lose more money than he wins as a consequence of losing more bets than he wins.

It must then also be true that for the fixed-sum or random punter, damage control will over time prove to be pointless, because it can have no effect on the overall percentage value of the house edge.

Target betting succeeds against the house edge and the dire expectation it entails because dramatic win-loss pattern (WLP) swings in the house's favor are not the norm.

And as long as the target player has not yet reached his maximum bet value, he will be able to recover all his prior losses in far fewer winning bets than the number of "wrong" wagers it took to gobble up the chips that were temporarily sucked into the dealer's tray.

Even when his "max" has been reached, the target player has "the math" on his side.

Usually, the house needs a sustained advantage of at least 25% in order for a target bettor's bankroll to be seriously threatened, and a negative trend that is a dozen or more times greater than expectation for the game cannot last indefinitely.

That is why a strong bankroll is an essential weapon against the house. It will not be needed often, but like the big guns on a battleship, it needs to be there just in case.

None of this means that it is possible for a wealthy player to simply "buy the pot."

Money is very useful in a casino, sometimes even essential. But money alone will not guarantee a long-term win, as many a misbegotten high roller can testify.

Money and a plan...now that's a winning combination. As long as the plan is target betting.

So, to get back to the opening point of this post (and to repeat the advice in the blog's introduction), don't take my word for the value of target betting.

Learn the rules, and test them in your own time against games of your choice.

You can be sure of losing more bets than you win.

But you will still make money, even if the chips are not real.

Let's face it, if the house cannot win in spite of raking in your cash more frequently than it has to pay you off, the house has a problem.

You don't. And that is all that matters.

An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you.
_

Don't blame bad luck when you lose at a casino table game...it's more likely that bad betting did you in.

_
Anyone who walks into a casino hoping to win more bets than he loses is probably going to be disappointed.

But that is exactly how most gamblers approach the challenge of beating odds that they know from the start are against them.

It doesn't make much sense, does it?

It is a demonstrable mathematical fact that if you bet the same amount each time, or choose your bet values randomly, you will eventually fall prey to the house advantage, more likely sooner than later.

And even if you apply money management to the process, responding appropriately to trends for and against you and restricting bet values to a limited proportion of your bankroll, you won't win in the end.

You will simply get to play a little longer.

Casinos are not in the business of money management...player management is their game, and they do what they do so subtly that most gamblers believe that the choices they make are entirely their own.

For example, before a casino in my Nevada neighborhood burned down a year or so ago, its blackjack tables offered a betting spread of $2 to $200.

When it reopened, its fancy new layouts all had table limits of $5 to $100.

To the vast majority of punters, table (or spread limits) are a matter of supreme indifference.

Most people do not spread their bets wider than 1-5, and the bigger their bankroll and their opening bet, the tighter their spread is likely to be.

It is possible for them to make a little money if the house advantage maintains its predicted level for a while and if they press while they are ahead and pull back during a downturn.

They will be in trouble when the house gets a few bets ahead, because they will need an equal number of wins to recover, and because of the game's bias, that may not happen in time to save their meager bankroll.

By imposing table limits, casinos exploit the fact that most players are reluctant to quit a game during a losing streak, especially if the joint is jumping on a Saturday night, and finding another seat might take a while.

So for nearly all of the players who returned to that rebuilt casino in Nevada, their only complaint is likely to be that $2 bets are no longer permitted, not that the maximum spread has dropped to 1-20 from 1-100.

I do not have access to the books at Topaz Lodge, of course, but I can promise you that the house win per player numbers at its blackjack tables are up, in spite of a slump in casino traffic.

The reason is quite simply that $25 players can now only spread 1-4 instead of 1-8, and while spreads that tight are sure to lose in the end, the prospect of a late lucky streak has been summarily halved.

Gamblers are creatures of habit and highly predictable, and casinos depend on their knowledge of human behavior to maximize their profits.

"System" is a word that in the gambling context has become a pejorative, conjuring up images of snake-oil salesmen and the gullible fools they prey upon to profit from their evil schemes.

Outside of casinos, the word is more likely to connote discipline, orderliness, good sense and professionalism, and sundry other attributes.

Inside casinos, only the management is systematic, secure in the knowledge that mathematics, perhaps the most orderly discipline in the known universe, will smooth out minor fluctuations in player behavior and the ups and downs of fate and fortune and deliver a profit at the end of the day.

