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Odds in poker

Any good poker player should have at least a basic understanding of how to work out their chances of winning in a given situation. It does not matter if you plat at full tilt or elsewhere.

First off, all of you who hate maths needn't worry. The majority of situations you will be in, either at the flop or the turn, will be easy to work out since you'll be in them so often. For example, if you need one more heart for a flush and someone goes all in at the flop then you know that you have a 35% chance of getting that heart by the river.

The purpose of this page is to show you how you work out the odds which are in our Odds Chart - how did we know that we had a 35% chance of making our flush by the river??

Working Out Odds - Will we get our flush?

You are on the big blind and get dealt . There is one caller in middle position and the small blind folds. You check.

The flop comes :

You decide to check and the guy who is in middle position decides to go all in. You believe that he has a pair and that if you get another heart you'll win the hand.

What are the odds of you hitting another heart

  • (a) On the Turn?
  • (b) On the River? (ie. missed a heart on the turn)
  • (c) On the Turn or River

Working Out Odds - Doing the math!

First of all, lets look at some facts. There are 52 cards in a standard deck of playing cards. You have seen 5 cards - The you have in your hand and the you have seen on the flop. Now you know the player in middle position has two cards of his own but since we dont know what those cards are we can't count those cards in our calculations - they might as well be back in the deck!

We also know that there are 13 cards in each suit (hearts, diamonds, clubs, spades) and currently we have seen 4 hearts - 2 in our hand and 2 on the flop. That means there are 9 hearts out there somewhere. They could be in the deck, they could have been folded by other players - they could even be in the other players hand just now. Since we dont know we have to include these 9 hearts in our calculations. These cards are known as outs ie. we have 9 outs to catch a card to help us win the hand.

So lets work out the odds of making our flush!

(a) On the Turn

We have 9 cards that help us from 47 cards that are left so the odds of catching a heart on the turn (4th Street) is simply 9 divided by 47 which is 19.15%.

Another way of expressing this, which you see a lot in gambling, is by writing it X to 1. How do we work out our odds in this way? Simple. You simply divide the 47 cards by our 9 outs and then take 1 away. So since 47/9=5.222, the odds of us catching a heart by the river is 4.22 to 1.

(b) On the River

In this situation we assume that a non-heart card came on the turn. What are our odds of now catching our heart on the river?

We still have 9 cards that help us but there are now 46 cards left (2 in our hands and 4 on the board) so the odds of catching a heart on the river (5th Street) is simply 9 divided by 46 which is 19.5652%.

How do we write this as X to 1? Same as last time except its now (46/9)-1 = 4.11 to 1.

(c) On the Turn or River

In this situation we assume we're still at the flop. We want to know the odds of catching a heart on either the turn or the river.

As we saw in (a), the odds of catching a heart on the turn is roughly 19.1%. However, 80.9% of the time we will not catch our heart on the turn. Which means that 80.9% of the time we would need to catch a heart on the river and as we have seen before the % of us catching a heart on the river is roughly 19.6%.

So the odds of catching a heart on the turn or the river is 19.1%+ 80.9% x 19.6% = 34.96%.

So the odds of catching a heart on the turn or the river is 35% or 1.86 to 1.

Now clearly we don't want to have to work out complicated calculations whilst at the poker table. Thankfully, we never have to because you'll be put in the same situation time and time again and will remember your odds. You'll have 9 outs to make your flush, you'll have 8 outs on an open ended straight, you'll have 4 outs on a gutshot straight etc.

Here is a quick and easy way to work out the odds of catching your hand. It isnt exact but its close enough for you to make a good decision in the middle of a game.

At the flop multiply the outs you have by 4 to get a rough estimate of the odds of hitting your cards by the river.

At the turn multiply the outs you have by 2 to get a rough estimate of the odds of hitting your cards on the river.

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