Blackjack can be consistently beaten without a millionaire's bankroll. But beware of "Catch-21" (the "rule" that what you know won't help you win)!

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"Catch-22" author Joseph Heller devised a fictitious military decree that only insanity can get you out of the Army, but if you are sane enough to know you're nuts, then you don't qualify for a medical discharge.

In similar vein is the cliche that insanity can be defined as doing the same thing over and over again and expecting a different result.

Does it apply even if the results you get every time are positive?

Personally, my favorite (tangentially gambling-related) funny story involves a conversation overheard in a schoolyard: "My little brother thinks he's a chicken and me and Dad want him to see a psychiatrist. My Mom won't let him - she says we need the eggs."

Defying the conventional wisdom that house table games cannot in the end be beaten, and spending several decades proving that the house advantage can indeed be overcome, qualifies as madness in most people's opinion.

And I would have given up the effort years ago if the numbers coming at me from a succession of increasingly powerful computers, and ever more sophisticated spreadsheet models, did not keep turning the "invincible" house edge on its ear.

Like many of you, I am disappointed that so far a method of winning with little or no risk has eluded me.

But on the other hand, I figure that if casino operators have to front millions (billions!) of dollars to make blackjack, baccarat, craps, roulette and other beatable games available to us, we should try not to resent having to invest a little time and money to win at them!

I have said in earlier posts that the basic principles of target betting can benefit pretty much anyone tackling a casino table game, given a reasonable level of discipline and a bankroll to match.

But nothing I have learned and am attempting to pass on to you for free can do you any good if you believe the academic argument that past outcomes from games of chance, however large the sample or mathematically, objectively impeccable the analysis of them, cannot predict the future.

It's nonsense, of course.

In every other field of human activity, from a baby's first steps to the most complicated scientific research imaginable, the past is our surest guide to what's ahead. We learn from our missteps, in other words.

But not in gambling, say the experts...random numbers (stats, probabilities, percentages or whatever else you might choose to call them) are so uniquely and magically erratic that studying them is fruitless.

Baloney!

Common sense is probably a player's best ally if he expects to win consistently, as long as it (sensibly) rejects the idea that you can't win at games of chance.

And I should say again at this point that anyone who approaches a casino game with a will to win and the mental and monetary means to do it should never think of himself as a gambler.

Gamblers are, by their own definition, losers who say they want to win and might even believe it, but then repeatedly do everything they can to sabotage their own efforts.

Frequent players know that in big picture terms at least, table games are broadly predictable, repeating patterns of wins and losses along with seismic swings north or south of the wiggly line that we think of as "the norm."

What most players don't know is how to effectively exploit those mostly reliable patterns, betting in such a way that more wrong bets than right ones do not in the end mean more money lost than won.

And that, of course, is what target betting is all about.

All that really concerns us is the frequency of paired or "twin" player wins even when the overall trend of wins vs. losses is dramatically in the house's favor.

As long as we are not betting at our maximum level, meaning that we no longer have wiggle room and switching locations will probably not help us, twin wins will quickly get us out of trouble. And if the MSL rule is applicable, a win-loss-win sequence will do the trick.

On average, paired wins occur about five bets apart, enabling disciplined target betting to stay constantly ahead of the game in spite of more bets lost than won over the long haul.

Once in a while, the right pattern will become as scarce as hen's teeth and bet values will soar. But it happens rarely and never lasts for long, making the long-term prospects for target betting consistently positive.

It is simple enough to create an RNG model that will visually confirm the frequency of "twins" in spite of a relentless HA (anyone interested can e-mail me for an Excel example). Much as I dislike "sims" I have to accept that from time to time, they can be useful.

Academics who see themselves as the guardians of the status quo, defending the gullible from snake-oil salesmen like me (never mind that I am not actually selling anything!) insist that progressive betting is suicide.

I insist exactly the opposite, and have proved it again and again, oblivious to claims that since "it can't be done" I must be either crazy or a crook.

All target betting really says is that because you will certainly lose more bets than you win in the long term, you must see to it that you win more when you win than you lose when you lose.

Sure, we have been there before, I know. But defying the conventional wisdom demands almost endless repetition of what I see as the obvious but others somehow find controversial.