It comes down to this: a player who does not bet systematically will lose.

It may not happen today or tomorrow, but it will happen in time, as surely as 2+2-5 is a negative number.

And in spite of that undeniable truth, 99.99% of all gamblers will tell you that there is no system known to man that can beat the house advantage.

Here is a different look at the latest pencil log from my BST blackjack trial:


The big numbers in the BST screenshots should come as no surprise by now, and I have stopped providing breakdowns of each step along the way to a final win because by now the point should have been made.

What may surprise some of you is that throughout the session, losing series, defined here as recoveries achieved in spite of more bets lost than won, are in the majority.

It should not come as a shock, but too many people are inclined to assume that luck is the only factor that can make you a winner in a casino, and it simply is not so.

Since none of us can ever know ahead of time if the very next bet is going to win or lose, systematic betting is our only option.

Call it money management if you like - call it grzignflumpf, even - but however you may choose to gussy up or disguise it, a "system" is what is needed here.

Casinos know this and are constantly on the alert for players who do not bet (and lose) the way they are "supposed to."

Table limits are one way to reign in players who may have the means and the inclination to "bet the farm" in the midst of a punishing losing streak and recover all their prior losses in a single bet.

Another is to come down hard on punters who are "foolish" enough to revert to the best known - and thanks to the gambling business, most reviled - system of them all, the double up, double down or the Martingale.

Unless we believe in luck, along with Santa Claus, the Tooth Fairy, and other invisible benefactors, we all know that over time we are going to lose more bets than we win.

It that were not so, there would be no casinos.

It therefore follows that the only way we can win in the end is to rake in more money from a smaller number of winning bets than we give up from a greater number of losing bets.

A Martingale does the job very well: -1, -2, -4, -8, +16 delivers a 1-unit or +3.2% win against a house advantage of -3/5 = 60%, average win 16u, average loss 4u.

A Martingale also happens to be unplayable in a casino, except by professionals who spend their time in motion, losing no more than three bets in any one location before moving on in search of the single win that will give them a profit.

They find themselves out on the sidewalk from time to time, but they don't care: there is always another casino just a few steps away.

Nor do they care that "the math" is apparently against them: they are grateful that all but a tiny percentage of gamblers believe that to be so, leaving the field open to them.

Consider an opening bet of $5 and a relatively modest baccarat table limit of $15,000 (the current green ceiling at Harrahs Stateline), then the fact that 12 consecutive losses will be needed before the next bet in the progression ($20,480) will be unplayable.

Now think about the odds against 12 consecutive losses: roughly 0.002% or 2% of 1% or 1 in 4,016.

Next, consider that if our "Martingaler" places and wins a $15,000 bet at baccarat, he is $5,480 "in the hole."

End of story? Of course not! His chances of winning that first $15,000 bet are a little less than 50-50 (49.3 to 50.7), meaning that he will probably lose. But what he now has to ask himself is how likely it is that he can get just two bets ahead of the house ($30,000 less $10,240) after falling 12 bets behind.

Thanks to the house advantage, a force that pulls both ways, those chances are better than good.

The so-called Gambler's Fallacy is the assumption that because an inordinate number of bets have been lost, a win is somehow more probable at this moment than it would be otherwise.

When applied to individual bets, the delusion is well-named as a fallacious disregard of the negative odds that apply equally to every bet, regardless of what went before.

But our Martingaler has just lost 12 bets in a row, then won a single wager, indicating a house advantage for the sequence of -11/13 = 85%.

The known house edge for baccarat is about 1.4%, so how "probable" is it that the house will stay 11 bets ahead indefinitely?

Not very.

It is at this point that a large bankroll becomes essential to the task of eliminating the negative effects of the house advantage.

I have had many a mathematician scold me with a reminder that in theory, an egregious imbalance like the example above need never be offset sufficiently to enable a progressive bettor to recover his losses.

But I have yet to be provided with a real-play example of the house edge running amok without eventually returning to compliance with negative expectation for the game.

There is a good reason for that: It can't happen.

It can take a while, but the house edge cannot stay at 85% (or even close) forever. Remember, we are not betting the farm on a complete counter-swing of the pendulum, just one or two wins.

Mythematicians love to trot out runaway sims to "prove" their specious prophecies, so it seems fair that I offer one of my own, an Excel RNG that signals HELP! when the house edge exceeds 50% and SAVED! when paired wins occur.

