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Basil Nestor is author of "The Smarter Bet Guide to Craps," "The Smarter Bet Guide to Blackjack," and other comprehensive gambling guides. Got a question? Visit and drop him a line.

Let's say you have a net loss during a session. Does that mean there is a leak in your game, or is it just bad luck? Let's say losses happen three consecutive times. Or maybe it's a three-session positive streak. Is that due to luck or skill? How far does a trend have to go before you can determine the effect you have in creating that trend?

Note that these questions seem obvious. They begin with the premise that you should be able to evaluate the quality of your play by the results you achieve. After all, blackjack isnít slots, right? The whole point of blackjack is that you control the contest to some degree.

ButÖ brace yourselfÖ The Zen-like truth is that the degree of your control may be quite small, and the perception that you have any control whatsoever may be entirely due to cognitive bias in many situations.

What?! But you play basic strategy perfectly, and you count cards like youíre a veteran of Ken Ustonís team. No control? Poppycock!

Okay, Iíll prove it, but first letís make the math simple. Letís say bets are $10, and the most you should "theoretically" lose during six hours of perfect play is 1% of your action (the lower limits of basic strategy). Likewise, the most you should theoretically win is 1% (generally, the upper limit of counting). Right away, players who know the game intuitively realize that they often seen results after six hours of play that significantly stretch beyond this "theoretical window."

Hereís the math: Itís 60 hands per hour x 6 hours = 360 hands x $10 = $3,600 of action. And 1% of that is a $36 loss or win. For the sake of argument, letís be generous and say itís plus or minus four bets (i.e., $40). And weíll further say that you get at least three naturals per hour, and also receive all your expected opportunities for doubling and splitting. Keep in mind that a drought in any of these areas will inevitably hammer your bankroll, regardless of how well you play.

So the theoretical window is plus or minus four bets, but the actual probability of falling into that window (as determined by a binomial analysis) is only about 36% or slightly higher than 1 in 3. Indeed, about two-thirds of players will win more or lose more than four bets net. And it gets wilder! About 32% will win or lose net ten or more bets (i.e., $100). And you have about 7% chance of beating the casino for 15 bets (i.e., $150) or more, and nearly the same chance of losing 15 bets.

So the results of "perfect play" after six hours will be hardly uniform.

Now letís stretch our play to 6,000 decisions, or about 100 hours. Your theoretical window of plus/minus 1% works out to $600 win or loss. But you still have about 12% chance of falling outside that window, either winning more or losing more than 60 bets (i.e., $600). Triple it to 18,000 decisions and 300 hours. Your theoretical window is plus/minus $1,800. And finally, the probability of falling outside the window shrinks to slightly less than 1%. But by that point itís a huge window, so falling inside tells you very little about the quality of your play except that youíre not incredibly inept or unlucky.

In other words, you can play blackjack perfectly for thousands of hands and hundreds of hours and still see little apparent correlation between the quality of your play and the results you get.

Should this discourage you? Does this mean you can disregard basic strategy and other proven tactics for winning? Of course not. But it does mean that an optimal strategy is not a magic potion that will automatically make you win. Rather it helps you win more when luck is going your way, and it helps you lose less when the gambling gods punish you. Just try playing without optimal strategies (try doubling on 7 against an ace) and the "window" will turn into a money-sucking vortex. From that standpoint, itís easy to measure the effects of good play. Judging this way, you have plenty of control.

However, once you implement optimal strategies, itís difficult to judge how effective they are based on your results in one session, ten session, or perhaps even fifty sessions, except to say youíre doing way better than using no strategy.

What you can judge is the absolute mistakes you make. Specifically, if you double down incorrectly, and you lose, then thatís an absolutely measurable loss. Ditto if you play a game that pays 6:5 naturals and you win $60 for a snapper. It would have been $75 at a 3:2 table. Thatís a measurable loss.

All the rest is cognitive bias, which is an interesting yet troublesome phenomenon for players. Essentially, itís glitch in the human brain that causes people to perceive many things such as trends, connections, and proofs that actually donít exist. There are many different types of cognitive bias, but the ones operating here are an illusion of control, confirmation bias, and self-serving bias. Iíll cover them in depth in another article. Right now, Iíll just say that the human brain makes you want to believe that your session win is a result of good play, and your loss is probably a result of bad play, when the actual evidence is that it was all probably luck, unless you can absolutely determine a particular mistake you made in implementing strategy.

Itís not an excuse to play sloppy, but it is a reason to worry less and concentrate more on playing well regardless of the short-term results.

Play your best strategy, and donít be discouraged when your bankroll takes a hit. Winning and losing is part of the contest.


© copyright 2012 Basil Nestor

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