Irrefutable logic supports target betting as the best way to win consistently at casino table games. So yet again, the conventional wisdom is wrong!

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(The truth is that when the word conventional precedes "wisdom" it is more often than not a synonym for false or erroneous. Remember the flat earth theory? Or all the "expert" assumptions about house prices and Wall Street?)

This has never been an argument about whether or not the house advantage exists in games of chance. Of course it does, or the games themselves would not exist.

And I have never disputed that the house edge is the undoing of at least 99.9% of all gamblers: anyone who bets either relatively flat or random amounts is sure to lose eventually.

I am accused of being innumerate or (my favorite) discalulic, because I can prove the obvious over and over again.

And in the minds of many who consider themselves smarter than the rest of us, when the obvious contradicts the conventional wisdom, then the obvious is obviously wrong.

You would think that the following statement is too logical to run any risk of being disputed:

If the combined value of a smaller number of winning bets exceeds the combined value of a greater number of losing bets, then the negative expectation derived from (L-W)/N or losses minus wins divided by number of bets is not relevant to the end result.

In other words, "If you win more when you win than you lose when you lose, then losing more often than you win will not hurt you."

But by golly, stalwart defenders of gambling's status quo contradict the notion all the time.

There is, they claim, no way to prove the "win more" concept, because past outcomes from games of chance are always anecdotal or subjective and can never be used to predict the future.

Never mind that the target betting principle can be applied successfully to any sample of outcomes of almost any size from any honest and objective source.

Or that using just the "LTD+" rule and none of the camouflage against countless outcomes as yet unplayed will confirm that target betting - progressive betting - makes the house edge irrelevant.

My critics keep falling back on the argument that if you lose more bets than you win, than you must in the end lose more money than you win.

And that makes me wonder exactly who those critics are, since casino operators everywhere know full well that their games can be beaten and are constantly on the lookout for players who threaten the house's bottom line.

I take comfort in the fact that those who are skeptical of target betting contradict themselves and each other all the time.

For example, the hundreds of thousands of real-play outcomes that I offer as indicators of target betting's power over the house advantage are routinely dismissed as anecdotal and mathematically suspect.

But when I confirm that there were two "busts" among 59,901 recovered series (a win rate of 99.997%), the response I get is: "Aha! That proves that your ideas are nonsense!"

Target betting has so far achieved a "hold" of 8.1% against 84,000 rounds of blackjack with a collective house edge of between 0.74% and 5.7%, winning $306,530 when it "should have" lost at least $27,000.

It won about the same amount against 202,000 rounds of baccarat, in spite of an indicated loss (house edge of 1.19% x total action) of $101,000.

It "tanked" twice in an additional 114,000 rounds of baccarat, confirming that target betting is not a 100% winning proposition, and therefore should not be treated as such by the gambling industry.

I look at it this way: Odds of better than 29,500 to 1 in my favor are logically and irrefutably superior to odds of 49-51 against me.

The caveat that we all need to be aware of is that the application of any rigid set of rules to a very large sample of outcomes, retroactively or in advance of play, contravenes normal human behavior.

Likewise, the pretense of accuracy, honesty and relevance for a runaway sim that denies the "player" any response to conditions and circumstances is disingenuous.

The Wizard of Odds, for example, is a well-funded shill for the gambling industry. His website touts his $20,000 "systems challenge" and its reliance upon a billion-bet simulation to "prove" that the house advantage is always unbeatable.

But what does any sim - let alone one that claims to represent at least 10,000 years of continuous betting! - have to do with real play? Answer: Nothing.

I have been using variations of target betting for more than 30 years now, and my application of the flexible rules depends on the current level of two things: my confidence and my bankroll, which while connected do not always move up and down together.

There is not a player alive who would sit through the kind of punishment that is routinely dished out by simulations that eliminate not just the critical human element but cards, dice, tables, wheels, balls, chips and real time.

