Showing posts with label progressive betting. Show all posts
Showing posts with label progressive betting. Show all posts

Thursday, April 30, 2009

"Just who are you preaching to? Even if your ideas about beating the house edge made sense (and they don't), no one could afford to use them!"

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This is a criticism I hear from time to time, and my only answer to it is that making money is never cheap, except in everyone's dreams.

Setting up a business on fabled Main Street, for example, requires a huge outlay on premises, remodeling and inventory, just for starters, and often profits are not seen for years.

Building a casino costs billions these days, and since some players manage to win now and then (sometimes in the millions) the house has to keep huge sums handy to cover downturns and stay ahead.

There is no mathematically supportable way to beat the odds at games of chance without occasional risk, and betting a wide spread is inevitably expensive before it can be profitable.

Your own data show occasional enormous losses that wipe out hundreds of hours worth of winnings. That kind of disaster could happen any time, possibly in successive sessions. That means that your strategy could be suicidal. Admit it: you are working for the gambling industry.

Casino table games are all about probability. It is possible for target betting to lose because its win rate is less than 100%. But it is not probable.

In simple terms, you are looking at favorable odds of far more than 5,000 to 1 if you bet progressively using the target betting rules, and the odds against two successive losses are therefore at least 25 million to 1.

It has always seemed strange to me that the so-called systems debunkers whom I often refer to as mythematicians insist that if a betting strategy can lose just once, it must be worthless.

The house has the best system of them all, a passive strategy that encourages players to bet and behave in a certain way, but does not force them to put money on the table or tell them how much to wager. But even the house loses occasionally.

What happens with target betting is that even in the face of occasional "high exposure," profits come in rapidly and consistently, just as they do for the house.

Sometimes, winning is harder than usual, just as it is for the house.

And once in a very great while, the team has to take a hit, just like the house.

All of the figures posted here and elsewhere in support of target betting are honest and accurate, and all of them demonstrate that very infrequent setbacks are quickly recovered.

Your chances of being killed in a car crash in the U.S.A. are estimated at around 20,000 to 1 against. Does that guarantee that you will be road kill before the end of your 20,000th trip? Of course not!

What you get from auto safety data is much the same as the message derived from target betting trials, and that is that your risk of crashing and burning is too insignificant to preclude either driving a car or betting in a casino!

That assumes, of course, that you drive safely and sensibly on the road, and that you defy the odds in a casino by using target betting to win consistently.

Sounds like you never heard that insanity is doing the same thing over and over again and expecting a different result. Your "proof" is not proof at all because your data are subjective and suspect at worst, and anecdotal and irrelevant at best. You can't use prior outcomes to develop a betting strategy that will work against future outcomes.

I am comforted that insanity is never defined as doing the same thing again and again and expecting the same result, which is what I do with each new target betting trial.

It is also why I recommend to those who are rightly at first skeptical about my ideas that they don't take my word for anything, but instead apply my method to "future outcomes."

They will quickly learn that they have nothing to fear, and much to gain.

It makes no sense to dismiss past outcomes as non-representative.

Even casinos do not do that!

A new game or a rule change to an old game might initially be tested against what I always refer to as runaway sims because they totally eliminate human control and restraint.

But that is never more than a first step.

A casino will insist that a new game must be tested against real players in actual "gaming" conditions before it has a chance of being introduced to the floor.

The gambling industry knows very well that people do not play like computerized robots, and that sims therefore cannot accurately reflect reality.

Face it, no one with the kind of money you say is needed to make target betting work would put it at risk the way you want them to. Gamblers may not be the smartest people on the planet, but they are not the stupidest either. They know that if you want to win, you have to protect your bankroll. You say the opposite.

"Conservative" betting is almost as dangerous to a player (please, let's not call him a gambler) as greed, which is Punter's Enemy #1 in a casino.

The house always wants people to bet conservatively because the math says that they are more likely to lose that way.

The ideal player, from a casino's point of view, is someone who bets a narrow spread (never more than 1 to 10), pulls back when he is losing, and responds timidly to a potential winning streak.

Table limits (spread limits) exist entirely to encourage players to be cautious in their betting habits, so that when they start losing, it is far more difficult for them to bet their way out of the hole.

It is a very simple matter for arithmetic to demonstrate the folly of narrow spreads, and you can be sure that the gambling industry knows that.

Nothing that I have published here or elsewhere in the dozen years since I first posted the principles of target betting for free on the Internet is new to the casino business.

Casino operators know very well that progressive betting is the only way to consistently and reliably overcome the house advantage, and they go to extraordinary lengths to discourage it.

I tell the "experts" that they should try progressive betting for themselves before helping the gambling industry disseminate more deliberate disinformation about how it can't possibly work.

It does work, and casinos hate it.

As for high rollers, most of them have survived expensive lessons on the hazards of trying to "buy the pot."

Big bets alone can never guarantee success at games of chance, and "whales" earned that nickname from the gambling business not because of the size of their bankrolls, but because they keep on taking a dive, then resurfacing for another go-around.

Las Vegas casinos love to put out press releases about the huge sums won by a high roller in from Hong Kong or the land down under. But you will never see publicity about a "whale" who dumped $10,000,000 at baccarat (or whatever) before limping home.

That's because winners bring in losers; losers are bad news, except for the bottom line.

Money alone will not beat the house advantage.

Money and a plan - a plan I call target betting - will always get the job done.

Losses will occur. But winnings will always exceed losses.

As I keep saying, the only way to stay ahead in a casino is to win more when you win than you lose when you lose.

There is nothing revolutionary (or insane!) about that idea: It is wholly logical, sensible and scientific.

If you keep on winning back your losses in fewer bets than it took you to fall behind in the first place, the house edge becomes meaningless.

So...here are the latest BST blackjack results. More of the same old same old!


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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Tuesday, April 28, 2009

The appeal of online "casinos": No nosy pit critters or facial-recognition software, and very little risk of being barred from play!

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I am interrupting myself in a way to make a few comments on a report in yesterday's New York Times, highlighted today by CNBC.

Online gambling has been illegal in the U.S. since 2006, but with belts tightening in Washington D.C., there is growing interest in the possibility that reversing that policy could generate federal and state tax revenues of $10 billion a year.