For a Martingaler who is betting below his green ceiling, a single win is enough to recover prior losses. For a target player, it sometimes (about a third of the time) takes TWO, otherwise one is all that is needed.

Ask me nicely, and I will send you the file. Meantime, here are a couple of out-takes, and the formulas are at the bottom of this post.



Mythematicians, the guys who will defend the power of the house advantage no matter what, concern themselves with what is possible rather than what is probable, arguing that if a given betting method can fail even once in 50,000 bets, it should not be trusted at all.

In casinos, all manner of wondrous outcomes are possible, but not probable, and the probable outweighs the possible by a percentage just great enough to hand the house a profit at game over.

For example, a royal flush is possible on a $5 video poker machine, paying out $20,000 and making the lucky winner very happy.

But on average, at least $21,500 will have to be fed into the machine for every $20,000 paid out, making the house even happier.

And more than 98% of the people who play that machine between jackpots will take out considerably less money than they "contributed."

The HELP! SAVED! file is no more representative of an actual game of baccarat than any other runaway sim, but it serves to illustrate the important difference between what's possible and what is probable.

Once in a great while, a serious threat to the bankroll will emerge. But the greater likelihood is that by then, so much money will have been won that the potential damage from the exposure has been reduced or eliminated.

The sim features a Martingale rather than target betting as I prescribe it, but it confirms that if only paranoid pit personnel would permit double-up to be played, even that simple strategy will consistently overturn the house advantage.

Any pit boss you talk to will confirm that progressive betting of any kind, and the Martingale in particular, cannot possibly win in the long run.

But if your response to that is, "OK, then you won't mind if I give it a try," you will quickly learn that what he says is not what he believes.

The standard retort to any defense of a progression is that it risks too much to win too little, a nonsense criticism that would be meaningful only if it did not apply at least as much to every other method of betting, and to the house's exposure, too.

Think about it: the house permits players to bet whatever they want within the limits discussed earlier, anticipating a "hold" that can be less than 2% of total action.

In truth, the house's share of the churn is much higher than the predicted edge for table games, ranging from 1% at blackjack to 5.26% at roulette, but that's because most players bet as if they want to lose.

A player who can walk away with his bankroll intact, plus 2% of his action, does not have a whole lot to complain about - but systems "debunkers" pretend otherwise in defense of an agenda that is never clear.

The Martingale can be said to win "just $5" when a losing streak finally ends with a turnaround win, but it doesn't: It wins all prior losses PLUS $5.

If you are tempted to venture a Martingale, I recommend varying it a little to boost the bottom line: 5, 10, 20, 50, 100, 200 500, 1000, 2000, 5000 and so on.

But do not get too attached to this approach. You will not be allowed to play it for long!

I have been relentlessly scrutinized and harassed over the years, more often than not with a charm that is skin-deep, and that hardly makes sense from an industry that claims to welcome progressive betting.

Before Caesars Tahoe banned me from its blackjack tables (unaware that target betting works almost as well at baccarat, craps and roulette, among other games) my wife and I were invited to a dinner show.

We had been seated barely five minutes when the Maitre D' brought another couple to our booth, explaining that the show was fully-booked and since we had been comped, our help would be appreciated. It was a large booth, so why not?

Almost before he had settled in his seat, our new table-mate introduced himself as "Tony" and boasted that he and his wife were there because of the huge sums he bet at baccarat in the casino's salle privee.

He was, he said, a high roller.

"So, what system do you use?" he asked, with no further preamble. "Mine is really simple: After I win, I bet five chips, after I lose I bet one, and because I never bet less than $500, I am happy if I get only one chip ahead per shoe."

I replied that I preferred blackjack to baccarat, and that I did not have a system - I was just lucky, I guess.

The same question was asked repeatedly - gently, but firmly - through dinner and the show that followed, and my answer was always the same.

Why on earth would a player with a "winning system" be interested in how someone else stayed ahead of the game?

He wouldn't, of course.

But the house would want to know.

For the record, Tony's "system" is a total disaster. Target betting is not.