Sim proponents like the Wizard of Odds (a great moniker when it was first used by someone else on TV in the '70s) would have us believe that human behavior can have no long-term effect on the probabilities that apply to gambling games.

That makes about as much sense as a claim that a rider cannot control a horse, or that a speeding car will crash with or without a driver behind the wheel who knows the difference between the gas and the brake pedal.

For a flat or random bettor, it may be true that "damage control" will make matters worse about as often as it improves them.

But a target player can recover prior losses in a fraction of the time it took for him to get into trouble in the first place. And a win-loss pattern that will cause him serious problems is, at worst, about a 10% probability.

The truth about the random game outcomes that we call hands, rounds, spins or rolls is that while they are individually unpredictable, in concert they form patterns and trends that are reliable and cyclical.

We know, for example, that most wins for either side, player or house, are immediately followed by an opposite result, that half as many are paired, and half as many again constitute a three-bet "streak." It's called arithmetic.

And in spite of all the "expert" claims to the contrary, the rules of probability keep a tight rein on the pattern variations that can occur in the course of a game of chance like blackjack, baccarat, craps or roulette.

There are exceptions to every rule, but they are rare enough to be of almost no consequence.

Here are some results that the conventional wisdom says are impossible, or at best fraudulent:


The good news for you and me is that the results above (for baccarat and blackjack samples with the optimal target betting rules applied) are scrupulously accurate, and confirm a consistency that is mathematically predictable.

The more complex the target betting tactics become - with the objective of increasing win values while camouflaging the strategy from prying eyes - the wider the variation between one positive outcome and the next.

And since additional strategic switches necessarily increase overall action and, by extension, potential risk, it makes sense to add them gradually, as the bankroll grows stronger.

Adjusting a betting method intuitively to suit circumstances and/or available resources is not something that "sim" supporters like the Wizard of Odds will ever permit.

Their systems-busting weapon of choice will only work for them if the "player" at the heart of them behaves like a suicidal idiot.

Like hurricanes in The Hamptons, aberrational departures from probable win patterns hardly happen.

But they will occur, and the player response to them before they can prove fatal becomes absolutely critical, while being blithely ignored by the Wiz and his ilk.



As the caption above points out, casinos themselves are much less impressed by computer game simulations than they are by real-time research out on the floor.

No new game, or modification to the rules of an old one, will ever happen without reliable data "from the field" to support its predictable contribution to the house's bottom line.

The summary below confirms that when the non-essential (but very effective!) target betting switches are turned off, session outcomes fall within a much more narrow range.


One of the jobs of a blog like this is to state the obvious the way the "experts" do ad nauseam, so let me say that given an average per-session win of around $10,000, it makes very little sense to persist with a million-dollar "bust" limit.

I would urge readers to take a very close look at this summary, and pay particular attention to the numbers on the far right, which track the win per round for each session.

Those numbers are, you will see, mostly within a percentage point or two of one another.

They confirm the consistency and predictability that I felt confident must exist in win-loss patterns in games of chance when I began this quest in 1978.

The "sore thumb" above, of course, is the double-whammy red splat next to sessions 14 and 15 from the Rodriguez baccarat data set.

Damage control would not have been merely optional in those two instances, it would have been strictly enforced by the casino's own table limits.

That being so, would the huge losses indicated in the summary have been possible in real play?

All the other numbers in the summary answer that question: No way.

Another question that is begged, of course, is the effect on all the other results of spread limits enforced throughout exactly as they would have had to have been in the losing sessions.

The honest answer: little or none.

That is because prolonged negative trends are rare events, and the chances of one of them continuing from suspended play into the very next session are slim indeed.

In the next post, I will put up results from the baccarat+blackjack database with a $25,000 to $250,000 spread limit applied.

Ignore any experts who tell you that what I am doing here amounts to experimentation with anecdotal data until a winning strategy is found.

Right now, all we are concerned with is the application of a target betting rule that has been in the public domain for a dozen years, plus an end-of-series rounding up rule which is nothing more "experimental" than a nod at reality.

