Chances Are by Michael Kaplan

is simply that the player takes that risk of an overdraw first; as in Russian roulette, there is value in being second.
    The basic strategy in blackjack describes when you should “stand,” hoping the dealer either fails to match your total or goes bust; and when you should ask to be “hit” with another card. Here, the player has choice where the dealer must obey mechanical rules. So experienced players ask to be hit on a hand of 12 to 16 when the dealer’s first card is high, and they stand when it’s low. They double their bet (where allowed) on a hand of 10 when the dealer shows less than 9—and so on. There is a big, publicly available matrix of standard decisions in blackjack that help reduce the house advantage to an acceptable minimum.
    How, though, can the player reverse that advantage? By taking account of the one variable in the game that changes over time: the number of cards left in the shoe. Decks, when shuffled, are supposed to be random—but, as we saw in roulette, randomness can be lumpy. An astute observer, watching and keeping track of the cards as they come out of the shoe, can judge whether a disproportionately high or low number of top-value cards (10s and face cards) remain in the shoe. At this point, the player can modify the basic strategy to accommodate the unbalanced deck; the dealer, confined by house rules, cannot. After many deals, as the end of the shoe approaches, the careful card-counter has a brief moment of potential superiority, which, if supported by robust wagering, may lead on to moderate riches.
    An engineering professor, Ed Thorp, developed a computer program to recommend strategies based on the running count of cards; having applied its results successfully, he was banned from all casinos. The owners, recognizing the threat to the one immutable law of gambling—probability favors the house—reacted predictably. One-pack shoes were quickly replaced by two, four, or eight-pack shoes, so players would have to sit for hours, keeping track of more than three hundred cards, before their advantage kicked in. Nonetheless, if he were really willing to memorize several charts of modified strategy, mentally record a whole evening’s play, and give no indication to sharp-eyed pit bosses that this was what he was doing, a card-counter can still seize the edge for a deal or two—but anyone so skillful could make a better living elsewhere.
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    As an optimist, you would say that life has no house edge. In our real battles with fate, an even-money chance really is even. That may be so, but probability theory reveals that there is more to a bet than just the odds.
    Let’s imagine some Buddhists opened a casino. Unwilling to take unfair advantage of anyone, the management offers a game at completely fair odds: flip a coin against the bank and win a dollar on heads, lose a dollar on tails. What will happen over time? Will the game go on forever or will one player eventually clean out the other?
    One way to visualize this is to imagine the desperate moment when the gambler is down to his last dollar. Would you agree that his chance of avoiding ruin is exceedingly small? Now increase the amount you imagine in his pocket and correspondingly reduce the bank’s capital; at what point do you think the gambler’s chance of being ruined equals the bank’s? Yes: when their capital is equal. Strict calculation confirms two grim facts: the game will necessarily end with the ruin of one party—and that party will be the one who started with the smaller capital. So even when life is fair, it isn’t. Your chances in this world are proportional to the depth of your pockets—the house wins by virtue of being the house.
    This explains why the people who appear most at home in the better casinos look so sleek, so well groomed, so . . . rich. They have lasted longest there, because they arrived with the biggest float. They alone have the secret