If you are losing at blackjack, baccarat, roulette or whatever and are betting fixed amounts or randomly choosing the value of each new bet, you must either win more bets than you lose to get out of trouble...or win more money than you lose from now on.

The first option is completely out of your control, and may be achieved if you get lucky. But luck is not something you can count on.

The second option is only partially out of your control. You can determine bet values, but however clever you may be, you cannot know the outcome of each bet ahead of time.

To get around that little problem, you must make certain that when you win, you derive maximum benefit from having things go your way for once.

If you are playing at a 1.0% game such as blackjack, every single bet you place faces the same negative odds (495-505 to 1 against being one way of describing those odds).

When you choose to increase your bet value (and that never happens except in response to a mid-recovery win) you must know exactly how far behind you are, and therefore the precise amount you will need to win to get "out of the hole" plus a small profit.

The optimum rules set I have described throughout this blog is, to some, an aggressive approach that increases risk while proportionately increasing potential profits.

I can prove that to be a false assumption, but must concede that a $25,000 maximum bet and a $1,000,000 bankroll is beyond the reach of most players, whether they think of themselves as gamblers or not.

Just remember that erratic, emotional, irresponsible play will not win without a lot of luck even if there's a million bucks in the bank - high rollers don't win more, they just bet more, and don't hurt as much when they lose!

The solution to the added challenges of "economy play" is to scale back on some of the target betting strategy's more ambitious rules, saving them for that not far-off day when the bankroll has grown enough to make them less scary.

From the top, the optimum opening loss (OL) multiple I recommend is x5, meaning that if the $5 opening bet in a new series goes south, the next bet (NB) will be the previous bet (PB) x5, or $25.

Next is 2L x 3, meaning that if the second bet loses, NB=PBx3 = $75. Right after that comes 3L x 1.33 (you guessed it, after a 3rd consecutive opening loss, NB = $100).

All of the OL rules can be shelved to shield a limited BR, although be warned that the effect of that is to extend recovery time and thereby potentially increase risk.

Target betting's win progression (WP) component is another critical profit booster, and before I go any further, we should revisit the whole question of exploiting opening winning streaks.

If you ask a blackjack dealer the best way to "chase" a winning streak, the probable answer will be a "plus one" progression (+$5,+$10,+$15,+$20) that is the standard house recommendation, and is not surprisingly far better for the house than for you.

Think about it: Three successive wins at $5 followed by a $5 loss puts you $10 ahead; bet the house's way and you will also end up $10 ahead, your only hope being that along the way from $10 to $20, you hit a 3-2 natural or score a winning split/double.

The house likes "plus one" because a high percentage of potential winning streaks play out +$5, -$10, handing the dealer's tray an extra chip more than the conventional +$5, -$5.

Dealers do not always give bad advice: they usually preface every little lesson with the words "The books says..." But giving good advice is not part of their training, for obvious reasons.

The WP xfactor I recommend is 2, but the most critical WP rule in target betting is that you should not do as a dealer would recommend and fall back to a minimum bet after an opening winning streak ends. Bad, bad, bad idea.

Instead, you should treat the losing bet as your new loss to date (LTD) and set about recovering it in full.

Failure to optimally exploit winning streaks costs more players more money than just about anything else that happens in a casino, other than over-indulgence in "free" cocktails! (Greed and stupidity play a big role, too, but that's another story).

The WPx2 rule caps out at +$100, meaning that you don't double after PB=$200 but instead add $100 after every subsequent win.

And when the streak ends, as it always will, the recovery series is written off (with a profit of not less than $590) if the lost bet was worth $500 or more.

I am not opposed to the "plus one" approach, as long as the eventual loss is converted to the LTD and eventually recovered.

Skip that rule, and you will regret it.

Next up among "adjustable" target betting rules is the MSL or mid-series loss rule, referring to a second attempt at recovery (a do over) if the first LTD+ bet fails.

It's a major boost to the strategy's long-term efficacy because because most house wins are followed by an opposite outcome, as are most player wins. I recommend an MSL value of $1,000, meaning that a second LTD+ bet will follow a failed turnaround bet if its value was $1,000 or less.

On a budget, you can cut the MSL value all the way down to $100 (the lowest value I would be happy with) or even to ZERO if you have the fortitude to smile through all the series that would have turned around, if only...

