The Odds of a Pot
POT ODDS
Pot odds are the odds the pot is giving you for calling a bet. If there is $50
in the pot and the final bet was $10, you are getting 5-to-1 odds for your
call. It is essential to know pot odds to figure out expectation. In the
example just given, if you figure your chances of winning are better than
5-to-1, then it is correct to call. If you think your chances are worse than
5-to-1, you should fold.
Calling on the Basis of Pot Odds When All the Cards are Out
When all the cards are out, you must decide whether your hand is worth a call,
and that depends upon the odds you are getting from the pot and what you think
of your chances of having the best hand. It is a judgment problem more than a
math problem because there is no way to calculate your chances of winning
precisely. If you can beat only a bluff, you have to evaluate the chances that
your opponent is bluffing. When you have a decent hand, you must evaluate the
chances that your opponent is betting a worse hand than yours. Making these
evaluations is often not easy, especially when you have a marginal hand like
two pair in seven-card stud. Your ability to do so depends upon your
experience, especially your ability to read hands and players. Some things can
be learned only through trials by fire at the poker table.
Calling on the Basis of Pot Odds with More Cards to Come
What about deciding whether to call before the draw in draw poker and in stud
games when there is one card to come? Now the math becomes important. If you
know you have to improve your hand to win, you have to determine your chances
of improving in comparison to your pot odds. With a flush draw or an open-ended
straight draw-we'll assume the games is five-card draw poker you would be
correct to call a $10 bet when the pot is $50 since your chance of making the
flush or the straight is better than 5-to1. Specifically, the odds of making
the flush are 4.22-to-1 against and the odds of making the straight, 4.88-to-1
against.
Figuring the odds for making a hand is done on the basis of the number of
unseen cards and the number among them that will make the hand. In five-card
draw there are 47 unseen cards- the 52 in the deck minus the five cards in your
hand. If you are holding four of a suit, nine of the 47 unseen cards will give
you a flush and 38 won't. Thus, the odds against making the flush are 38-to-9,
which reduces to 4.22-to-1. If you are holding, say any 6, 7, jack, or queen
makes the straight, reducing the odds to exactly 2-to-1 against. Sixteen cards
make the hand, and 32 don't. The smaller the pot odds vis-a-vis the chances of
making your hand, the more reason you have to fold. With only $30 in the pot
instead of $50, calling a $10 bet for a flush draw or a straight draw (assuming
you do not have a joker in your hand) becomes incorrect- that is, it becomes a
wager with negative expectation - unless the implied odds are very large, as
they might be in a no-limit or pot-limit games.
It is because of the pot odds that people say you need at least three other
players in the pot to make it worth paying to draw to a flush in draw poker.
With the antes in there, the pot odds are about 4-to-1, and when the bug is
used, your chances of making the flush are 3.8-to-1. Notice, incidentally the
effect of the antes, the higher they are, the better the pot odds, and the
easier it is to call with a flush draw. On the other hand, with no ante and
three other players in the pot, you'd be getting only 3-to-1 if you called a
bet before the draw, and so you'd have to fold a four-flush then eight of the
47 unseen cards will make the straight --- four 8s and four kings -while 39 of
the cards won't help, which reduces to 4.88-to-l.
When a joker or bug is used, as in public card rooms in California, you have an additional card to
use to make flushes and straights, which improves the chances of making the
flush to 3.8-to-1 and of making the straight to 4.33-to-1. With a joker in your
hand, the chances of making a straight improve dramatically; instead of having
eight or nine cards to help your hand, you might have 12 or even 16. For
example, if you are holding.
More Categories:
The Mathematics of Poker 