Given a winning previous bet (PB) of $5,000 and an updated loss to date (LTD) of $775, would would your next bet (NB) be?

If your answer is $775, you are not wrong, exactly, just a little out of touch with the demands of real play...

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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Waiting for the other shoe to drop could take a lifetime (and it may never happen at all!)

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The assumption that mythematicians like to cling on to and batter us about the head with is that if you are certain to lose more bets than you win in the long run then you must also be doomed to lose more money than you win.

They don't care that models and data summaries covering millions of outcomes with a clear overall house edge include countless thousands of profitable series that consisted of more losses than wins.

They just keep chanting that the sample, however large, was "not representative" and warn that at some point, the sum total of all losses must exceed the sum total of all wins. So, beware, insolent peasants, and be ready to pay your dues.

Here's the latest BST log:

Click on the image to enlarge it
It's true that from time to time, a win-loss pattern will set in that has a succession of isolated wins (wins immediately followed by one or more losses). And if the PB value is outside of your MSL ("do over") range, two wins separated by one loss will not save the day before the cavalry rides over the hill in the form of "twins" (two wins in succession!).

The horrors of long stretches in which the NB keeps jumping skyward with each failed EOS bet diminish dramatically as your confidence grows. But it never hurts to keep in mind that you are playing a game in which the odds are almost always against you.

As I explained in the summary, table limits usually extend the battle to climb out of the hole because without wiggle room in your bet values, the green ceiling forces you to keep betting the max until the WLP switches to a more positive trend.

But that assumes you do not have the option to back away from the layout that has put you in the hole, and resume play at a location where you can continue to strictly follow the target betting rules.

Here are the target betting bets applied by the spreadsheet model to the outcomes in the pencil log shown above. The final totals differ from the numbers at the bottom of the log because the recommended responses to dealer naturals and dealer 21s are not applied. I'll fix that at some point, but my purpose here is to keep on demonstrating that more lost bets does not translate to more lost dough!


Click on an image to enlarge it
The blocks of numbers in the spreadsheet line up with the checks and crosses etc. in the log, so if you print out the three images, it should be fairly easy to match them up.

As always, there were numerous turnarounds that delivered a profit from a negative situation, and overall, the house edge was almost 2.0% gross, confirming that more hands went south than north, so to speak.

The NET AV was +2.79%, demonstrating once again that properly-applied doubles/splits really do deliver a player advantage. We already knew that a 3-2 pay-off is better for the bottom line than a 1-1 pay-off!

Real math (as opposed to mythematics) is reassuringly predictable when it comes to data from games of chance. An analysis of recovered series will invariably show that one third contained fewer wins than losses, one third had an equal number of wins and losses, and one third had fewer losses than wins. Surprise!

The bigger the sample, the more precise the distribution becomes. This set (the outcomes from 090309) made a liar out of me, temporarily, with 45 positive series, 18 negatives, and 21 break-evens, but that's not the norm. The current trial sample (all bets against Ken Smith's BST app) are also out of whack (547/369/315) but the distribution will settle down eventually!

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 "no frills" approach to target betting is a consistent winner. But all those bells and whistles help boost the bottom line.

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(Click on the image to enlarge it)
The idea that it should be possible to win more from fewer winning bets than you lose in a greater number of losing bets first occurred to me in 1978, and the following year I bought my first computer.

The new system was a Xerox 820 CP/M contraption with a trailblazing 64kb of RAM, no hard drive, and twin floppies with a combined storage capacity of less than 100kb.

The whole kit and caboodle, including a daisy-wheel printer only a little smaller and lighter than the family car, set me back $13,000 and was intended primarily as a word processor because words were the source of my living back then.

I was intrigued, though, by the prospect that the Supercalc spreadsheet program that was bundled with the system might help me speed up the process of testing my ideas for betting at blackjack.

As it turned out, it took around another ten years for computers and spreadsheets to grow powerful enough to be of much use to me as a betting aid, and quite a bit longer for me to become proficient enough to properly employ all that theoretical muscle.