Here are the primary cell conditionals for the HELP/SAVED simulation:

(A1)=IF(RAND()<=0.49,1,-1)
(B1)=+A1
(C1)=+B1
(D1)=+B1/C1
(E1)=IF(AND(D1>=50%,C1>=10),"HELP!","")
(F2)=IF(AND(B2<0,A2>0,A1>0),"SAVED!","")
(G1)=IF(AND(G1<0,H1<0),A2*MIN(15000,ABS(G1)*2),A2*5)
(H2)=IF(H1<0,G2+H1,G2)
(I2)=IF(AND(H1<0,H2>0),1,"")

That will get you started with a DIY version of my sim.


An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you.
_ale

"What can be asserted without proof can also be refuted without proof."

_
The quote above is from Christopher Hitchens, an author and philosopher who has the temerity to suggest that evidence is an important prerequisite for belief.

Those who doubt the existence of the house advantage at casino games of chance need only venture money and time to gather their own evidence that, barring blind luck, winning does not come easy.

It is also mathematically demonstrable (a pencil stub and the back of an envelope will do) that if you lose more bets than you win, you will most likely lose more money than you win.

But credulity begins to strain past breaking point when the mathematicians who bolster the gambling industry's disinformation machine insist that the numbers that support the house edge can under no circumstances be used to render it ineffectual.

A pencil and a scrap of paper confirms that if you can consistently win more when you win than you lose when you lose by a percentage significantly greater than the prevailing house bias, losing more bets than you win will not cost you money.

If in 100 bets against a 2% house edge your 49 winning bets bring add more chips to your stash than your 51 losing bets take away, you will end up ahead of the game in spite of negative expectation.

And if you can keep doing that again and again, you will soon become your local casino's worst nightmare.

Academic mathematicians (most of whom are way too smart to gamble), insist on a series of gambling axioms that beggar belief.

One is that blocks of outcomes from casino house games (blackjack, baccarat, craps and roulette among them) are uniquely random and therefore have no patterns or cycles that can be studied, and then relied upon to predict future results.

Another is that computer simulations based on random number generators (RNGs) very rapidly produce outcomes that closely match those that will be encountered in a real-time game of chance.

A third is that because of Rule #1 above, any sample of past outcomes, however large or objective - verifiable and unpolluted might be another way of putting it - is anecdotal and therefore totally irrelevant to any study of gambling, which is in itself a fatuous undertaking.

There is no evidence to support any of those contentions, but the position the "experts" take is much like a firm parent wagging a finger at an errant child: "It's so because I said so."

First, patterns.

Here are screenshots from two iterations of an Excel file that uses the Windows RNG to supply 5,000 outcomes in objective order with the house edge set at (-)1.5%.

(Click on an image to enlarge it)

SS#1 ended up with an actual house bias of more than 3.7% overall, which happens. Often.

Target betting relies on paired or "twin" wins to achieve turnaround for a recovery series, and you will see that in spite of the house bias, there were almost as many paired wins (339) as there were paired losses (343).

The simulation does not "double dip" meaning that three wins in a row do not count as both a double and a triple. This confirmed by the "streaks total" numbers on each side, which closely approximate the total number of wins and losses, each pair consisting of two bets, each triple, three bets, and so on.

Given 5,000 rounds, there were more of each category of losing streaks (pairs, triples, quads and so on) than there were matching winning ones, which we would expect in a sample with a high house edge overall.

In the second SS, there was a negligible house edge, which also happens. Not often enough.

There, twins, triple wins, quads and so on matched or exceeded the frequency of their "opposite numbers" but all in all, the difference was not worth much.

The file generates a new set of 5,000 rounds with each tap of the F9 recalc key, and anyone who would like to study it more closely is more than welcome to e-mail me for a copy.

I know I am safe in using a low-grade, less than perfect RNG because mathematicians everywhere love them to PCs (sorry) and will bravely stand up for them as accurate simulations of a real game.

So now to that second preposterous claim: the one about RNGs being reliable indicators of how an actual casino table game will apply its known pro-house percentage.

For anyone betting randomly or wagering flat or fixed sums, a prolonged negative trend or pattern is very likely to prove fatal, and it is possible that any attempts at damage control will ultimately fail.

"Damage control" in this context means either reducing bet values to ride out a negative trend of unknown duration, or walking away from a beating in progress hoping for a friendlier pattern at a different layout or game.

The same does not apply to a target player who has full confidence that as long as he has not yet reached his maximum bet value, two consecutive wins will get him out of trouble.

What makes the use of RNG output against a betting strategy both disingenuous and reprehensible is the knowledge that human beings have an essential role to play in the gambling process.

