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Let's say you are playing hold 'em,
and after the flop you have a four-flush that you are sure will
win if you hit it. There are two cards to come, which improves your
odds of making the flush to approximately 13/4-to-1. It is a $10-$20
game with $20 in the pot, and your single opponent has bet $10.
You may say, "I'm getting 3-to-1 odds and my chances are 13/4-to-1.
So I should call." However, the 13/4-to-1 odds of making the
flush apply only if you intend to see not just the next card, but
the last card as well, and to see the last card you will probably
have to call not just $10 now but also $20 on the next round of
betting. Therefore, when you decide you're going to see a hand that
needs improvement all the way through to the end, you can't say
you are getting, as in this case, 30-to-10 odds. You have to say,
"Well, if I miss my hand, I lose $10 on this round of betting
and $20 on the next round. In all, I lose $30. If I make my hand,
I will win the $30 in there now plus $20 on the next round for a
total of $50." All of a sudden, instead of 30-to-10, you're
getting only 50-to-30 odds, which reduces to 12/3-to-1.
These are your effective odds - the real odds you are getting from
the pot when you call a bet with more than one card to come. Since
you are getting only 12/3-to- 1 by calling a $10 bet after the flop,
and your chances of making the flush are 13/4-to-1, you would have
to throw away the hand, because it has turned into a losing play
- that is, a play with negative expectations. The only time it would
be correct to play the hand in this situation is if you could count
on your opponent to call a bet at the end, after your flush card
hits. Then your potential $50 win increases to $70, giving you 70-to-30
odds and justifying a ca11.
It should be clear from this example that when you compute odds
on a hand you intend to play to the end, you must think not in terms
of the immediate pot odds but in terms of the total amount you might
lose versus the total amount you might win. You have to ask, "What
do I lose if I miss my hand, and what will I gain if I make it?"
The answer to this question tells you your real or effective odds.
Let's look at an interesting, more complex application of effective
odds. Suppose there is $250 in the pot, you have a back-door flush
draw in hold'em, and an opponent bets $10. With a back-door flush
you need two in a row of a suit. To make things simple, we'll assume
the chances of catching two consecutive of a particular suit are
115 X 115. That's not quite right, but it's close enough? It means
you'll hit a flush once in 25 tries on average, making you a 24-to-
I underdog. By calling your opponent's $10 bet, you would appear
to be getting 26-to-1. So you might say, "OK, I'm getting 26-to-1,
and it's only 24-to-I against me. Therefore, I should call to try
to make my flush."
Your calculations are incorrect because they do not take into account
your effective odds. One out of 25 times you will win the $260 in
there, plus probably another $40 on the last two rounds of betting.
Twenty times you will lose only $10 when your first card does not
hit, and you need not call another bet. But the remaining four times
you will lose a total of $30 each time when your first card hits,
you call your opponent's $20 bet, and your second card does not
hit. Thus, after 25 such hands, you figure to lose $320 ($200 +
$120) while winning $300 for a net loss of $20. Your effective odds
reveal a call on the flop to be a play with negative expectation
and hence incorrect.
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