By then, I had a vast backlog of questions that needed answering, and boxes of notebooks packed with real-time play logs that looked about the same as the ones you will find in this blog.

All the logs had to be keyed into my third or fourth new system (an early Gateway, as I recall) and that alone was a monumental task.

I had learned early on not to trust random output from a computer and to stick faithfully to actual game records.

The problem with "sims" is not just that they tend to recycle huge chunks of output, delivering blocks of outcomes in the same order over and over again, but that use of them requires an assumption that simply cannot apply to "real play."

Mythematicians love sims to bits because in just a few minutes, they will "prove" that no betting strategy can ever hope to beat the house advantage in the long run, and it is very important to the economic health of the gambling industry that players everywhere believe that to be true.

But sims depend on the daft presumption that a player who is losing his shirt in a prolonged downturn will sit still and suck it up until his money runs out, at which point he will slink away from the game and start saving his pennies so he can lose another shirt another day.

If the same logic were to be applied to automobile safety tests, the rules would requite that a car survive being sent at full throttle down a winding mountain road with no one behind the wheel and the brake and gas pedals disabled. Come on!

Anyone who has ever gambled in a casino for more than an hour or two knows the value of taking a break when a prolonged losing streak sets in, and listening to a combination of experience and gut feelings that signal when a change of scene is needed.

This isn't hocus-pocus or silly superstition, it's just common sense (something gamblers are meant to be lacking, it's true).

I am asked from time to time why I use QuattroPro for most of my spreadsheet work, instead of following the herd and relying on Excel. Simple answer: It's a better program, just as WordPerfect is still a better word processing program by far than Microsoft Word.

For one thing, Excel limits users to nine conditionals in any one formula. QPro allows as many as can be squeezed into 1024 characters, and that's a lot.

The spreadsheet platform is perfect for betting analysis. It enables different rules or conditionals to be applied to the same set of outcomes so that the long term effects of a specific method can be measured at least to a degree.

Of course, no one set of outcomes from a truly random source such as real play can ever be exactly like any other (a reality that does not apply to RNG-based sims that constantly recycle old data). But large data sets do not differ that much in terms of win-loss patterns, and certain assumptions can be made.

For example, isolated wins and losses are about twice as frequent as paired wins and losses, which are in turn about twice as frequent as triples, and so on. If the house edge for a given game is known ahead of time (and you should not be playing it if it isn't!) it is safe to predict that the larger the sample of outcomes, the closer the actual value (AV) of the sample will match negative expectation (the house advantage).

The "gamblers fallacy" that a very large number of losses increase the probability that a given bet will be a winner deserves its name, because it is nonsense. But study of any representative sample of outcomes (more than 100) will confirm that very large swings in one direction will be to some degree offset by swings in the opposite direction.

To me, the ideal losing streak is one where the NB value is low (surprise!) because I am happy to watch 15 $10 bets in a row go south knowing that sometime soon, there will be a positive swing that will recover all my losses and give my bankroll a handy boost.

Anyone who doubts the certainty of swings and offsets is welcome to e-mail me and request an Excel file that will prove the truth with every tap of the recalc button! Wins of course cannot be predicted on a bet by bet basis (it wouldn't be gambling if they could) but we can be confident that over the long haul, there will be about as many wins as losses, less the prevailing house edge.

The chart at the top of this post serves to illustrate the effects of specific "tweaks" in the betting strategy rules.

Look to the right of the bold labels and then at the green numbers along the center of the chart. You will see that against the current set of outcomes (my blackjack trials never end!) a bare-bones version of TA/T with only the after-a-win LTD+ bet applied managed to overcome a gross house edge of 4.6% and an expected LOSS of $195,000 to deliver an overall profit of $72,000 (+1.7% of action).