Any RNG-reliant sim, mine included, demands the assumption that a player would make no attempt to defend himself against a prolonged negative trend, either by varying his betting policy or walking away from the game and resuming play elsewhere.

Add this to the fact that sims also exclude cards, shoes, dice, wheels, dealers, money and real time, and the mathematicians who depend on them as indicators of actual play do not seem so smart after all.

I am much more comfortable with actual output from real games, so here is a streak analysis of a block of 5,000 bets taken at random from the BST blackjack trial that is still ongoing. (OK, not wholly random, because I took today's date, 0517, and extracted outcomes 517 through 5016 from BST blocks #5 and #6).


As you can see, there's not a whole lot of difference between the blackjack analysis and those for two RNG samples set at a 1.5% house edge. I would have preferred a clear negative expectation, but this is what happens when you select data at random: 4,884 rounds from BST05 and 16 from BST06.

Repeating patterns are everywhere in the course of any game of chance. But unless you know how to be ready for them so that you can use them to your advantage, that knowledge will be of no help to you.

You will not be able to see them coming, so you must bet in such a way that whenever favorable patterns occur, you will derive maximum benefit from them.

Successful betting, like so much in life, depends on good timing. But "good" does not have to mean "accidental" if you have a plan.

Skeptics often point to the size of the recommended bets for target play, usually because they do not understand that a narrow spread and a low maximum will invariably result in more action - and therefore more risk - than the levels I call for.

Here are some more patterns, tracking maximum wagering in two very large samples of baccarat outcomes, plus 80,000 or so rounds of "real" blackjack against Ken Smith's Blackjack Strategy Trainer.

Once again, any one set of data looks pretty much like any other...





The summaries at the bottom of each of these panels probably provide enough information for most readers.

Those of you who are more detail oriented might want to know the following:-

- The numbers in the second column refer to lines in each separate sample with the overall actual value (AV) to the right, indicating how many bets the "house" was ahead at the moment when the bet level hit the max.
- The AV for the series can be deduced from the next two columns to the right, which show first the series starting line, then the AV at that point.
- Skeptical mathematicians will often claim that there is no reason to hope that once the bet limit has been reached, robbing target betting of its "wiggle room", an egregious negative trend will abate sufficiently to permit recovery. This is invariably not the case, as columns 6 (ending line #) and 7 (AV at that point) confirm.
- The reason for predictable offsets to a very unusual house spike is shown in column 8, in bright red numerals: the series-to-date house edge at the moment when the first "max" bet was required. The average is around -50% and since generally it requires at least 25 bets to dig that deep a hole, numbers that large do not happen often.
- The next column to the right shows how much deeper the "hole" became before recovery was achieved. Usually not much, but once the max has been reached, the bankroll must be large enough to withstand an occasional ongoing slump before turnaround.
- Next comes the number of bets in the whole series, followed by the number of rounds it took to get into trouble in the first place.

The three separate summaries are very similar in many ways, confirming that outside of our inability to predict the outcome of the very next wager are options that enable us to win consistently in spite of the house advantage.

I have gone to great lengths here to refute the idiocy of some mythematical assertions with evidence, rather than without it, as Mr. Hitchens suggests in the quote at the top of this post.

Mr. Hitchens specializes in skewering traditions and attitudes that he believes have no basis in reality and no place in modern times.

The standard academic prohibition of the study and use of past outcomes is perhaps the most idiotic gambling axiom of them all, worthy of his attention if he were ever to turn it to earthly matters.

We cannot predict the outcome of the very next bet, or any one bet at any one point in the future.

We all understand that, with many of us falling back on the old cliche, "that's why they call it gambling..."

But when bets in quantity are studied collectively rather than one by one, distinctive patterns always emerge, as they must.

Denying the validity of analysis and its potential for prediction in "big picture" terms is both illogical and unscientific.

What on earth could make gambling's math distinct from any other kind of math? Nothing, that's what.

Perhaps there is one very good reason why house-trained mathematicians seeking to support the "you can't win" conventional wisdom refuse to accept the relevance of prior outcomes.

The study of what's past will invariably prove them wrong.

And wrong is something an academic (especially one with an agenda) hates to be.

An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you.
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When crossing a minefield, should you march in a straight line and hope for the best, or tread carefully and make a few detours to stay alive?

