Introduction 
PROBABILITIESProbabilities are expressed by a number 0 (impossibility) to 1 (certainty), thus when tossing a true coin the probability of it falling a head or a tail is 0.5 heads and 0.5 tails. So if a gambler were asked to stake 10 chips on his choice, and to receive 20 if correct, the game would be fair. The payout is 20; the probability is 0.5, so the expectation is 20 X 0.5, which equals 10. As 10 is the stake, the poker game is a perfectly fair one. For a slightly more complex example imagine a pack of cards stripped of the picture cards, so that the pack contains Aces to 10s only. The gambler is asked to cut the shuffled pack, and whatever card is turned up he will be paid that number of chips, i.e. one chip for an Ace up to ten chips for a 10. What should he pay for each turn? The question is worked out as follows.
The total return is 220 poker chips. If he receives 220 chips over 40 trials, for it to be a fair game he should pay 220 divided by 405.5 chips per try. If he pays five chips per try, over the long run he wins; if he pays six, he loses. * Always work our your expectation Do not bet unless the odds being paid to you are greater than the odds against making the hand. Suppose you hold two pairs, and think you will win if you can improve to a full house. Table 9 shows the odds against this are 10.8 to 1, i.e. there are almost 11 chances of failure to one of success. Your chance of success is one in 12. If the pot is 60 chips, your expectation is 60 x 1/12: 5. If it costs you five chips or fewer to call, it is worth betting, if it costs you six chips or more, it is less worth it. Looked at another way, if the odds against winning poker the pot are 11 to 1, and it costs you five chips to call, the pot should be worth at least 55 chips for you to bet. 

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