I have no idea how the pundits could come up with a number that high, given that total worldwide revenue from Internet gambling in 2008 is estimated at less than $23 billion.

Nevada's casino win numbers have taken a calamitous hit in the recession, down 30% in some areas, and the win is generally figured to be around 12% of the total handle or churn.

Gambling taxes are never more than 25% of post-skim revenues, so the inference is that online betting in the United States could quickly total $350 billion a year!

Quelle crappe...that's more than $1,000 from every man, woman and child in the country.

Numbers aside, I know from personal experience (Metro and William Hill before Congress shut down their U.S. operations) that target betting has virtually (hah!) unlimited potential against Internet games.

I was warned years ago that online operations programmed their software to flag and counteract progressive betting, but I never saw any evidence of that.

I did well against "invisible dealers" before my suspicion of unregulated gambling using simulated shoes, dice and wheels got the better of me and I pulled the plug.

One thing I do remember was a $750 EOS bet that snagged a natural. That kept me revisiting Metro's "casino" for an extra day or two before the allure of real play in real time in real casinos in my neighborhood won out!

Assuming that they are honest (probably a naive assumption!), online operations are appealing because they allow lower minimum bets, and bet-by-bet logs are available for post-play analysis.

In 2003, Metro's house limit was $2,000 against an opening bet of $1. And since a 1-2,000 spread cannot even now be found at any one layout in Nevada and spreading wide is the key to winning, I felt pretty comfortable with occasional sessions lasting an hour or so at most.

My thousands of spreadsheet files confirm that the numbers that underpin target betting consistently conquer the house edge at games of chance. But real play requires a flexibility that would make computer models suspect.

For example, obstinate betting against a prolonged negative trend (a hallmark of most gamblers' play!) is not possible for a target bettor because of the tight spreads imposed by table limits. And the clumsy bet values calculated by a rigid application of the rules written into a computer model have to be rounded up in real play.

My experience has always been that real-time, real money play is far less dangerous than the automated equivalent, because intuition - the human element - enables damage control, and damage control really does make a difference.

It is impossible to simulate the gut feeling that your bankroll will suffer a fatal hit if you don't take steps to protect it. Or the times without number that I have taken flight from a "hot" dealer and then recovered my temporary losses within a few bets of moving to a new layout.

All my models are based on outcomes derived from actual play, but I know for sure that a flesh-and-blood player would never keep betting against the over-a-cliff negative trends that show up in the charts from time to time, usually in the baccarat samples.

The baccarat sets from Lorenzo Rodriguez (Zumma) and Lee Jones cover entire shoes played from start to finish.

My own blackjack data includes losing patterns that would have driven me away in real play, but I sat through them to demonstrate that target betting can get a player out of trouble that would be fatal to a random bettor!

But as usual, I digress...

Online application of the target betting method has great potential because of the impersonal relationship between automated "dealers" at one end and shrewd players at the other.

If the games are as fair and honest as, say, Ken Smith's Basic Strategy Trainer for blackjack, they can be consistently beaten.

The best real-play policy is to separate accessible casinos into different categories ($5 to $500, $500 to $2,500, $2,500 to $10,000, $10,000 to $25,000, for example) to camouflage the strategy.

The same approach could easily be applied to online targets.

Keep in mind that the math of target betting does not require every recovery series to be played from opening bet to EOS without interruption.

Constantly perambulating back and forth between casinos to turn around a prolonged series is not a practical option, so I favor taking a series to a preset point when necessary, suspending it and starting another, then stepping up to the next level with a handful of higher value targets.

I have been doing that for years, after being barred from one casino (Caesars Tahoe) because I naively assumed no one would notice my repeated progressions from $5 opening bets to $1,000 turnarounds, and I was wrong.

Switching casinos online is far easier with today's computers than it was in 2003.

Four gigs of RAM and decent speed combined with broadband can easily handle multiple browser tabs kept constantly live, even if once in a while an online "casino" posts a threat of imminent shutdown because of inactivity!

I have serious doubts that Congress will reverse itself on Internet gambling anytime soon, and I do not recommend online play against unregulated virtual casinos before then.

It's something to think about, though...

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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Tuesday, April 7, 2009

There's no escaping the fact that math rules in the casino. And it's also easy to see that mathematics does not rule out progressive betting.

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The consistent success of target betting or any method that breaks the fixed or random mold is assured by the fact that outcomes in games of chance are collectively predictable.

In blackjack, for example, a reasonably representative sample (say, more than 1,000) will confirm that pushes occur about 9% of the time, player naturals bring in a little extra from about 4% of all hands, and doubles and splits governed by strict basic strategy play will win about 20% more often than they lose.

You can also be sure that paired wins or losses will occur about half as often as isolated wins or losses, triples will be encountered roughly half as often again, and so on.

"Roughly" and "about" are words that academic mathematicians hate to hear, but the smaller the sample of outcomes, the harder it is to predict what will happen with absolute certainty.

Luckily for the target player, absolute certainty is absolutely unnecessary.

Regular readers will know that I say with monotonous regularity that If you can win more when you win than you lose when you lose, then losing more often than you win won't hurt you.

A picture is worth a thousand numbers, so here's a summary for the 100,000-plus baccarat rounds supplied by Lorenzo Rodriguez and Zumma Publishing:-

(Click on the image to enlarge it)

The first thing to notice is that after a single crash-n-burn and 13,640 successful recoveries, the AWB/ALB number is a relatively unimpressive 104%, but still enough to deliver an overall profit.
The overall HA/AV for this set was 1.6%, which is high for baccarat but not desperately so.
Two out of three recoveries were achieved with a single win, although as negative expectation required, more recovery/turnaround attempts were lost than won (the house had a 1.16% edge in that area).
Series requiring 10 or more rounds to recover were less than 9.0% or 1 in 11 and 62% of all series were wrapped up in five bets or fewer.
The average bet value was high according to some at $592 but bets of $1,000 were required only 4.4% of the time (less than 1 in 20).


Many a mythematician might be inclined to dismiss 114,000 rounds as anecdotal or non-representative, so keep in mind that the sample is equal to well over a year of play for a fulltime baccarat fanatic.

Also keep in mind that according to the same self-styled (and often house-trained) "experts" the results you see above are impossible.

