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EXAMPLES
OF THE FUNDAMENTAL THEOREM OF POKER
Example 1
Suppose your hand is not as good as your opponent's when you bet.
Your opponent calls your bet, and you lose. But in fact you have
not lost; you have gained! Why? Because obviously your opponent's
correct play, if he knew what you had, would be to raise. Therefore,
you have gained when he doesn't raise, and if he folds, you have
gained a tremendous amount.
This example may also seem too obvious for serious discussion,
but it is a general statement of some fairly sophisticated plays.
Let's say in no-limit hold 'em you hold the and your opponent holds
an offsuit
You check, your opponent bets, and you call. Now the ace of diamonds
comes on fourth street, and you bet, trying to represent aces.
If your opponent knew what you had, his correct play would be to
raise you so much it would cost too much to draw to a flush or
a straight on the last card, and you would have to fold. Therefore,
if your opponent only calls, you have gained. You have gained not
just because you are getting a relatively cheap final card but
because your opponent did not make the correct play. Obviously
if your opponent folds, you have gained tremendously since he has
thrown away the best hand.
Example 2
Suppose there is $80 in the pot, and you have two pair. You are
playing draw poker, and you bet $10, which we will assume is all
you can bet. Your single opponent has a four flush - that is, four
cards to a flush. The question is - are you rooting for him to
call or fold? Naturally you want him to do what is most profitable
for you. The Fundamental Theorem of Poker states that what is most
profitable for you is for your opponent to make the incorrect play
based on complete information about both hands. Since your opponent
is getting 9-to-1 odds (his $10 call might win him $90) and is
only about a 5-to-1 underdog to make a flush, it is correct for
him to call because a call has positive expectation. Since it is
correct for him to call, following the Fundamental Theorem, you
are therefore rooting for him to fold.
This sort of situation comes up frequently. You have the best hand,
but your opponent is getting odds good enough to make it correct
to call if he knew what you had. Therefore, you want your opponent
to fold. By the same token, it is correct for you to chase when
you are getting sufficient pot odds. If you don't chase, you are
costing yourself money and, therefore, making money for your opponent.
Example 3
Since it is correct for your opponent to call when he is getting
sufficient pot odds, you can sometimes make an opponent fold incorrectly
by showing more strength than you actually have on an early betting
round.
You are fairly sure he has kings. You now proceed to make a pair
of 6s on board, and you bet. Your opponent will almost certainly
fold a pair of kings since he is afraid you have made aces up.
Some people might say, "Well, wait a second. Why don't You
want your opponent to call as long as his pair of kings is worse
than your two small pair?" The answer is that if there are
cards to come and your opponent is getting proper odds, you do
better to win the pot right there. A pair of kings versus two smaller
pair needs very short odds to justify a call. Since your opponent
would have been correct to call, you gain when you make him fold.
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