The numbers head north as more and more target betting "switches" are flipped on, and they are as follows:-

OLx is the response to an opening loss in a new series (1 means follow it with a bet of equal value, 2 means x2 and so on.
2Lx is the response if the second bet loses and
3Lx shows the 3rd loss response, if any.
WPx is the PB multiple after an opening win in a new series, and any subsequent wins until the streak ends with a loss. The value is usually 2, but 1.5 also works well and I will add it to future summaries.
WP max is the maximum amount NB can be in relationship to PB (keep redoubling until PB is $200, then add $100 after each additional win.
Tgt is the profit you aim for each time an EOS opportunity comes along. I recommend a minimum of $25 or 5u.
Min is the value of the opening bet, $5 in most trials but $5 tables are becoming increasingly hard to find, at least in Nevada.
Max is the self-imposed maximum bet for these trials. A target bettor won't reach this stratosphere for quite a while, but this method is not about making easy money with minimal risk (let's face it, that simply is not possible in the long run). $5,000 to $15,000 table limits are commonplace in Nevada these days, even in rinky-dink Stateline, and high-roller rooms or salles privees offer much bigger limits.
Bust Crash-and-burn limit. No one should imagine that a million bucks in the bankroll is a guarantee against losing. It's spread that makes the difference, not how much you can afford to lose.
MSL to MSL means mid-series loss, and it's a little wrinkle that ought to make for riskier betting, you might think, but doesn't. It's basically a "do over" bet when a hoped-for EOS wager fails. Here, a second EOS bet follows a loss if PB is $1,000 or less. Above that amount, you have to wait longer for another shot at the brass ring!
WP to is the PB value at which loss recovery attempts are abandoned when an opening winning streak ends. By the time you lose a $500 bet, you will be at least $1,090 ahead on the series and "eating" the loss will drop you back to a profit of $590 from a string of nine bets (8 wins and 1 loss). Not bad. When the WP max is reached, a loss is followed by a minimum bet and the start of a new series.
Push+ is the maximum amount by which NB can exceed PB after a push. Note that in the chart, introducing the after-push rule boosts the win by about 10% but also inevitably cracks up the overall action.
Pushx is usually 2, meaning that after a push NB=PBx2 to a maximum of PB+$100.

You will see two different AV (actual value) or HA (house advantage) numbers in all blackjack trials, so I will explain why again. The GROSS value summarizes the number of overall wins less the overall loss total, counting naturals and multiples of the original bet as single wins and losses.

The NET value tallies the absolute value of each outcome (-2, +1.5 and so on).

So for example, the GROSS value of -2,-10,-5,+4.5,+15 is -1 and the NET value is +2.5. In the summary above, the NET value matches expectation for blackjack much more closely than the GROSS number. The discrepancy exists because 3-2 payoffs for naturals exceed the original bet value (naturally!) and double/split opportunities in blackjack give about a 20% edge to the player, assuming he plays "by the book."

I'll sign off with the latest BST log:-


(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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There's mathematics, and then there's mythematics (the "proven" notion that casino games of chance are ultimately unbeatable!).

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The only thing that is demonstrable about the (hopefully) random win-loss patterns derived from house-biased games is that a player who bets flat amounts or bets randomly is certain to lose in the end.

It's a simple enough truth, although some academics have felt the need to produce formulae that run to several pages to demonstrate that if you lose more bets than you win, then you must also lose more money than you win.

And if it is inevitable that losses must always exceed wins, the question that has to be answered is, What's the point of playing?

The lure of gambling of course is that it is possible to win in the short term, if you get lucky either by winning more often than you lose, or by accidentally timing your bets in such a way that the combined value of your fewer wins exceeds the combined value of your more numerous losses.

The problem for must gamblers is that the more they win, the more likely they are to keep playing. And the more they play, the more likely they are to lose. If you're a blackjack player (and a fan of satirical novels) you could call this dilemma a Catch 21!

Much has been written down the centuries about what's known as the "gambler's fallacy" or the idea that after an unusually high ratio of losses to wins (a ratio that exceeds the known negative expectation for the game at hand), a win is more likely.