Now please consider a much larger sample of baccarat outcomes, more than 200,000 supplied by Lee Jones, a systems promoter who can verify their accuracy and with whom I have no connection (he might even consider me a most unwelcome competitor since I don't charge for my ideas and his are for sale).

(Click on the image to enlarge it)

The AWB/ALB product is higher at 109% vs. a more standard house edge of 1.18% and the average bet value is way down at $352 ($592) but the rest of the numbers in the summary closely resemble those for the smaller and quite separate sample from the Zumma books via Lorenzo Rodriguez:

EOS 1-5 62.5% (62%)
EOS 6-10 29% (29.3%)
EOS 10+ 8.5% (8.7%)
Positive series 35% (35%)
Neutral series (29%) (28%)
Negative series (36%) (36%)
1-win EOS 66% (66%)
EOS wins/tries 49.1% (49%)
Bets of $1,000+ 3.6% (4.4%)


The biggest difference between the two baccarat samples lies in the final target betting win (2.86% for the larger data set vs. 0.16%). The reason, of course, is that the first sample included a bust, one that was triggered by such a precipitous plunge that only the "robot" at the heart of every runaway sim would have sat through it!

Baccarat holds far fewer surprises (good or bad) than blackjack, but the stats for the first 75,000-plus outcomes in the BST blackjack trial are remarkably similar to the baccarat numbers, except for a much higher win percentage for target betting and a dramatic jump in the AWB/ALB product:-

(Click on the image to enlarge it)


And here are data for double-up (a Small Martingale) against the baccarat outcomes. The "win one unit" original version has the double disadvantage of being easily spotted and blocked, and a slow win rate that means that a single "bust" would wipe out years of profits.

(Click on the image to enlarge it)

We are now looking at close to 400,000 "real play" outcomes, which is a representative sample according to any objective, sensible standards.

We can see that ruin (the loss of our $1,000,000 bankroll) is a rare occurrence indeed, and that in spite of a single crash-n-burn, target's notional profit at this point is closing in on $4 million

Spread is the critical factor, we have learned. A spread of less than 1-1,000 is doomed, in the long run.

We do not have a monopoly on that knowledge: the casinos are well aware of the danger to their bottom line posed by progressive bettors with a disciplined plan and a fat bankroll behind them. They and will do whatever it takes to thwart them.

Obviously, a player confined to a single casino or, worse, to a handful of table options, can never hope to spread from 1-5,000 (the recommended optimum) or even 1-1,000, in the same place.

The solution to that is an over-abundance of patience, and strong legs. Spreading from $5-$100 (1-20) from the opening of a new series is plausible, but after that, 1-5 is the limit to aim for ($100-$500, $500-$2,500, $2,500-$10,000 and $10,000-$25,000, for example).

One player flying solo might find the range hard to achieve under ever-increasing casino staff scrutiny, and tough as it sometimes is to run smoothly, team-work is probably the answer.

For now, all we are concerned with is "The Math." And it is on our side.

If you doubt it, here are new numbers from the BST trial (I just began batch #16):


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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Thursday, April 2, 2009

Winning with target betting is easier, quicker and just plain better than all the alternatives. For the others, it's mostly impossible.

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When the contest is between progressive betting and the only alternatives (flat/fixed or random betting), it's no contest at all: progressive betting wins, the other methods do not.

And since this has always been as much a mathematical challenge as a practical one, tailoring my version of progressive betting to the needs of the underfunded player seeking to beat the odds during occasional weekend trips to Las Vegas has never been a priority.

One simple truth I never lose sight of is that my application of the demonstrably sound principle I call target betting (the rules that I apply from first bet to last in each recovery series) cannot be claimed to be the optimum approach.

There may well be a better way to do this, and I am confident that if I fail to find it before my final visit to a casino, someone else will, and hopefully they will tell the rest of the world about it for free.

Why not sell my ideas rather than giving them away?

It is not because, as some of my critics have suggested, my ideas are worth even less than I charge for them.

It's because for me, this has always been about exposing as myth an axiom that I always felt served the gambling industry far better than the people whose wallets the casinos suck dry.

More than 30 years ago, I experimented with the simplest, most basic form of progressive betting in several Las Vegas casinos, and in every case encountered impressively efficient interference by pit staff.

Drunks, neophytes and other suckers were committing fiscal self-destruction all around me, and I was the only one singled out for friendly advice about how best to preserve my bankroll and save myself from certain ruin.

Why are all these nice people so afraid of a betting method that they say is a danger only to me and my money? I wondered, since fear (or at best, self-interest) seemed to me the only reason they would take me under their wing while leaving everyone else to their own devices.

In the years since, gambling industry representatives (many disguised as truth-seeking academic mathematicians) have either denied that casino staff will ever step in to stop progressive betting, or have patiently offered up implausible explanations for a policy that anyone will encounter within minutes of starting a Small Martingale.