The greatest value of the "L" rules is that they make it possible to turn a mounting loss around with a single win, a handy reversal that can occur more than 70% of the time at blackjack!

Blackjack is the best possible game for target betting because of the real (but not absolute) control afforded the player by consistent adherence to sane and sensible basic rules of play.

Skeptics dismiss past results as proof of anything, but against 85,000-plus rounds from Ken Smith's Blackjack Strategy Trainer, I have managed to keep the HA down to well below 1.0% overall in spite of almost always choosing the 8-deck shoe option.

I do that because there are usually far more split and doubledown options against a multi-deck game, and because I welcome the "streaky" nature of output from a long shoe.

If I don't like what I am getting, I can always go somewhere else - a rule that every target betting player should keep high on his list!

The results illustrated below can easily be dismissed as anecdotal or completely irrelevant but I believe they have much more to say about how we can hope to win at blackjack than runaway sims that do away with every single aspect of the casino experience other than random numbers.

Imagine if all casinos offered were heads-up games against a random numbers generator, with rules requiring that you bet from your lowest value to your highest in the same place, and forbidding you from quitting when you felt like it.

If you walk in a straight line across a minefield, paying no attention to where you put your feet, chances are you will be blown to bits before you reach the other side.

If you drive a car very fast down a winding mountain road without touching the steering wheel or the brake and gas pedals, you will probably crash and burn long before you get to the valley below.

If you jump out of a high-flying plane without a parachute you...well, by now you probably get my drift.

So it is with "runaway sims": they eliminate cards, dice, tables, dealers, players, wheels, chips and almost everything else including real time, and are then claimed to accurately represent what you can expect to encounter in a casino game of chance.

They don't.

I am sometimes accused of dreaming up arbitrary rules that by sheer luck prevail against a given set of outcomes, and will never beat another sample of any size.

That might be fair if the rules of target betting were derived from the blackjack outcomes summarized here.

In truth, those rules have been around since the early 1990s and were first published on the 'Net in 1997, while the BST outcomes trounced here date back just a few months (the product of more time at my computer than I care to admit to!).

Take them or leave them.

The same advice applies to all of the charts and summaries published here.

They are warts-and-all slices of objective data that demonstrate conclusively something most people already know: If you bet fixed amounts or randomly, you will lose.

Progressive betting is not suicide, it is survival.

Winning is not always easy, and it gets harder the more you tighten your spread and the smaller your available bankroll.

But at worst, it is a whole lot more fun than losing.

Here's that blackjack data:


The run-through summarized here features target betting's performance top-lining in the chart, with the session results to the right of the line seen headed boldly north-east.

The other blocks of data are from a souped-up version of Oscar's Grind, a standard Small Martingale (-1, -2, -4, -8, +16) and a more aggressive Martingale (-1, -2, -5, -10, +25).

Target betting invariably does best of the alternatives programmed into my models, which are included simply to underscore the superiority of almost any method of progressive betting over a hit-and-hope, seat-of-the-pants approach.

It is important to understand that the deeper the hole you are in, the bigger the shovel you will need to get out of there!

That means freezing the bet value after any mid-series loss, assuming MSL is not in play, and making sure after a win that you press as hard as your BR permits.


Again, the BR has been cut to 20% of the $1m optimum, and the spread has been tightened to 1-2,500 while increasing the minimum bet from $5 to $10.


Above, we still have a $200,000 BR, but the minimum is up to $25 and the spread is 1-1,000.


And here's what we get with all target betting's bells and whistles in play: one crushing loss, then a sustained string of wins suggesting that serious threats are so rare, they can almost - almost - be discounted.

Note that none of these data summaries conform with the so-called conventional wisdom, which would probably accept 85,000 rounds as a reasonably representative sample, and require that the final outcome be within range of the product of action multiplied by the 0.85% HA.

Expected or indicated results - what "should have" happened are plain to see in all the summaries.

The HA is, to target betting, a mere nuisance.

My version of Oscar's Grind (owing very little to the disaster recommended by the author of a best-selling book called "How to Gamble in a Casino"!) at least managed to do a little better than break-even.

But we are not about breaking even, are we?

We want to win. And we know how!

The most effective antidote to the house edge is making bet values as variable as your BR permits, keeping in mind that variable does not mean random!

