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There is no need to factor in changes to your BS playing advantage every time you go from one casino to another. Minor variations will not affect the calculation of your bet size enough to worry about. The main consideration used by counters to determine their advantage at any given point in the game is the true count (TC), as explained in chapter 6. Professor Peter Griffin has calculated that a player’s advantage is the BS gain (as shown above) plus approximately half the TC. Therefore, playing in a casino with rules that provide you an even game, your advantage in percent is always roughly half the TC.
Applying the Kelly Criterion, you can easily determine any proper bet size by multiplying your advantage in percent (i.e., half the TC) times your bankroll. If your bankroll is $1,000 and the TC is +2, then your ideal wager should be $10. Unfortunately, this bet-sizing guide is only recommended for conservative players when the TC is +4 or less, since other factors should also be taken into consideration before deciding upon the amount of your wager. The 2% Rule is one; it is explained in chapter 5.
The smaller the portion of your bankroll that you bet when you have an advantage, the more likely you will end up doubling it instead of losing it. (Many players decide to end sessions once they double their playing stakes; this acts as a signal that they have accomplished a short-term goal.) Various mathematicians have proven that betting a maximum of only 1% of a players total bankroll even when he has as little as a 2% advantage, results in doubling the bankroll over 9S% of the time! (See Richard Epstein’s The Theory of Gambling and Statistical Logic.) With less than 1% advantage, you will double your hundred-unit bankroll almost five out of every six sessions, betting only one unit per hand. Epstein coined the phrase “minimum boldness” to describe this approach. If this seems hard to believe, consider the following:
Suppose your bankroll totals $1,000 and your game plan is to play until you double it (or lose it all). You decide to bet only when you have a 2% advantage over the house, i.e., when the TC = +4. If you plunk it all down on one hand, your chances of winning (and therefore doubling your bankroll) are only 51%, since the casino will win with these odds 49% of the time. Only two times out of a hundred will you achieve your objective with this bold gesture.
However, if you continually wager only $10 on each hand (i.e., 1% of your bankroll) with this same advantage, you will end up doubling your bankroll over 98% of the time. In other words, for every hundred such sessions, you would lose your entire bankroll (i.e., suffer “gambler’s ruin” as described below) only twice. If you divide your bankroll or playing stake into fifty betting units, i.e., $20 a hand/your chances of doubling it falls to slightly over 88%. This is still a good win-rate resulting from the maximum percentage (2%) of one’s bankroll that is recommended to be wagered on any one hand, no matter what figure the Kelly Criterion might suggest. (This is the 2% Rule; see chapter 5 for more details.) Although not nearly as exciting, placing the smallest possible bets you are allowed to make (i.e., table minimums) when you have any sort of odds advantage gives you the greatest possible chance of doubling your money while never really risking anything.
More aggressive players choose to follow the Kelly Criterion by regularly making wagers greater than 2% of their bankroll as the TC rises, but they risk ruin far more often. For example, by betting up to 10% of their bankrolls with the same 2% advantage, their chances of doubling them drop to 60%. There are some high-rolling VIPs who habitually bet large sums with apparently no regard to the Kelly Criterion whatsoever. For example, in 1995, Keny Packer, Australia’s richest man, effortlessly won $20 million on a forty-minute blackjack spree in Las Vegas. It should be remembered that, unless he was a skilled counter and was ranging his bets according to the TC, Packer could have lost that amount of money in the same length of time just as easily.
This is precisely the mathematical principle upon which casinos thrive. By letting a small edge grind away at millions of wagers over the years, overwhelming successes are virtually guaranteed. How else could a game like craps, with an advantage of only 1.4%, be such a big moneymaker for the house? As any businessperson can attest, the answer is volume; it is much better to have a small percentage of a lot of money than a large percentage of a little.