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Expectation And Hourly RateThe Fundamental Theorem Of PokerThe Ante StructurePot OddsEffective OddsImplied Odds and Reverse Implied OddsThe Value of DeceptionWin the Big Pots Right AwayThe Free CardThe Semi-BluffDefense Against the Semi-BluffRaising
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  Mathematical expectation is the amount a bet will average winning or losing.

  It is an extremely important concept for the gambler because it shows him how to evaluate most gambling   problems.

  Using mathematical expectation is also the best way to analyze mistake most poker plays.

  Let’s say you are betting a friend $1, even money, on the flip of a coin. Each time it comes heads up , you win;   each time it comes up tails, you lose.

  The odds of its coming up heads are 1-to-1, and you’re betting $1-to-$1.

  Therefore, you mathematical expectation is precisely zero since you cannot expect, mathematically, to be either   ahead or behind after two flips or after 200 flips.

  Your hourly rate is also zero. Hourly rate is the amount or money you expect to win per hour.

  You might be able to flip a coin 500 times an hour, but since you are getting neither good nor bad odds, you will   neither earn nor lose money.

  From a serious gambler’s point of view, this betting proposition is not a bad one. It’s just a waste of time.

  But let’s say some imbecile is willing to bet $2 to your $1 on the flip of the coin. Suddenly you have a positive   expectation of 50 cents per bet.

  Why 50 cents? On the average you will win one bet for every bet you lose.

  You wager your first dollar and lose $1; you wager your second and win $2.

  You have wagered $1 twice, and you are $1 ahead. Each of these $1 bets has earned 50 cents.

  If you can manage 500 flips of the coin per hour, your hourly rate is now $250, because on average you will lose one   dollar 250 playing a hand one way and your expectation playing it another way.

  Whichever play gives you a higher positive expectation or a lower negative expectation is the right one.

  For example, when you have a 16 against the dealer’s 10, you’re a favorite to lose.

  However, when that 16 is 8, 8, your best poker play is to split the 8s, doubling your bet.

  By splitting the 8s against the dealer’s 10, you still stand to lose more money than you win, but you have a lower   negative expectation than if you simply hit every time you had an 8, 8 against a 10.