Target betting rules do all a player's thinking for him, and that in itself lifts a huge burden (although some critics have suggested that I have taken all the "fun" out of gambling by replacing spontaneity with discipline).

Tom Ainslie's glacial interpretation of Oscar's Grind keeps bet values on an upward climb, it's true.

But because it lacks a win progression and adds just one unit in response to a mid-recovery right bet, it is doomed to comply with the HA in the long run.

My upgrade of Oscar applies a +1 WP and permits the bet to be doubled after a mid-series win until turnaround is within reach, so it actually makes consistent headway.

But in spite of the turbo-charge, OGX (short for Oscar's Grind Extra) falls far short of even the most cautious version of target betting.

Against the BST blackjack data set, "Ainslie's Grind" ended up losing 0.67% of its overall action, which was at least a slight improvement over the net HA of 0.85%.

Maybe that's why Mr. Ainslie's book is not titled "How to WIN in a Casino"!

OGX came in at +0.63%, not quite flipping the HA into a significant player edge, but making a contribution to expenses.

The tamest, most toned-down version of target betting delivered a win equal to +3.65% of its total action.

As an old-time mathematician would put it: "Q.E.D."!

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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Casino table games are sucker traps. And if you don't play like a sucker, the welcome mat will be whipped out from under your feet.

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First, the latest from the ongoing BST blackjack trial...


Skeptics who don't question my honesty or the accuracy of my published results will sometimes suggest that target betting might work in theory, but cannot be successful under real-play conditions.

It is certainly true that a prolonged negative trend (defined for target betting as clumps of losing rounds separated by isolated wins) will drive bet values very high very fast, making it impossible for a strategy player to remain in one location.

In my experience, table-hopping in one casino or moving from one casino to another as the win-loss pattern demands makes good sense for all sorts of reasons, not the least of them being that it helps a target player to avoid attracting attention.

As always, it is all about common sense. If you are in a near-empty casino at 3:00am, then jumping in and out of games with a wide range of bets is going to set off alarms left and right.

The same is not true mid-evening on a Friday, when all the games are in full swing, and finding a seat at layouts under $100 can require a whole lot of walking.

The mathematical question that comes up involves the effect constant mid-series motion is likely to have on long-term profitability, and the short answer is: None.

Anyone who has studied gambling games knows that negative expectation is a constant factor, like gravity, or the slow-moving DOWN escalator I described in an earlier post.

Supporters of card counting in blackjack insist that a rich deck value reduces or eliminates the house edge, but most players do not count cards and even those who do have often lost heavily in spite of conditions that seemed to favor them.

In a game with any house edge (and casinos do not offer games without one), the percentage of negative expectation applies equally to every bet, meaning that in a 2% game, the player's odds of winning the very next bet are 49-51 against him.

All of the target betting models track not just winning EOS bets but failed attempts too, and naturally more potential turnaround bets go south than succeed and save the day.

If that were not true, there would definitely be something wrong with my methodology.

So the only difference between theory and practice is a little thing called time.

In the models, as with all simulations, bets are placed without regard to table or house limits, and the only inhibiting factor is the standard target betting "bust" limit of $1,000,000 in funny-money.

In actual play, it is not smart to spread wider than 1-5 in any one location, although if the risk of attracting unwanted attention is low, there is some room for maneuver.

An exception is at the bottom level: $5 to $100 (1-20) is generally OK, but again, sometimes it is better to suspend a series sooner than that after assessing local conditions.

And suspending a series does not have to mean taking yet another walk, especially if you know it will be a while before you can find an empty slot.

It works just as well (and saves shoe-leather) if you cut a series off in mid-recovery, remember or jot down the LTD/NB numbers, and begin another series with a minimum bet.

When you have several targets stored in your sharply-honed, always reliable grey cells, you can move on ready to recover them one by one elsewhere.

All simulations, including mine, eliminate the human factor, which happens to be at the top of the list of factors that determine long-term success at gambling games.

When the human factor (hn in those terrific TV commercials!) is reintroduced to the formula, everything changes for the better except if the human being involved is one of those who thinks that losing is fun.

When spread limits are applied, series that begin with a $5 bet and end with a $25,000 win simply cannot happen - but that in no way alters the fact that a threat to the bankroll can be turned around 99.99% of the time (or better) with target betting.