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My "spring cleaning project" (tidying up my data files so anyone can understand them) is going well, and I should have more to say about that by the middle of next week.

One topic that the task has brought to the surface again is the extent to which runaway sims differ from what a living, breathing player is likely to encounter during real play in real time for real money in a real casino.

The question at the top of this post sums it up, I hope.

It is fashionable for academic mathematicians to respond to my criticism of RNG game simulations by saying that I don't like them because my betting method cannot beat them.

They are free to bolster their position on the arithmetic of gambling with as many wobbly pit-props as they can find, but the truth is that no one alive plays the way a runaway sim tackles a gigantic sample of random numbers.

I have just started reading Sam Harris's controversial polemic, "The End of Faith," and take great delight in the analogies and allegories he uses to demonstrate the weakness of positions that some very smart people have been taking for centuries.

Mr. Harris and I have different objectives, of course, because I do not deny the existence of the house advantage at games of chance: I simply reject the contention that it cannot be beaten.

I fully accept that because of the house edge, any gambler is certain over time to lose more bets than he wins, and I have always conceded that the only way to avoid that certainty is to stay away from casinos and never place a bet.

Mr. Harris relies on irrefutable logic to back his arguments, and so do I.

Who in his right mind would question the proposition that if you win more when you when than you lose when you lose, then losing more often than you win will not cost you money in the end?

The argument is so solid that I often forget to add the qualification that of course the product of the percentage by which your average win value exceeds your average loss value must be greater than the product of the house advantage applied to overall action.

In other words, a difference of pennies between the AWB and the ALB simply won't cut the mustard!

Example: A 2% house edge was confirmed at the end of 100 hands because you lost 51 bets and won 49; happily (but not by chance), your AWB at $11 exceeded your ALB at $10 by 10%, giving you an overall win of $29 (+2.8%) rather than an "expected" or "indicated" loss of $21. Had AWB/ALB summed +3% (say, $10.30/$10), you would have won $504.70 and lost $510 for a final outcome of -$5.30 (-0.52%), less than negative expectation but not "less enough."

We must first agree that it is possible to consistently achieve an AWB that tops our ALB sufficiently to offset the house edge that most people think is unbeatable.

If you do not think it can be done, you should be reading someone else's blog right now (or be planning your next losing trip to a casino!).

I mention the Harris book because its premise is that throughout history, countless millions of people around the world have been persuaded to adopt beliefs that make no sense.

Getting gamblers to accept that games of chance are so uniquely magical and mysterious that they have their own special laws of mathematics is no stretch at all in comparison with the tenets that Mr. Harris cites.

The truth is that consistent winning does not take a miracle...just discipline, commitment, and an abundance of cash.

Target betting's primary rule, NB=LTD+ in response to a mid-series win, is on its own enough to achieve the "win more" goal at blackjack, and even betting the field at craps, because both games pay back 100% of the bet on a win, and occasionally more than that.

Blackjack's naturals and the x2 or x2, x3 craps "bonuses" for 1,1 and 6,6 have no equivalents in baccarat, so additional ammunition is often needed to get ahead of the house edge in that game.

Baccarat ranks below blackjack for target betting, but above craps and roulette, which should always be abandoned as soon as a series LTD begins to look like real money.

Logic supports both the OL (opening loss) and MSL (mid-series loss) rules, which seek to exploit the high probability that a house win will be immediately followed by a player win.

The math could not be simpler: isolated wins are the most common outcomes on both sides of the table, which helps the MSL and OL, 2L and 3L rules but works against NB=LTD+.

Paired wins come next, followed as we would expect by triples, quads and so on.

The core rule of target betting invariably pays off well ahead of serious trouble because the NB value is always modestly more than the LTD value, and an eventual win will save the day.

Thanks to the MSL, OL, 2L and 3L tactics, more often than not a target betting player does not even have to wait for two consecutive wins ("twins") - a single right bet will turn the recovery series around.

Given that reality, casino table games are logically less hazardous for a player who can recoup his prior losses in two wins or less than for a fixed-sum or random bettor.

Mathematicians repeatedly state that trying to run away from a prolonged negative trend is pointless in the long run because the house advantage will always see to it that matters will get worse ("out of the frying pan and into the fire") just a little more often than they get better.

Possibly true for a haphazard player, but logically not so for player in search of an oh so slight offset to a threatening downturn.

