Poker tutorial1.4 pot odds and counting outs

In tutorial 1 to 1.3 there was plenty of information about starting hands before the flop. In this tutorial we will learn how to calculate outs and pot odds, to determine the postflop winning chances.

Pot odds

Lets say the pot is 100 and you have to call 50. In that case you have 2 to 1 pot odds.

The concept of pot odds is important, because it makes it possible for players to stay in the hand, even if their winning chances are lower then 50%. As long as they get good pot odds they can stay in the hand. With those 2 to 1 pot odds given in point one you can stay in the hand with just 1/3, or 33% chance of winning or better. The 33% is the break even point between losing and winning money by calling these pot odds.

Estimating odds by counting outs

Most flops miss most hands. If you have AK the chances of flopping an ace or a king, or a two pair is only 1-(44/50)*(43/49)*(42/48)=0,32, or 32% the rest of the time you will have nothing but a small chance of drawing the ace or the king on the turn or the river. There are 3 aces and 3 kings left in the deck, these make up for a total of 6 “outs“.

The 4 and 2,2% rule gives a way to quickly estimate your chances of improving your hand. When you are still waiting for the turn and river cards to come you estimate your chances of improving by multiplying  your amount of outs by 4%. For instance in the case of AK you had 6 outs, which gives you a chance of: 6*4= 24% of improving (turn and river combined).

If you have only the last card to go, you calculate the percentage by multiplying the amount of outs by 2.2%. In the case of AK that gives you 6*2,2=13,2% chance of improving to a high pair.

Death cards

Do note that outs aren’t exactly the same as the winning cards that could come. It is always possible that an out is a death card. For instance your opponent is having a chance of getting a flush. In such case one or two of your outs may be improving your opponent to a flush while it gives you only a pair.

Lets say you have AKs and you flop two of your suit. In that case you have 13-4=9 outs that improve you to a flush. Multiplying by 4 gives you a 36% chance of getting the flush.

In the case of a straightdraw things are a bit more complicated. Lets say you have:

89TJ

In this case a 7 or a Q improves your hand to a straight. There are 4 sevens and 4 queens, for a total of 8 outs. Which gives you 8*4=32% chance to improve to a straight on the turn or the river/

There is also the possibility of having an inside straightdraw:

89 JQ

In such case you need a ten and you have 4 outs, giving you 16% chance of hitting it on either the turn or the river.

There are also more complicated situations. For instance you have 6 cards that can give you a high pair and you have a flush draw. In such case you can add the 6 and 9 together for 15 outs total.

But lets say you have both a flushdraw and an up and down straightdraw. In such case the 8 cards that give you a straight have 2 cards that make you the flush. So in that case you only have 8+9-2=15 outs.

Outs with a set on the flop

Lets say you have the following:  88  and the flop comes:

8h3hTh

you hit your set, however your opponent has a flush, how many outs do you have now?

Well you improve to four of a kind if the last 8 hits and you improve to a full house with any 3 or any T, to pair the board, for a total of 1+3+3=7 outs on the turn and on the river you have one extra card to pair the board, which gives you 3 extra outs, for a total of 10. In such case you get: 7*4+3*2,2=28+6,6=34,6% chance of hitting the full house or a four of a kind.

In the rare situation that you have more then 16 outs, you should multiply them by 3,5% instead of 4 with 2 more cards to come.

Hidden outs

There are also hidden outs that you may not be aware of. For instance:

You have AA.

Your opponent has 56.

the flop gives:

56T

your opponent has two pair now, but if a T hits, you will improve to a higher two pair: aces and tens, while your opponent will only have sixes and tens. So on the turn you have 3 extra outs and on the river even 6 outs, because the turncard could also make you a pair on the river. In this case the hidden outs give you 3*4+3*2,2=12+6,6=18,6% extra chance of winning, besides the 2 outs (or 8%) you allready had for hitting a set..

To summarize:

pot odds calculating

When you have to make a decision on the flop or turn, you count the amount of outs. Multiply it with 4 or 2,2% to get the chance and calculate the pot odds you need to call:

1:1     =>   50%+

1,5:1  =>   40%+

2: 1     =>  33%+

2,5:1   =>  28,5%

3:1      =>  25%+

4:1      =>  20%+

5:1      =>  16,6%+

Implied odds

It isn’t always necessary to have pot odds to make the call. In such case you need enough implied odds.  You have large implied odds if you have multiple opponents with very large stacks in the hand and you have a chance of getting the nuts. If you want to know more about implied odds go to:

Implied odds and expected value

 

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