It just takes a while longer in real play.

There is, I can reassure you, no contradiction between my assessment of your prospects when you bail out to comply with spread limits and your chances if you back out of a game to duck a particularly deadly downturn.

Whatever your reason for moving, the numbers are the same: a quick 2-win turnaround is a 10-1 probability, with the odds in your favor.

So staying put through a negative trend that threatens your bankroll makes no sense at all, and trusting your gut is the right thing to do.

Gamblers only get into trouble when their "gut" is allowed to set bet values, and target betting does not permit that. The strategy wins because there is a rule for every eventuality.

Occasional threats are inevitable, but you can take comfort in the fact that in order for a maximum bet to be required, the house edge will have had to balloon to 30% or more, a far cry from the 1-5% that usually applies.

If you had to rely on a 100% correction of an egregious swing in the house's favor, you would probably be out of luck.

But with target betting, just a short offset against the trend that got you into trouble is all it takes to rocket you out of the hole and back into profit.

A glance at any of the thousands of AV charts that track negative expectation in my models confirms that substantive offsets in the player's favor are a reliable feature of the WLP after (and often during) a downturn.

Without a bankroll big enough to keep you afloat through rough waters, you and your money will be out of the game before one of those offsets can happen.

And that is why a wide spread and fat wad, the same weapons that the house wields against you, are essential to long-term success.

You have to be able to think like a casino operator and have full confidence that "the arithmetic" will take good care of you, no matter what.

In theory, a 1.5% house edge means that the house can be sure of keeping $15,000 for every million bucks that goes back and forth in a given game.

In fact, the gambling industry does much better than that.

Casinos win more money and more often than negative expectation says they should because the only house advantage that really matters is that the house has a bigger bankroll than the players do. All of them put together, that is.

If you check the Nevada casino win numbers, dwindling as they may be in a down economy, you will not find a game where the reported win percentage matches standard expectation.

Blackjack, for example, has a house edge of 1-2%, depending on the level of a player's compliance with basic playing strategy.

The win for all of Nevada's blackjack layouts in February 2009 was 11.65% (10.4% for baccarat and 26% for 3-card poker!).

In March of '09, the matching numbers were 11.69%, 10.3% and 26%.

Who says gambling games are "unpredictable"?

And that is really what it all comes down to, isn't it?

I say, and can prove, that win-loss patterns for games of chance are broadly predictable and so can be exploited with the right math-based approach.

My critics argue that casino games are unique in all the universe, able to generate WLPs that, like quicksilver or Tinkerbell, cannot be second-guessed, and woe betide the heretic who tries.

I am going to wrap this up with a spread pattern breakdown of a random sample of series.



It is possible to produce an almost infinite number of these things, but I think just one tells the story well enough.

In actual play, the majority of recovery series turn around rapidly and without incident, paying a modest profit even though most of them have a zero or negative actual value.

When a move is called for (shaded light blue above), the chances of a turnaround remain the same: about 90%.

Once in a while, spread limits will require a series to be suspended a second or third time, or as often as it takes before two consecutive wins deliver EOS.

Overall, the average length of a recovery series is less than six bets.

You know you are going to lose more bets than you win, over time, and that reality must always translate to more money lost than won unless you can win more when you win than you lose when you lose.

Target betting delivers on that promise for tens, even hundreds of thousands of rounds in succession, although sometimes, a sizable chunk of your bankroll will have to be put into play before it can be bolstered by yet another big win.

There is no winning alternative to progressive betting, and as far as I know, target betting is the best method of money management available anywhere.

Steve Wynn, credited as the creator of the modern Las Vegas, said on "60 Minutes" the other night that the only way to beat the house is to be the house, and he needs you to believe that.

Even though he knows better...

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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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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The YCW (you can't win) Brigade will tell you that if you can't be sure of winning, you should never attempt a betting strategy...

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...but if you don't have a plan, you are much more likely to lose.

It is plain to see who benefits most from the gambling attitude promoted by mythematicians, who go on to say: "You should think of gambling as entertainment, nothing more, and only bet what you can afford to lose."

My advice is fundamentally different: "Play to win, but don't play at all if you can't afford to win."

In other words, if a penny-ante bankroll is all you can muster (and there's no shame in that!) then you will probably be better off to trust to blind luck and hope that at worst, you break even.