There is, it is true, no way of knowing if what might be a long losing streak will reverse itself if we stay put and tough it out instead of bailing out.

So we have to look at the numbers and apply them to any threat situation.

If a downturn continues (and, again, it may not), serious harm might come to our bankroll.

If we choose to suspend play for a while and walk away from a potential threat, the odds are better than 10 to 1 in our favor that we will quickly encounter paired wins, or a well-timed single win.

That is because most of the time, the win-loss pattern in a table game bounces back and forth (-1, +1, -2, +1, -3, +2, -1, +2) with just a slight bias for the house.

Paired wins show up, on average, every five bets or so. Single wins are slightly less than a 50% probability.

Most players bet a very tight spread, pick their bet values more or less randomly, and bet either too much or too little during a prolonged downturn.

They also hope (but mostly do not expect) to win with very little risk, and so they come to the table with an inadequate bankroll that is quickly wiped out if a long losing streak sets in.

Time to drag out a little homily: If you can't afford to win, you shouldn't bet.

Against most players, fluctuations in the win-loss pattern (WLP) do not have to be very great to hand the house the "contribution" it figures it is due.

Against a target strategist, the ups and downs of a gambling game have to be seismic for the house edge to prevail.

The gambling industry has always been very effective in sending players a mixed message which says, "Hey, we're offering you a chance to make more money than you could hope to earn any other way...but chances are you will lose."

Steve Weinberg, credited as the creator of modern-day Las Vegas, was on "60 Minutes" a while back telling viewers that the only long-term winners are the folks who own casinos.

I hate to use the name most people know him by, because to me a casino operator changing his name to WYNN is like a doctor adopting the moniker KYLL: It is insensitive at best!

So I will just say this in response to his cheery You Can't Win message: "Steve, you know better."

It is, however, very important for Mr. Weinberg's chosen business that its customers believe that winning is impossible, and losing is fun.

Money alone is not a guarantee that a player will beat the house edge and boost his bankroll in spite of losing more often than he won.

Money and a plan - the right plan - will invariably get the job done.

Spread, spread and spread are the three keys to success at gambling, which is why a casino does all it can to limit spreads, exploiting the average player's inclination to stick to the same game and keep betting far longer than he should.

And of course a target bettor will face severe challenges from time to time, and that is when he will need his discipline, confidence, commitment and money the most.

His exposure is greatest when he has reached his maximum bet, whether it is self-imposed or mandated by the house rules.

The good news is that in order to push his bets that high, the current house edge will have to have reached a number far above the norm for the game.

The experts tell us that past outcomes can have no effect on future outcomes and smugly quote what is sometimes called the Law of Independence of Trials.

In the short term, it is a powerful principle. Long term, it is hogwash.

When the house edge for a given sample reaches, say, 40% in a 1% game like blackjack (and it does happen, occasionally), we cannot state with certainty that there will be a significant offset in the next 10 or 20 bets.

We can however be sure that a swing against the house must come eventually in order for the laws of real mathematics (as opposed to mythematics) to be complied with.

It may not be - probably will not be - a 100% swing in the opposite direction from the prolonged negative trend.

But it invariably will prove to be enough, as long as the player's cash resources are likewise.

Prospects are helped by the fact that the rules of target betting simply will not permit a player to stay in one place longer than it is safe to do so.

After starting a new series with, for example, a $5 bet (at craps or roulette or even 3-card poker if all the available blackjack tables have a $25 minimum), it is probably safe to spread as wide as 1-20 or $5 to $100 in a busy casino before moving on.

Generally, a 1-5 spread is as wide as you should go in one place, to avoid attracting the unwanted attention of pit personnel ("Thousand in play! Up from $100! Come get him, Boss!").

That means that in a prolonged downturn, you will be moving from layout to layout and even game to game quite a bit before EOS.

And each time you do that, there is better than a 90% probability that EOS is just a few bets away.

There is also a 90% probability that if you had stayed where you were, recovery would have happened in a hurry.

But since your NB would have had to have been inside the danger zone, who cares?

Runaway sims that depend on robot "players" wandering blindfold into a minefield require us to believe the preposterous without question.

Some people do that every day of their lives. You don't have to...

An important reminder: The only person likely to make money out of this blog is you, Dear Reader. There's nothing to buy, ever, and your soul is safe (from me, at least). Test my ideas and use them or don't. It's up to you.
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