Some examples:
  1. Anyone dumb enough to try double-up or Martingale betting has obviously never wagered in a casino before and is in serious need of advice and counsel. Interesting, but implausible. Pit people in reality never offer advice unless asked, at which point they are usually courteous but non-committal, often starting out with, "The book says..." if the questions are about blackjack, or "Some people like this bet because..." Drunks hurling their money down the drain are only cautioned or removed from a layout if they upset other players by hurling something else, or knocking over drinks. Idiots who play or bet badly but don't ask questions are invariably left alone.
  2. Pit staff know that a double-up player can do very well for a short period of time but will always crash and burn eventually. They are just being friendly when they advise against the use of this suicidal betting method. And pigs play poker sty-lishly! The entire gambling industry is geared to relieving players of their bankrolls as quickly and quietly as possible, while constantly reminding them that losing is "fun." The notion that a betting method that is certain to fail would be blocked is beyond silly, but no one is ever allowed to bet double-up without house interference. Casinos are constantly devising new long-odds side bets as sucker bait to bolster the relatively low house edge at blackjack and baccarat, and adding non-traditional table games that make roulette and pai-gow poker seem like easy money. If the Martingale was a surefire loser for gamblers, casinos everywhere would be promoting it as an "Exciting New Feature!!!" and printing new layouts to highlight it. Instead, pit staff respond to it like vampires to bright sunlight (not that I am suggesting that those nice people are bloodsuckers, mind you).
  3. A progression will always fail because once the bet exceeds the table limit, prior losses cannot be recovered, and casino staff feel you should know the risks you face. This is one of my favorites, because it betrays how little the experts think of the rest of us. A $5 opening bet at a $5-$500 layout will bump up against the table limit after 7 consecutive losses requiring an 8th bet of $640. It doesn't matter that a losing streak that long is less than a 1.0% probability: it happens. A Martingale bettor who has a bankroll that is up to the challenge (quite likely, because he never loses if he is allowed to play) simply takes his business to a layout with a higher table limit (say, $100-$5,000) and continues betting at the required level. One win, and he starts the process all over again. If he is playing blackjack and he draws a natural, he's in clover! Given a house limit of $25,000 a double-up player will have to lose 13 bets in a row to hit the "green ceiling" and that's just a 1/8192 probability. And he's not dead yet...although that's a topic for another time.
  4. If double-up really was a winning method, more players would use it. No one does because it's suicide, and casinos discourage anyone who plays irresponsibly. This is one of the biggest of the big lies that gamblers are asked to swallow whole. And most do. In fact, anyone who has ever spent more than a few hours at casino table games will have seen "Martingalers" at work, probably without recognizing them. They are the annoying people who place two or three bets, lose, and move on, leaving people who have been glued to their seats for hours wondering why their game has been so rudely disrupted (or so they believe). It happens a lot in a busy casino when empty seats are hard to come by and dealers and pit personnel have too much going on to monitor any one player's movements. The rule is three bets at the most at any one layout, then on to the next game. Casinos try to thwart Martingalers by prohibiting "entry" between shuffles at blackjack and baccarat, but that's just a minor inconvenience. Craps and roulette tables are never restricted, and field bets at craps have special appeal because of the 2x payouts for 2 and 12, which used to be 2x and 3x before the accountants that devised 6-5 payouts for naturals at blackjack did a little more dirty work.
  5. Progressions are a bad idea because the ancient laws of mathematics state that any amount bet against a negative outcome must eventually have a negative outcome. Pythagoras and his peers and successors were and still are in essence stating a rule confirmed by logic, which is that because negative expectation will ultimately result in more player losses than wins, more money lost than won is an inevitable consequence. And as long as bets are of a fixed or randomly selected value, a long term win is highly unlikely. However, a progression is not random. Bet values are determined by the immediately prior outcome, and while that outcome is random and subject to the negative expectation for the game, the response to it never varies. A Martingale is a bad idea not because it does not win consistently but because it is too obvious. It requires camouflage to avoid quick detection, and that is what target betting is all about.
My conclusion long ago was that constant re-doubling is impractical in spite of the satisfaction gained from repeatedly recovering prior losses in a single bet.

Waiting out a losing streak by freezing or reducing the wager and then going for a one-bet turnaround seemed like a mathematically-supportable alternative, primarily because in most table games, the house's chances of winning a given bet are only marginally better than they player's.

Put another way, while each bet at a game with a 2.0% house edge faces negative odds of 49-51, there is no such thing as a fractional win or loss: you either beat the negative number, or you don't.

All of my blackjack and baccarat spreadsheet models track the performance against the same sample of outcomes of both a standard double-up method (the Small Martingale) and a variation that I call SM-Plus which modifies the progression to deliver a bigger win from drawn-out recoveries.

Against the blackjack outcomes (78,000 and counting) the standard double-up had one "bust" in 18,972 series, the pumped-up version had 3 busts in 18,055 series, and target betting had...no busts at all.

Here's the SM, SM+ and target betting summary for the blackjack trial to date.


(Click on the image to enlarge it)

The baccarat trial is especially relevant in this context because the data sets were supplied by two verifiable sources that are independent of each other and (more important) independent of me.

There were well over 300,000 rounds of baccarat in all, equivalent to almost three years of play for a very dedicated player putting in 30 hours a week with two days off each week but no vacation time.

Here's a summary of how a simple Martingale performed, along with data for the more aggressive double-up method, and for target betting.


(Click on the image to enlarge it)

I guess it's possible to make this stuff up, but why? The results achieved have been so consistent (predictable is another way to put it) that anyone applying the rules of these different approaches to target betting fairly and accurately is certain to see very similar numbers.

The other question always begged by results like these is how much better any disciplined betting strategy might do with human intervention allowed, meaning that prolonged negative trends might (or might not) have been avoided if defensive action had been taken.

High-speed simulations of any kind, my own included, require the wholly unwarranted assumption that a player in the early stages of one of those deadly downturns that we all know can occur (those of us who actually place bets in casinos, at least) would NOT back away from a punishing situation and resume play somewhere else. There are some certifiable masochists out there, I know, but I am not one of them.

The conventional academic argument is that since each outcome is independently subject to the same measure of negative expectation, attempts to escape a negative trend can have no long term benefit.

It may be true that a player who bets fixed or random amounts is as likely to get into more trouble after a move as he is to see an end to the negative trend that made him flee.

But for a target bettor, all that is needed is to get out of trouble is two consecutive wins, and the decision to bail out of a bad run is as much about morale as it is about math.

The math, though, supports preemptive "damage control" when a recovery begins to drag out uncomfortably, because the great majority of series (well over 60%) are over in six bets or less, and a tiny percentage drag on for 10 rounds or more.

As the Chinaman said, "A long losing streak must always begin with a short one, and it is better to lose a little than a lot."

Worth noting is that in less than 80,000 rounds of blackjack, target betting "won" (how I wish those quote marks were not necessary!) almost as much as it did in almost four times as many baccarat bets, confirming that blackjack is clearly the optimum table game for this strategy.

Here's the latest BST session...

(Click on the image to enlarge it)

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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Wednesday, April 1, 2009

Confidence, consistency, cold cash and commitment: The keys to winning at table games can be summed up in two letters, P & S, Progression and Spread.

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Years ago, a Las Vegas resident who promoted himself as the world's #1 expert on casinos and gambling told me that no betting method ever devised could beat the games in his city.

"Even if it could be done, the casinos would find a way to stop it," he said. "All they would have to do is limit spreads."

He was right. The casinos have the edge against 99.9% of all players, reporting a win percentage that is several multiples of the negative expectation at the toughest table game, roulette (5.26%).

Meaning that most players make such dumb choices when they are in a casino having "fun" that they guarantee that they will go home with a lighter wallet.

