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Poker plays can also be analyzed in
terms of expectation. You may think that a particular play is profitable,
but sometimes it may not be the best play because an alternative
play is more profitable. Let's say you have a full house in five-card
draw. A player ahead of you bets. You know that if you raise, that
player will call. So raising appears to be the best play. However,
when you raise, the two players behind you will surely fold. On
the other hand, if you call the first bettor, you feel fairly confident
that the two players behind you will also call. By raising, you
gain one unit, but by only calling you gain two. Therefore, calling
has the higher positive expectation and is the better play.
Here is a similar but slightly more complicated situation. On the
last card in a seven-card stud hand, you make a flush. The player
ahead of you, whom you read to have two pair, bets, and there is
a player behind you still in the hand, whom you know you have beat.
If you raise, the player behind you will fold. Furthermore, the
initial bettor will probably also fold if he in fact does have only
two pair; but if he made a full house, he will reraise. In this
instance, then, raising not only gives you no positive expectation,
but it's actually a play with negative expectation. For if the initial
bettor has a full house and reraise, the play costs you two units
if you call his reraise and one unit if you fold.
Taking this example a step further: If you do not make the flush
on the last card and the player ahead of you bets, you might raise
against certain opponents! Following the logic of the situation
when you did make the flush, the player behind you will fold, and
if the initial bettor has only two pair, he too may fold. Whether
the play has positive expectation (or less negative expectation
than folding) depends upon the odds you are getting for your money
- that is, the size of the pot - and your estimate of the chances
that the initial bettor does not have a full house and will throw
away two pair. Making the latter estimate requires, of course, the
ability to read hands and to read players, which I discuss in later
pages. At this level, expectation becomes much more complicated
than it was when you were just flipping a coin.
Mathematical expectation can also show that one poker play is less
unprofitable than another. If, for instance, you think you will
average losing 75 cents, including the ante, by playing a hand,
you should play on because that is better than folding if the ante
is a dollar.
Another important reason to understand expectation is that it gives
you a sense of equanimity toward winning or losing a bet: When you
make a good bet or a good fold, you will know that you have earned
or saved a specific amount which a lesser player would not have
earned or saved. It is much harder to make that fold if you are
upset because your hand was outdrawn. However, the money you save
by folding instead of calling adds to your winnings for the night
or for the month. I actually derive pleasure from making a good
fold even though I have lost the pot.
Just remember that if the hands were reversed, your opponent would
call you, and as we shall see when we discuss the Fundamental Theorem
of Poker in the next page, this is one of your edges. You should
be happy when it occurs. You should even derive satisfaction from
a losing session when you know that other players would have lost
much more with your cards
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