Beating negative odds requires a bankroll large enough to keep you in the game through the inevitable rough spots when the house edge is temporarily far greater than standard negative expectation.

The latest batch of BST figures is not much different from its predecessors. It shows "the house" getting way ahead in terms of player losses vs. player wins, and as long as the 1-200 spread limit is applied, the result is another loss for the good guys (who don't work for the casino, let's be clear about that!).

Set target betting loose with an appropriate bankroll, and as before, we end up with an overall win with the total action (sessions A and B combined) greatly reduced. Also per prior experience, we see far more "big ticket" bets when the BST table limit is applied than without it.

So much for "conservative" play!

The BST results have been truly demoralizing lately, without target betting giving up a thin dime.

Here are the current "Batch #s 1-15 to date" numbers:-

Win Rate TD 100.0000%

ALL ahead +$1,715,420 = +5.17% of
$33,161,885 action
$25,000 max
$444 avg bet
$2,299 per hour
5.2 x avg bet


RISK (181,475) = 18.14% of bankroll
return 945%

EOS x 13,403 in 74,620 rounds
Avg EOS 5.6 rounds

AV/HA -5.28% (3,938) -5.28%
Expected ($1,750,087) per gross AV or (597) per net AV of -0.80%
TA/T 2.0 x expected result


+ MAX 12
- MIN -16
ABV $444
$1,000+ 3,536 4.74% of all bets

+ series 4,286 32%
0 series 4,153 31%
- series 4,964 37%
1-win EOS 8,737 65%

Most of the data are self-explanatory. Note that betting my way, big-ticket wagers were less than 5% of the total, and that the win to date represents better than a 5.0% "hold" of total action, against an overall house edge of between 0.8% and 5.28%, depending on the method of measurement.

Sometime soon, I will post average bet and $1,000+ data for a 1-200 spread for all 15 BST models, but it is safe to predict that action will be way up, the result will be an overall loss in line with negative expectation, and max bets will be in the majority, not a rare event at 1 in 20 or less.

I use a "net" number for the house edge (HA) or actual value (AV) which factors in doubles, splits and 3-2 payoffs for naturals. The old-fashioned way is to count hands as either won or lost: do that, and you end up with an HA that's more than SIX TIMES greater than my more inclusive approach.

As you can see, winning series (hey, they were ALL winning series) with more bets lost than won greatly outnumbered series with more wins than losses. Series that were negative or neutral still account for 68% of the total, so "expectation" demanded either a break-even or a loss in all those instances. Sorry, expectation.

The trial opened with a $1,000,000 bankroll almost 75,000 blackjack hands ago, and that has long since been covered by winnings, plus a 70% return on the investment which does not include $1,000,000 in profits left in the bankroll to take us through future downturns.

Maximum exposure for the initial bankroll was $181,475, or a little more than 18%.

I do not expect target betting to keep winning forever.

At some point, a win-loss pattern will be encountered that first pushes the strategy to its maximum bet, leaving it at the mercy of an ongoing negative surge that exceeds expectation for the game.

Then, the strategy will cease to be a strategy at all...it will have to wait out the surge and hope that sanity returns before the balance of the bankroll is swallowed up.

In the 300,000+ baccarat outcomes discussed in earlier blog posts, there was just one "crash and burn" and target betting came out way, way ahead in spite of it (see the archives or do a baccarat search).

The certainty is that winning sessions will always hugely outnumber losing sessions if you follow my rules.

The experts warn that the million-dollar bust could happen today or tomorrow, long before you have built up enough profits to avoid actual loss of your original buy-in.

But my way, probability is overwhelmingly on your side. Their way, it's against you every time you belly up to a blackjack table. The choice, of course, is yours!

The (nearly) 75,000 BST outcomes break down as follows:

(Click on the image to enlarge it)

Just for the fun of it, each of the target betting models also tracks results for two versions of the widely derided Martingale, the old-fashioned x2 kind (-5, -10, -20 etc.) and a more aggressive update which brings in more dough with a modified progression: -5, -10, -25, -50, -100, -250 etc.).

The YCW preachers scorn double-up as suicide, warning that "you will hit the table limit, and then what?"