But the house advantage and the billions in easy money it brings in every year is not enough for the gambling industry.

Whenever casino personnel identify a player who they believe is winning "too often" they first satisfy themselves that he's not cheating...then treat him as if he is.

When mathematician Ed Thorp published his card-counting best seller, Beat the Dealer more than 40 years ago, Las Vegas casinos over-reacted by changing the rules of blackjack to block counters, prompting howls of protest from customers who didn't know how to count cards and didn't care to learn.

Double-downs and splits were cut back, and most annoying of all, shuffles were increased, slowing the game to a crawl.

Pretty soon, the gambling industry realized it had used a sledgehammer to crack a nut.

Players willing to study how the game could be beaten and able to apply their new knowledge with skill and consistency were in a tiny minority, and blocking them meant losing revenue from everyone else.

Perhaps more than anywhere else in the world, time is money in Las Vegas, and the faster hands are dealt, the more chips are raked into the dealer's tray.

In a matter of months, blackjack's rules returned to normal, and the crisis that wasn't a crisis at all was over.

Running a game is for the most part a passive process that permits the casino to provide the layout (the rope) and let the players do the work (hang themselves).

The house's influence is subtle, limiting the ratio of the highest permitted bet to the table minimum, to reduce the players' ability to recover prior losses while knowing that most punters limit themselves far more severely.

Spread limits are effective only against players who believe that the only way to combat a downturn in a given game is to keep on betting in the same location, hoping that sometime soon the tide will turn.

But a surprising number of gamblers play that way. Badly, in other word.

Players with a plan know where there's a table limit, there is a higher one not far away. If the next bet needed exceeds the table limit, there is a simple solution: Go play somewhere else.

It is an indisputable fact that both flat and random betting must eventually fall foul of the house edge at all games of chance.

It is also true that most players who are "in the hole" will fall into a pattern of robotic fixed betting, or will randomly hurl good money after bad by cranking up their wagers.

The hole will get deeper and deeper and the ladder (the bankroll) will get shorter and shorter, until eventually there is no way out.

Haphazard betting won't work. Flat betting won't either.

That makes progressive betting the only alternative.

And the realities of gambling also ensure that progressive betting will be relentlessly targeted for derision by anyone whose livelihood depends on promulgating the conventional wisdom that in the end, you can't win.

Blind luck can make you a winner for a while, but as we all know, luck never stays around for long.

Never forget that losing is a progressive process, because with each loss, the amount you are "behind" gets larger.

Betting the same amount each round against a negative trend will not enable you to recover, unless of course the win-loss pattern (WLP) changes and you are able to win more bets than you lose.

Betting less won't help either because even a prolonged winning streak will not get you out of trouble.

Again: Progressive betting is the only viable alternative. And the irony is that as long as you apply a disciplined, consistent plan, progressive betting is also less risky than any other option.

Say what?

It's like this: The vast majority of players tackle casino table games with far less money than arithmetic indicates is necessary to prevail against the house edge.

So in spite of the fact that the house advantage has to be relatively tiny in order to make occasional overall wins by players possible (without them there would soon be no customers) its relentless grind against an inadequate bankroll almost always proves fatal.

"Underfunded" players lose. Again and again. And losing is a very expensive way to have fun.

Progressive betting demands more up-front money, for sure.

But it very quickly builds the bankroll with recovery after recovery.

And as time goes by, ruin becomes a rapidly-diminishing threat.

Look at it this way: If you can't afford to win, you shouldn't play. Why even think about taking on the house if you know you probably don't have enough money to get the job done?

All of the BST logs posted here demonstrate that table limits serve the house, not the player.

No big surprise to some of you, but many people do not think about the fact that the quicker you get to your green ceiling, the more likely you are to be a victim of the house edge.

In blackjack session after session, playing up to the table limit and never beyond resulted in up to twenty times the number of high-value bets that unrestricted target betting required, and in consequence, far higher average bet and overall action values.

More action always means more risk. That's a gambling given.

Here are data from the current BST blackjack set (#15):

(Click on the image to enlarge it)

What we see here is that a betting spread tighter than 1-1,000 (the BST limit is 1-200) is certain to lose, over the long haul.

The two optimum spread ratios are $10-$25,000 (1-2,500) and $5-$25,000 (1-5,000).

$25,000 bets? That's madness! No, it's not.

It was never my hope, or my intention, to come up with a betting method that would permit a weekend punter on a shoestring budget to go home with his pockets bulging with casino cash.

That just is not possible, unless blind luck intervenes.

A successful player (not a gambler) has to think like the house, with big bucks up front and complete confidence that disciplined betting and The Math between them will make him a winner.

Look at the action numbers in the summary above and you will see far higher action/average bet figures for narrower spreads than 1-5,000, with a 1-500 spread losing after requiring risk that was almost ten times greater than the bet levels that optimum target betting needed to WIN!

A fluke, say the skeptics. A sample of just 7,300 hands is "not representative"! The data shown are anecdotal, meaning that they apply to this set of outcomes and have no relevance to future bets.

OK, so let's look at the summary for more than ten times as many outcomes (all the data sets in the current BST trial).

(Click on the image to enlarge it)

Bigger numbers, same story.

In coming posts, I will provide data from the two extended baccarat trials of target betting, the Jones outcomes and the Rodriguez sets covering more than 315,000 rounds over which I had no control, and that are verifiable at their independent sources.

Not representative? Of course not! One thing you learn when you challenge the status quo is that any sample of data, however large, that upends the YCW (you can't win) conventional wisdom is always non-representative and anecdotal.

Here's more BST fun and games...



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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Saturday, March 28, 2009

You will never be able to predict the outcome of the next bet, but target betting makes sure you always bet the right amount at the right time.

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"Negative" is a word that frequently crops up in discussions about gambling and how to win, and the axiom is that negative expectation must eventually have negative results.

It's nonsense.

The truth is that the house advantage at casino games of chance can be the player's good friend, because the baseline percentage value can never be large enough to make winning impossible.

Casinos would be happy to offer games with a house advantage far greater than blackjack's +/- 1.0% or even roulette's 5.26%, and sometimes it seems not a day goes by without some new "side bet" appearing on table layouts to tempt easy money from players who can't or won't do the math.

