Connecting Pot Odds to Hand Odds

by Scott Paterson

How should you proceed when you know
you don’t have the best hand, but you have
a decent chance to make the best hand and
take down the pot?

You should connect the pot odds to your
hand odds to see if your pursuit of the best hand
will be profitable in the long run.

How do you do this?

Count the number of outs that you feel will give you
the best hand. Convert your outs to odds against.
Compare the pot odds to your hand odds
(the general rule is that your pot odds should be greater
than the odds against you making the winning hand).

Example

You possess the K 10 of spades.
The flop comes A of spades, 4 of hearts and 8 of spades.
You’ve flopped a four flush and have a draw to the nut flush.
From the preflop action you’ve deduced that your opponent
possesses a big A, or a medium pocket pair. He probably
has top pair with a good kicker, but he may also have a
set (888). In either case you are likely going to need the
nut flush to beat him (if he has top pair with a big kicker
you’ll need runners to beat him and even then you might
not because one of your runners could easily give him
a bigger two pair).

How likely is it that you’ll get your flush on the turn?
You have two cards in your hand, and there are three
on the board. That means that there are 47 unseen
cards left. You have two spades in your hand, and there
are two on the board. That means there are 9 spades left.
Among the 47 unseen cards 36 will not help you and 9 will.
The odds against you completing your flush on the turn
are 36:9 or 4:1.

Now we need to compare the odds against you making
your hand to what the pot is paying you to make the call.
The pot was at 400 chips just prior to the flop,
and after the flop your opponent bet 100 chips.
The pot now stands at 500 chips, and it will cost you
100 chips to call. The pot is paying you 5:1 on your call.

Now we can compare the pot odds to your hand odds.
Your pot odds (5:1) are greater than the odds against
you making your flush (4:1). This means that it will be
profitable in the long run to call your opponents bet.

Why is it profitable?

Your hand odds are 4:1, and the pot odds are 5:1.
If you pursue the flush 5 times, you will miss it 4 times
and hit it 1. The 4 times you miss will cost you a total
of 400 chips. The 1 time you hit will win you 500 chips,
plus you’ll get your 100 chip call back.

Note:
Outs are routinely calculated using unseen
cards because you’ll have no idea what other
people have folded.