"What," my friends (all of a sudden I'm John McCain?) is a move to a new location where the required NB is permitted. And if at some point you hit a house- or self-imposed green ceiling that can't be defied, then you keep on betting the max. The odds are very much in your favor that the WLP will stabilize and you will recover prior losses and then some.

Once again, I will say that I don't recommend double-up, not because it's a losing method, but because it is too easily spotted and casino pit staff will invariably interfere with its use.

I don't have double-up numbers for all 15 BST sessions yet, but here are the data for the current batch (#15). Notice that target betting is a more effective alternative.

(Click on the image to enlarge it)
Here are the newest BST numbers. I have to stop doing this. But maybe not quite yet?

(Click on the image to enlarge it)

The BST "table-limit" bets enormously outnumber max bets with target betting rules because in the current batch, a tight-spread punter would have been at the limit for the last 1,200 rounds. And since he's in the hole by more than $65,000, he is going to be betting the max until the cows come home.

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.
_

Mythematics: Any sample of outcomes, however large, is totally unique. Reality: If that were so, there would be no house advantage.

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The gambling industry's mighty disinformation machine holds that the house edge cannot be beaten in the long run because every sample of random outcomes differs from every other except in one component: negative expectation.

We are all supposed to believe that a sample of more than 70,000 blackjack outcomes like those in the current BST trial can never be duplicated, so a betting method that beats that data set will fail against another of similar size.

Quelle crappe! comme ils disent en France.

It is, like so much of the conventional wisdom applied to gambling, a partial truth. And we all know that a half truth is not a whole lot truer than a lie.

Within a representative sample of more than 50,000 outcomes, pair patterns will be constantly repeated, three-round patterns less so, identical four-bet sequences less often, and so on. By the time you widen the sample within a sample to look for identical patterns of 10 bets or more, you are going to be out of luck.

So it is true to say that one large sample of random outcomes can never be precisely repeated.

And that begs the terse two-word question: So what?

The house relies for its profits on broad or big picture predictability in two critical areas, player behavior and/or resources, and random win-loss patterns.

The house edge is more reliably predictable the larger the sample of outcomes, and much the same applies to gamblers (the bigger the crowd, the deeper the hole!).

There may be a few dozen outcomes in which the house advantage can barely be discerned, just as a handful of players in thousands might have the knowledge and bankroll to be a serious threat to the casino's bottom line.

But the further we "zoom out" in terms of sample size, the more likely it is that the house advantage will prevail and that the majority of gamblers, even those who won more bets than they lost, will surrender their bankrolls in dutiful compliance with with negative expectation.

Today's post revisits the topic of the certain danger inherent in tight betting spreads by examining expanded data from the BST blackjack trials.

Here's a summary:-

(Click on the image to enlarge it)
What this tells us is that narrow spreads (defined as 1-500 or less!) are virtually certain to fail, even with target betting rules applied. And the negative odds, bad as they already are, worsen still further if disciplined money management is not in play.

I have used a $5-$25,000 spread (1-5,000) throughout the blackjack trials, and I am well used to skeptics squawking in unison that a bet range that wide is ludicrously unrealistic and far out of the reach of the regular weekend punter.

To take the last point first, the regular weekend punter has neither the resources nor the desire to do what it takes to win consistently.

And in this context the only function of the "recreational gambler" is to provide the gambling industry with the profits it needs to pay off a few winners here and there without going broke.

Very large bets are indeed a reality, especially in casinos that try to cater simultaneously to shoestring players arriving by coach to fritter their tiny wads on the slots, and high rollers winging in from afar in private jets.

A $25,000 bet is 10% of what some "whales" will risk on the turn of a card, and no one knows better than the gambling industry that big bucks do not a winner make any more than does a penny-ante purse-full! In other words, the pot cannot be bought...it has to be earned.

I remember years ago playing at a blackjack table with an immaculately-dressed and courteous gent from Mexico City whose response when the dealer warned us of her current hot streak was, "You can't beat me; I have too much money."

He said it with tongue in cheek, but I got the feeling he believed it, and ever since I have wondered how he fared during his wild weekend in Nevada. Badly, I fear.

Money is essential to long-term success at gambling, there is no doubt about that. But money alone will not beat the house advantage in the long run.