The gambling industry knows, however, that winners play a critical role in their business. Why? Because games that could not be beaten would very quickly run out of suckers.

Casinos rely on the fact that most players are unconcerned about odds: they just want to be able to win once in a while, so they won't feel foolish. The only way that can happen is if the house edge is kept in check (usually less than 1.5% at mega-money games such as baccarat and blackjack).

Because of the random nature of all games, the house edge will sometimes tip far above the known expectation of 1.0% or whatever, a negative trend that will occur only a little more frequently than an opposite pattern.

Especially interesting to me is the fact that most players will bet more during a losing streak than they will against a winning one, making it almost impossible for them to "get out of the hole" when a prolonged negative trend is finally over.

It stands to sense (and simple arithmetic) that flat or random betting against negative expectation is more likely to lose than to win. So the only alternative to losing long term is a disciplined method of money management that minimizes the damage from losing trends and maximizes the profit from a positive pattern.

In two words: progressive betting. In two better words: target betting.

The casinos and their house-trained "experts" work very hard to make sure that the words above are perceived as dirty ones.

That's because progressive betting consistently upsets "the math" for the house, repeatedly and indefinitely enabling the player to make money in spite of losing more bets than he wins.

Obviously, you will never see those proliferating side bets I mentioned earlier flagged with signs warning players "Don't waste your money, this is a seriously dumb bet."

And for the same reason, people who bet stupidly without taking the trouble to learn the game they are playing are never taken aside and given helpful advice on how to protect and conserve their bankroll.

The only way you will ever prompt a lecture on odds and optimum play from pit personnel is if you are spotted betting a progression. (Please see the comments at left under the heading, "An easy way to test the lie that progressive betting can't win").

If you want the house to love you to bits, showering you with sundry "comps" to induce you not to go next door or across the street, bet randomly within a very tight spread (1-5 is standard for most weekend punters), and keep telling yourself that losing is fun.

If you want to win, do as I tell you!

Here are numbers from the latest BST blackjack attack...

(Click on the image to enlarge it)

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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Friday, March 27, 2009

Everybody gets lucky once in a while. Penny-ante punters depend on it. If you are target betting, you don't need luck (but be grateful anyway!).

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In the interests of political correctness, even though being PC is no longer fashionable, let me say right now that I have nothing against penny-ante punters.

I respect and welcome them, because without them there would be no casinos.

They mystify and occasionally (when they stray onto "my" blackjack table and play badly) they frustrate me, but I would not be without them for the world.

The latest BST session inspired me to state the obvious, as in the headline above this post.

But in a field where what little discussion there is tends to be dominated by academic mathematicians who may never have placed a bet in their lives, stating the obvious is essential.

Target betting succeeds with predictable consistency because win-loss patterns, regardless of the randomness of individual outcomes, are in themselves predictable and consistent.

When bet values are also selected at random, the house advantage is almost certain to win, the exceptions being lucky streaks (accidents!) in which the player wins more bets than he loses, or when by a fluke he achieves an average win value that exceeds his average loss value.

If you give target betting a fair and open-minded trial, you will learn that end of series (EOS) bets occur every three bets, on average (less, actually, but only mythematicians know how to place 0.7 of a bet!).

Most of those recovery attempts will FAIL.

The failure rate for EOS wagers is also predictable: roughly 53%.

But what might seem to you like a worrisome demonstration of the inevitability of more losses than wins is in reality the reason why target betting can fail only very, very rarely indeed.

That's because the value of each EOS bet is not randomly selected, making each failure just a temporary setback.

There will always be more failures than successes. But the combined value of the smaller number of successes will always exceed the total value of the greater number of failures. Result: happiness!

The first session in the latest BST trial (which now may not end until I have reached 100,000 outcomes) was a perfect example of how accidental good timing can improve the performance of a betting method that is already very difficult for the house to beat.

The sample had 7 more losses than wins, but in spite of that, the profit after the last EOS was $9,835.

That was with the BST 1-200 ($5-$1,000) spread/table limit in force.

Target betting without the wimpy TL did less well, but only because I'm still working on modeling my real-time responses to dealer naturals and 3+ 21s:

bst090327a: 7.5 net AV = +3.52%, target win $3,798 = 29.49% of $12,878 action
227.5 net rounds incl 3-2 naturals, average bet $60, bets of $1,000+ = 10


Modeling a $1,000 TL with the same target betting rules applied produced these results:

7.5 net AV/HA = 3.52%, target win $7,500 = +3.30% of $227,500 total action
227.5 net rounds incl 3-2 naturals, average bet $1,068, bets of $1,000+ = 213


The standouts in these data are the ones that always highlight themselves: a much bigger action number with the BST TL imposed, caused by a far greater need for bets of $1,000 or more (10 with a wide spread vs. 213 with a "house" spread).

I have to confess at this point that the last few BST summaries have exaggerated the number of big-ticket bets for the BST TL. It is one of the hazards of spreadsheet modeling that every once in a while, a "bad" cell will proliferate, skewing results until the glitch is exposed.

I am as a rule a demon error-checker, but this one got by me for a week or so. Turns out the exaggeration goosed the numbers, but not by much. Here's a revised summary with the miscount corrected:

(Click on the image to enlarge it)

As you can see, a tighter spread (1-200 vs. 1-5000) resulted in an overall loss for BST TL, along with 3.5 x target betting's total action and average bet value, and almost 20 times the number of $1,000+ bets for a method that most people would assume to be "less aggressive."

In every sample that had a negative net AV/HA, the BST table limit delivered an overall loss, rendering target betting as ineffectual as any other betting method, including fixed or random values. And that of course is the whole purpose of spread limits: to ensure that the house advantage exacts its ordained toll on players who dare to challenge it.

When a player is able to widen his spread to suit his current needs, the house advantage becomes almost irrelevant.

A wide spread enables you to win more when you win than you lose when you lose, so that losing more often than you win will not prevent you from walking away from the game a winner. Isn't that what everyone on our side of the tables wants?

The best news of all is that with target betting strictly applied, single wins are all it takes to achieve recovery around 65% of the time. That's important, because isolated wins occur about twice as often as paired wins ("twins"!).

