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introduction
 

"There are three subjects you can count upon a man to lie about: sex, gas mileage, and gambling. " R. A. Rosenbaum
we played our first Online Blackjack Games in January, 1970, at a small club in Yerington, Nevada. Much to the amusement of a local indian and an old cowboy we doubled down on (A,9) and lost. No, it wasn't a knowledgeable card counting play, just a beginner's mistake, for we was still struggling to learn the basic strategy as ill as fathom the ambiguities of the ace in "soft" and "hard" hands. The next day, in Tonopah, we proceeded to top this gaffe by standing with (5,4) against the dealer's six showing; my train of thought here had been satisfaction when we first picked up the hand because we remembered what the basic strategy called for. we must have gotten tired of waiting for the dealer to get around to me at the crowded table since, after the dealer made 17 and turned over my cards, there, much to everyone's surprise, was my pristine total of nine!

At the time, we was preparing to give a course in The Mathematics of Gambling which a group of upper division math majors had petitioned to have offered. it had occurred to me, after agreeing to teach it, that we had utterly no gambling experience at all; whenever travelling through Nevada with friends we had always stayed outside in the casino parking lot to avoid the embarrassment of witnessing their foolishness.

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Coming from Behind Is More Difficult Than You Think
 
If you ignore the extremely unlikely possibilities that you might make three tens or he might make a full house, basically the outcome is very simple: You win if you make a flush, and lose if you don't. The pot currently contains $1,000, and your opponent has bet all his remaining chips, which happen to be $300. Because your opponent is going all-in, there won't be any additional betting. You have to make a one-time decision. You have enough chips to call. Should you call?

You are currently behind. You know that the only way to win is for another spade to come. The odds against this happening are approximately Z-1 (expressed another way, one-in-three). The pot odds are better than that, though: For a $300 call, you can win $1,300 (the $1,000 that was already in the pot plus the $300 your opponent just added to it).
 
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