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.
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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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More about Ken Smith's nifty skill-building app, the Blackjack Strategy Trainer.

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One of the pitfalls of blackjack is that a player can make decisions that are so bad that he helps the house get its hands on his bankroll a little sooner. In most table games, when to bet on what and how much are the player's only choices, and that is more than enough pressure, thank you very much.

Something else that is unique about blackjack is that almost everyone who plays it thinks he or she is an expert, and feels qualified to tell other people what to do with their money.

My preference is to play one-on-one against the dealer whenever possible, or else to ignore what other players are doing and concentrate on the job at hand, which is to win a little money while attracting as little attention as possible.

In the end, while making smart hit or stand decisions is helpful, it all comes down to how you bet, not how you play.

And it isn't the piddling house edge (barely 1.0%) that will do you in at blackjack, it's having a bankroll that is too small to take you through occasional house spikes (prolonged negative trends) that may be offset by an opposite pattern too late to save your ass.

A good rule of thumb is never to bet less than 20% of your current loss to date (LTD), but that's a move that can be discussed at another time.

What I want to say here is that practice makes perfect, and in my opinion there's no more perfect way to practice online than with Ken Smith's Blackjack Strategy Trainer.

Eccentric as I am, I generally choose to play against a shoe rather than the single deck that the self-styled experts prefer. I like the streaks that can set in with a shoe and last for a dozen or more rounds (less likely with a single deck and all that shuffling!).

Lately, single-deck layouts in Nevada have tended to drop the natural pay-out rate from 3-2 to 6-5, an outrageous gouge that offends me to the roots of what little hair I have left (a 60% pay cut, aggghhhhh!) so I am even more likely to pick a shoe.


(Click on the image to enlarge it)

If your online connection is up to it, a useful way to imitate the multi-table environment of a casino is to load BST in several tabs and switch your LTD/NB numbers from one to the other as win-loss patterns dictate.

I turn off insurance (of course) in the BST options, and also the on-screen "coach" because there are several recommendations that I flat-out disagree with.

It is not necessary to play through each series from an opening minimum bet to EOS over and over again, as I do, because all the recorded outcomes will be plugged in to a spreadsheet eventually and the correct target bets will be processed there. All you really need is the outcomes in a chronological log.

My choice happens to be to bet as if the money was real, partly because I enjoy the practice, but also because there's a lot of satisfaction in repeatedly seeing a crappy set of outcomes being turned into a notional profit!

I would certainly welcome scanned pencil logs from anyone who cares to submit them! Mine look like this:


(Click on the image to enlarge it)

I may not be neat, but I get it all written down! Pushes matter because I double the bet, adding up to $100, after a push, not because I think I have a better chance of winning (of course I don't) but for the fun of it.

Xs with a ring around them indicate a dealer natural, which also prompts a doubled bet, and I even bump the bet after a dealer 21 with 3+ cards, using the push rule (NB=PBx2 to a max of PB+$100).

A line under an outcome signifies EOS. And a quick glance at any log confirms the clumping or streaking patterns that make target betting so effective.

Remember that the LTD+ bet in response to a mid-series win is the key to target betting's consistent success, and while quirky bumps push bet values higher, they also fatten the bottom line.

You can make the bet-by-bet strategy as simple or as complicated as you want, either just for the fun of it or to confound anyone who's watching too closely, just as long as you don't mess with the LTD+ "engine" at the heart of it all.

One thing to watch out for with the BST app is an annoying little flaw that doesn't mess you up often but is infuriating when it does. If when the screen prompt offers you the option to add another $1,000 to your depleted bankroll, you click ever so slightly to the right of the $ button, you will accidentally quit the session instead, wiping out all of the stats. It's too easy to do, if you have left your cursor where it was when you last opted to stand, and you click before moving it to the "money button". The glitch needs a fix, but I am too grateful to Mr. Smith for his neat little game to bug him with a complaint!

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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