So, if you gamble because you believe in luck and imagine that you can somehow get more than your share, be ready to lose. If, like me, you accept that luck is a fickle ally and a plan is a whole lot more reliable and predictable than flying by the seat of your pants, welcome to target betting.

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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Wednesday, March 25, 2009

"Even with a win rate higher than 99.99%, someone has to lose - and it could be you."

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Back in the good old days when gambling discussion forums were not fatally targeted by spammers (and newspapers still made a profit), the topic of progressive betting brought frequent posts from a contributor who always signed his name with "Ph.D." after it, his presumed purpose being to tell us he was smarter than us, so we'd better shut up and listen.

The other day, I came across an old post from the guy I came to know fondly as "Harvey Phudd" and I offer it to you for your comments...

"The pythagorean theorem is more than 3000 years old, and it is still correct. You are implying that since the mathematics you blithely ignore is more than a century old that that the theorems are invalid. Sorry, the various theorems of probability and statistics that lead to the inevitable conclusion that "money management" or progressions can (sic) change the fundamental expectation of a gambling game are still valid.
"Progressions due (sic) skew results. That is, the chance of walking out at even or better is significantly increased. In some case, the increase is significantly in excess of 99%. No one disputes this. What you don't seem to understand is that the average win, when the progression system wins, is reduced, sometimes greatly, and the average loss, when the system loses, is significantly elevated.
"This is comparable, in the extreme, to a game where there are 2 blue marbles and 999,998 yellow marbles in a jar. A marble is drawn at random. The player wins $1 if a yellow marble is drawn and loses $1,000,000 if a blue marble is drawn. In this case, the player will almost always win this game. At some point, assuming that many players play, a player will lose now and again. The house (the casino) will make money on this game and yes, many players will also make money on this game. Heaven help the poor souls who lose however."


Harvey's argument typifies mythematics, which requires its followers to fudge facts and fiddle numbers and do whatever it takes to support the casinos' ordained right to beat the (stuffing) out of the rest of us.

Funnily enough, a believer in progressive betting or money management does not defy ancient axioms, whether Pythagorean or not, because it stands to modern as well as ancient sense that if you lose more bets than you win and bet flat or randomly, you must also eventually lose more money than you win.

My argument is with the assertion by Harvey Phudd and his ilk that a betting strategy that follows known and broadly predictable patterns in random outcomes cannot ever turn negative expectation on its ear.

Hell's bells! In the current BST trials, we're up to almost 75,000 outcomes and as you can see from the summary below, 68% of the series from which we made a handy profit were either negative or neutral, indicating that target betting "should have" lost 37% of the time and at best broken even 31% of the time.

It.
Didn't.
Happen.

Expectation is being in effect reversed in more than 2 series in every 3, and is being exceeded in those that remain.

Harvey is at least expanding the usually rigid, tiny-framed picture a little by saying that progressive betting can win close to 100% of the time but among thousands of players who make money from it, one or more is sure to go broke. It's the billion-bet runaway sim in a different guise.

I can't fight the argument that if a player takes no defensive measures whatsoever, he will lose eventually. But what does it tell us? That stupidity in a casino (often in the form of greed, ignorance, fatigue, distraction, or over-consumption of free booze) is a bad idea? I think most of us knew that already, Harvey.

Harvey concedes that progressions do skew results, and as long as my odds are being skewed to the good, I am in favor of that idea.

In the end, the choice is between negative odds of 495 to 505 (in a 1.0% game such as blackjack) or positive odds of 9,999 to 1 or better (13,328 to 0 in the current blackjack trial!) and I think I can guess which option most gamblers would prefer.

Harvey's million-marble analogy is interesting, but absent a Ph.D. I struggle to get his point. If the "winning" marbles don't go back in the jar, then sure, the odds of picking the right color will diminish with each bet until some sucker is sure to make an expensive mistake. Otherwise, odds that good are far better than those we face every time we get out of bed in the morning.

I know it's just an analogy, Harvey, but are there really people out there willing to risk $1,000,000 to win $1?

I'm comfortable risking a virtual "mill" at target betting because I know that soon enough, accumulated winnings will exceed my original seven-figure stake and I will be able to put it back in the bank and play on with my profits backing me.

Harvey is wrong when he says that average wins are reduced by progressive betting: the diametric opposite is true. And I doubt he meant to say, as he does above, that money management can change negative expectation, even though, for once, he was right.

It may also be true that even if you and me and everyone we know adopts target betting and wins consistently with it until we each fall off our perch, it will not alter the fact that casinos collectively will continue to reap fat rewards from the house advantage.

That has more to do with the nature of most gamblers than the numbers for or against progressive betting. Most gamblers expect to lose, even want to lose, and will do little or nothing to improve their chances, so perhaps they deserve their inevitable fate.

I have been warned on occasion that challenging or tampering with the status quo is immoral and unfair, and that casinos have a divine right to profit from the idiocy of the average gambler.

I say that if house games can be beaten without cheating or breaking the rules in any way, as many people as possible should be taught how to do it.

Here's the latest BST session. And OK, it's time for me to admit to myself that I am addicted to this process! I keep hearing the skeptics cry, "But it won't work next time!" and I have to keep on saying, "Just watch me win again!" And then I do.

(Good news that will be supported in detail in a later post is that almost TWO of ever THREE winning series will end with a single win, rather than the "twin" wins that are required for recovery without the OL and MSL rules in place. OL is short for opening loss, and calls for NB=PBx5 if the first bet in a new series goes south; MSL is mid-series loss and says that if PB is less than or equal to $1,000, the NB=LTD+ rule is repeated).


(Click on the image to enlarge it)


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.
_

Sunday, March 22, 2009

A little progressive betting perspective here, and some thoughts on why robots can't ski, and gorillas can't putt...

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In a situation where you have lost several bets in a row or losses outnumber wins so much that you are in a deep hole, you have two recovery options:

Increase your bet values in the hope that going forward, a smaller number of wins will undo the damage done by a greater number of losses, OR
Keep betting the same amount each time, and cross your fingers that soon, the number of wins will exceed the number of losses, resulting in a profit.


Advocates of card counting will tell you that the only winning method is to set bet values according to the high/low ratio of the cards remaining to be dealt in the deck or shoe, and to control the spread to avoid attracting attention.

Counting only applies in blackjack, of course, and even then has to overcome the fact that a "rich" deck is only fractionally better for the player than for the house, if at all.

