Mathematical Expectation

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 most online poker games plays.

Let's say you are betting a friend \$1, even money, on the flip of a coin. Each time it comes up heads, you Win; each time it comes up tails, you lose. The odds of its coming up heads are 1to-1, and you're betting \$1-to-\$1. Therefore, your 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 of 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.
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When He Might Be Semi-Bluffing

Many players will wait until the betsize doubles on the river to raise with a strong hand. Also, many players will semibluff if they pick up a flush draw on the turn.

A semibluff is what used to be called raising with outs. It's a certain kind of raise that's made before the last round of betting, when there are more cards to come, and there is some chance that the raise will win the pot right there. Its a semi-bluff rather than just a bluff if you also have some fallback, some chance you'll end up winning the showdown anyway. Raising with a flush draw is an example of a semi-bluff. Basically, the idea is that you might win the pot right now, but if you don't, all is not lost because you might still improve to the best hand.

If the board looks like there is a chance your opponent has a draw (such as having two hearts on the board) then you need to always consider the possibility that your opponent is semi-bluffing when he raises before the last betting round.

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