Thursday, May 15, 2008

Calculating Outs

The first step to learning poker math is to learn how to calculate “outs”.
“Outs” are the cards in the deck that can give you a winning hand. They refer to the
cards that can hit the board. The more outs you have, the better. The more outs you
have, the stronger your hand.
For example… let’s say you’re holding:


The flop comes out:


How many outs do you have?
Well, a ten will give you the nut straight… and presumably the best hand. If either a King
or Ace hit the board, you’ll have top pair. So those cards can be considered outs as well.
The answer is 3 Aces +3 Kings + 4 Tens (straight draw) =10 Outs.
Now the turn comes and the board looks like this:


NOW how many outs do you have?
Well, now you’re just one spade away from a flush. So you’re number of outs just
INCREASED.
The answer is 3 Aces + 3 Kings + 4 Tens + 9 Spades (flush draw) – 1 Ten of Spades = 18
Outs.
Notice that the ten of spades was SUBTRACTED at the end of our calculation. Why? The
reason is because we already counted it with the four tens in the deck that would give us
the straight.
When calculating odds, never count the same card twice.
OK, so what if someone was holding a Jack and a Queen and had two pair. How would
that change things? Well, getting top pair would no longer give you the best hand…
which means the three Kings and three Aces in the deck are no longer outs.
This is important.
Outs are ONLY cards that will give you the winning hand.
The question becomes… how do I really KNOW what the winning hand will be?
And the answer is you don’t.
This is one of the primary limitations of poker odds and calculations… but it’s also good
because it maintains the unpredictable nature of the game and paves the way for other
strategies-- like tells and psychology.
In our example above, if someone bet heavily after both the flop and turn, you might put
them on a hand like two pair or three-of-a-kind. In that case, you would only calculate
the four tens, the nine spades, and then subtract the ten of spades in order to figure your
outs (the answer is twelve).
Obviously, you’ve got a fantastic hand since you’re on BOTH the nut straight draw AND
the nut flush draw. This is a rare occurrence, of course.
OK, let’s do another example. Say you’ve got pocket deuces and limp in before the flop.


You’ve hit your trips. But there are a lot of draws on the board for your opponents.
There’s a flush draw, straight draw, and possible straight-flush draw. All of these hands
BEAT yours.
Everyone checks to you. You lead out with a medium bet and get two callers. If someone
already made their flush or straight they would probably raise… so you’re putting both
opponents on draws.
A flush draw at this point has nine outs and a 35% chance of completing. A straight draw
has six outs if the player is holding a five… and only three outs if he’s holding the Ace.
Remember… a normal open-ended straight draw would have EIGHT outs instead of six.
But we must “discount” the Ace of diamonds and five of diamonds, since those would
complete the flush draws. (And the flush beats the straight.)
So… all in all there are fifteen cards in the deck that can beat you if one of your
opponents is on the open-ended straight draw and one is on the flush draw. There’s a
54% chance that one of these hands will hit the board and complete the hand. (We’ll go
over how I know these percentages a little later.)
BUT… even if one of these hands hit, you still have outs. There’s another two in the deck,
which would give you a four-of-a-kind. Or the board could pair up, which would give you
a full house. Both of these hands would beat a flush or a straight.
All things considered, this is a dangerous hand that can lead to someone losing all their
chips. You must be careful, because you can’t “expect” your trips to hold up. Especially
since someone might have already made their flush or straight.
But at the same time, if you hit quads or a full house, and one of your opponents makes
his hand, you’re going to win a MASSIVE pot. As we’ll discuss later, your “implied odds”
are enormous here.
OK, so that’s how to calculate outs. Remember that you want to calculate outs AFTER
the flop or turn… not when you just know your hole cards. Knowing your outs is the
“prerequisite” to figuring out percentages and knowing pot odds.
Of course, knowing your outs in any given situation will become instant to you in no
time. After a few poker games of consciously thinking about outs, you’ll quickly
remember that there are nine outs for a flush draw, eight outs for an open-ended
straight draw, four outs from an inside straight draw, and so on.

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