I have always questioned the message that comes across in pretty much every book about gambling that was ever written and in all mathematical papers on the subject: "Sorry, suckers...you can't win."

The truth is that you can win, and win consistently. But not if you play like a fool.

Over the years I have used several analogies to help illustrate the unscientific idiocy of applying clumsy runaway sims to the nuanced art of gambling well, and two of my favorites are the golfing gorilla and the robot on skis.

The golfing gorilla putts the way he drives, so in spite of the pinpoint accuracy of his long shots, he can never win a game.

The robot on skis sometimes gets to the bottom of the slope in one piece, but more often he ends up in a crumpled heap, defeated by such subtleties as trees and rocks, moguls and other skiers.

The reality of gambling is that you are, in the end, certain to lose more often than you win.

And if you don't bet in such a way that the sum total of all your wins exceeds the sum total of your greater number of losses, you are perforce doomed to lose more money than you win.

What is required is a combination of progressive betting and a keen sense of self-preservation.

Mathematicians argue that "damage control" is a waste of time and effort because negative expectation applies equally to every bet, so running away from a losing trend is as likely to make matters worse as it is to improve them.

They reject my contention that prolonged negative patterns are a relative rarity in games of chance, even though the runaway sims that mythematicians depend upon confirm what is in any case plain common sense.

A runaway sim will show a betting strategy nosediving into ruin after a pattern of losses than no human being would tolerate.

Like the golfing gorilla and the skiing robot, sims blunder into certain failure, unable to shift balance, steer away from trouble, or modulate their "stroke."

What I am hoping readers will take away from this blog is the realization that the technique I advocate can be applied with skill and subtlety, adjusting to changing circumstances and modifying the rules to match resources.

As in golf and skiing, sometimes brute force is appropriate, and sometimes precision saves the day.

There is an alternative, of course. It's called losing.

I have posted an Excel RNG file to make it available for download. LTD+1 RNG.xls uses a simplified set of target betting rules to demonstrate that a clear house advantage can be consistently beaten. Hit the recalc (F9) key several times, and you will see far more frequent overall wins than losses. When the green line dips drastically south of the Zero line, go look for the pattern that did the damage and ask yourself if you would stick around for such a battering if you were making the decisions rather than a robot on skis or a gorilla with a 5 iron! If you don't believe that a move has a better chance of helping than hurting, freeze the RNG values above the killer series, then watch the problem disappear. Life's like that, too: bend over, and you will be badly beaten; take steps to protect yourself and you (probably) won't. The odds in your favor are better than 7 to 1 in this situation.

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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Sunday, March 15, 2009

These pictures tell 201,000 stories: baccarat bets that target betting beat, creating the new gambling term un-negative expectation

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First of all, how about suspending disbelief for once and accepting my word that I had nothing whatever to do with the compilation or order of the outcomes summarized below (more than two years of play for a full time gambler!).

I have said in some of the related material that Lee Jones sent me the data as a set from two "systems tester" books put out by Zumma Publishing. Today I turned up some more archival material that tells me my memory played me false: the Jones data were packaged as "real-play shoes from casinos around the world."

What matters is that I did not originate the data set, and it can be verified by contacting Mr. Jones directly - he has his own proprietary method for winning at baccarat which I know nothing about other than that, unlike silly me, he's selling it rather than giving it away!

Another friendly statistician, Lorenzo Rodriguez, sent me the Zumma Publishing data, and I will post the results from his material next time. Years ago, I keyed in all the Zumma outcomes myself, then lost them in one of too many computer crashes (thanks a lot, Gateway).

I will let the screen shot panels speak for themselves...

(Click on an image to enlarge it)





There is an awful lot of material here, too much for most people to want to study, and a powerful turn-off for those looking for an easy way to get rich in a casino without risking real money.

That's a good thing. In the 30-plus years I have spent on this challenge, I have learned that consistent winning does not come easy, and that whoever first said that it takes money to make money (it wasn't King Midas, that I know - he had it way too soft) was, er, right on the money.

I also learned that anyone who says "progressive betting can't work" is either a liar or an idiot. Think about it! Losing is by its nature (because there are always more losses than wins for even the smartest player in the long run) a progressive process.

When you are, say, five bets behind the house, you will not recover prior losses by betting the same amount or less unless your luck flips and at some point the ratio of losses to wins reverses.

Catching up on a losses-to-wins basis is, at best, unlikely and the probability is that you will continue to lose more often than you win as you struggle to recover.

So, betting less or betting the same won't save you. Betting more might do the trick, but not if you do it randomly, because you're up against the rule that says any amount bet against a negative expectation must eventually have a negative result.

All that's left, then, is money management and its objective to minimize losses and maximize wins so that the deficit between the number of wins and the number of losses overall does not translate to money down the drain.

I have in previous posts spent some time on the Martingale or double-up method, and dismissed it solely on the grounds that casinos will not permit its use for long.

It serves primarily as an example of what can be achieved by the disciplined application of a rule or set of rules. Mythematicians deride it because of the certainty that however long the odds, at some point it will encounter a losing streak long enough to push the next bet above the table limit.

In fact, that's not a problem for a player with balls and a bankroll to match: table limits are progressive, too, and you just have to keep moving within escalating limits until you hit that critical single win!

Most of the time, a Martingale will keep raking in profits with a bet ceiling of $5,000 and a variation on the standard double-up: 5, 10, 25, 50, 100, 250, 500, 1000, 2500, 5000 and favorable odds of better than 1,000-to-1.

House-trained academics tell us that 10 losses in a row does not mean 10 wins in a row is "more likely" or that the number of wins will ever catch up with the number of losses. But because of the gentle influence of the house edge, which is always a very small fraction of 100%, the longer you play, the more likely it is that your negative and positive numbers will come substantially closer to balancing out.

When a positive trend arrives, you will be betting your maximum, which you did not reach until you were nine bets behind. You always want your average win value to exceed your average loss value by a percentage that is greater than the house edge for the series and this is one way to do it.

I say again, you will have to keep moving because no casino will let you bet a Martingale in one location for long. And if pit staff pick you out as a double-up punter even after you have tried to cover your tracks, they will steer you towards the nearest exit as quickly as possible.

Target betting is a better way to win.

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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