As for the claimed "uniqueness" of large blocks of random outcomes, casinos know that even a runaway sim cannot produce representative data sets in which prolonged negative trends are not at least partially offset by opposite patterns.

It simply can't be done.

A gambler who, like most players, relies on winning more bets than he loses will eventually surrender his bankroll. That's a fact. Even an equal number of wins and losses is a long-term impossibility in a game with a house bias (and of course, there is no other kind).

The only way to win, therefore, is to recoup losses from a succession of "wrong" bets with a smaller number of winners.

To repeat a simple example: 49 wins and 51 losses against a game with a 2.0% house edge adds up to red ink if the overall average bet value is $10; but if the average win value is $10.50 and the average loss value is $9.50, $514.50 in wins trump $484.50 in losses in spite of that same 2.0% house edge, delivering a profit equal to a 3.0% "hold" of action.

The house always has complete confidence that over time, wild fluctuations against it will be evened out by the anti-player bias, and that a slightly greater number of player losses than wins will, given random bet values, make the game profitable for the casino.

Without that "big picture" predictability, any game would be too risky for the house to venture. And that's the name of that tune...

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.
_

The difference between winning and losing at casino table games isn't luck. It's all about discipline.

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You may not know it, but the casinos you love to frequent have a plan for you, and it goes like this:

You will...

• Go to the table with an inadequate bankroll.
• Bet within a very tight spread (probably not more than 1-5) so that even a relatively short negative trend will wipe you out.
• Respond to a downturn by dropping back to minimum bets and playing scared or pushing out ever-larger bets until your money's all gone.
• Gratefully accept "free" cocktails so that your play becomes increasingly reckless and self-destructive as your inhibitions are buzzed into oblivion.
• React to a run of luck by raising your bets, then stubbornly sticking to high wagers when luck deserts you (as it always will) until all your winnings are back in the dealer's tray.
• Go home a loser, convinced that it was not your fault that you made another "contribution" and
• Come back again for another drubbing because you never learn anything from being beaten.

Casino personnel are trained to have a very low opinion of their customers' common sense quotient and to steel their hearts when they see someone losing far more than they can afford (no one forced the fool to gamble, after all).

The house's fat bottom line depends primarily on the fact that the vast majority of gamblers have no idea of the negative odds they are challenging, and assume that whatever the numbers may be, they don't apply to them.

A consistent winner, on the other hand, will...

• Accept that luck is an irrelevance because it favors the house as much as the player and
• Recognize that the house advantage makes it inevitable that over time, the smartest punter will lose more bets than he wins.
• Be fully aware of the negative odds he faces, while knowing that the tiny edge the house enjoys is far less of a factor in player losses than poor money management.
• Know that winning requires a substantial bankroll (something the house knows, too) and that long-term profit without risk is a mathematical impossibility.
• Grasp enough math to understand that if he is going to lose more bets than he wins in the long run, then the only way he can make any money is to win more when he wins than he loses when he loses (an objective that sometimes requires balls, but never crystal ones!).
• Learn the best way to play any "house game" he chooses to venture and ignore side bets and sucker traps such as Royal Match at blackjack and Pair Plus at 3-card poker (which is itself only suited to players with too much money).
• Play consistently and cautiously, knowing that what many people assume is conservative betting actually increases the house's already favorable odds.
• Study win-loss patterns and see in them the simple truth that they key to winning is exploiting positive streaks in such a way that cumulative losses can be recovered in fewer bets than it took to get into trouble in the first place.
• Do everything possible to avoid attracting the attention of paranoid pit personnel who assume that anyone who wins "too often" must be cheating. Effective camouflage includes:
• Varying strategy rules without ever flouting the core principle that a mid-series win must always be followed by a loss to date plus target bet (LTD+).
• Never spreading bets so wide in one location that pit staff or other players notice the low-high gap.
• Bailing out of any prolonged negative trend, knowing that house "spikes" are not the norm (in blackjack and baccarat, at least!) and that betting against a losing streak can be more damaging than moving.
• Knowing that moving from one layout to another (or a different game or even a different casino) has no effect on probabilities, as long as the next bet (NB) and loss to date (LTD) values are maintained.
• Never playing when tired, bored or otherwise uncomfortable, because winning can always wait a while and the tables aren't going anywhere!
• Never taking losses personally, because they are almost always temporary.

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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