It's not, of course. In a game with a 2.0% house edge, your odds of winning are 49-51, or a tad less than 50-50, every time you make a bet. So a betting strategy that depends on a win being "more likely" at any point in the game is doomed to failure.

Target betting dramatically boosts the next bet (NB) value in response to a mid-series win not because a second consecutive win is "more likely" than a loss, but because if fortune should smile in spite of negative expectation, all prior losses for the series (LTD) will be recovered, plus a small profit.

(If you are new to this method, a series begins with an opening minimum bet, and ends when turnaround or end of series aka EOS has been achieved. If a series opens with one or more successive wins, it continues until a loss, and the value of that loss becomes the LTD, with the NB value = LTD+T. If the streak-ending loss is immediately followed by a win, the series ends and the bet reverts to the opening minimum. If not, it continues per the strategy rules until EOS is achieved).

Mythematicians love to heap scorn on the Small Martingale or double-up betting method, which opens with a 1-unit bet and risks -1, -2, -4, -8, -16 and so on until a win finally comes along, recovering all prior losses with a single successful wager and delivering an overall profit of 1 unit.

The method is derided as suicidal because of the fact that repeated doubling is certain eventually to bump up against the table limit, and if the required x2 bet can't be made, an overall loss is inevitable.

That would be true if a double-up bettor was too dumb to move to a layout with a higher table limit before he got into serious trouble, and in theory, it might be possible for so many successive losses to occur that a $5 bet grows to exceed even the most generous house limit in Las Vegas ($25,000 is about average on "The Strip" these days, and high rollers can add several zeroes to that amount with special dispensation).

It's possible, but not likely. And gambling is all about what's likely, or probable, with blind luck ruled an irrelevance.

Interestingly, there is not a casino I have ever heard of that will permit x2 betting for long. Why? Because it is much more likely to succeed than to fail. And gamblers can never be permitted to win for long.

"Martingalers" can be seen in action in any busy casino if you know what to look for. The guy who muscles into a blackjack game, places two or three consecutive losing bets and then moves on is an x2 bettor in search of a single win. Blackjack is the perfect game for him, because a natural or a successful double/split will greatly boost his bottom line, giving him a final win exceeding his target 1u.

So, target betting is progressive betting, and progressive betting is certain suicide, right? Wrong.

In the current target betting trial, the TA/T strategy is ahead $184,000 or 5.6% of total action against a house edge of 4.6% indicating a mythematically expected loss of $149,000. A Martingale would be $37,000 (10.5%) ahead against the same outcomes. Average bet values and overall risk or exposure are both much lower for x2 betting, but it doesn't much matter because casinos do all they can to block the use of a Martingale.

My target betting method needs two successive wins to achieve turnaround/EOS/recovery, which is twice as tough to come by as a single win. But if you take a typical game session such as this one...


(Click on the image to enlarge it)

...and then highlight the paired (or better) wins, it is easy to see why my method is very tough for the house to beat. You will win more often with a Martingale, with less risk. But since the bad guys won't let you play it, why not win with a method that they have not yet figured out?



There can be some scary gaps between paired wins from time to time, it's true, but they become less of a threat to your bankroll the longer you play, as long as you take my advice and add at least half of each session's profits to your war chest.

Fact is, it is not the house edge that blows most gamblers out of the game: it's their pathetically inadequate bankrolls, coupled with the fact that they consistently fail to fully exploit winning streaks.

You WILL lose more bets than you win, in the long run. So you have to bet opportunistically (and optimistically!) in response to a potential winning streak, knowing that every positive trend has to start with a single win, but not knowing for sure that that win will be immediately followed by another.

I once had a gambling aunt who would tell me: "Luck won't find you, you have to step out in front of it." And that is what target betting is all about. (Auntie Betty once owned a nightclub in London's Soho, and was a died-in-the-wool gambler until the day she fell off her perch; when she won, she gave most of the money away; when she lost, she kept on cranking until the next big hit came along).

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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