Calculating your odds of winning after the flop and turn

Calculating your odds of winning after the flop and turn

It is easy to quickly determine the number of outs you have when you are on a draw in Holdem, but harder to translate these outs quickly into odds. The table below should be your bible to playing draws in Hold'em. Print it out and leave it by your computer. In fact, leave one copy on your bed-head so you can soak it in via osmosis.

How to read the table

Once you have calculated your outs, you simply need to read across the relevant row to determine your percentage chance of winning. To make it easier for you we have included some descriptions outlining some of the major common situations.

An example

Lets say you have 7h,8h and the flop comes 9h10c2d. With this flop you have an open ended straight draw. Any jack or six will complete this straight. There are 4 jacks and 4 sixes remaining in the deck (8 outs in total) that will make you hand. Reading across the table, you can easily see that with this flop you have a 32 per cent chance of winning. Since you are slightly worse than 3/1 to win, to be assured of a long run profit you need at least 3 other opponents to continue with this draw (three opponents gives you a 4/1 payoff for a 3/1 bet). It is about break even to continue with only two other opponents when you take into account that you will also win the initial blinds if you hit your hand. If a blank hits on 4th street, your chance of making your hand has reduced to 17 per cent. In some circumstances it might be correct to fold after the turn. Your simply need to calculate what you expect to win and compare that to your 17 per cent chance of winning.

Calculating your odds of winning after the flop and turn

Using the same example, what if the flop came 9h,10h,2d? With this flop you have an open-ended straight draw and a flush draw. You have 9 flush cards and 8 straight cards. However, two of your flush cards (the Jh or 6h) will make you a flush. Since you have already counted these as flush cards your total outs are reduced to 15 (9 flush cards and 6 straight cards). With 15 outs you are a 54 per cent chance of winning. You can always proceed with this hand an expect a long run profit.

The table below can be used for any possible draw in Holdem.

Outs Flop % Turn % Draw Type
2 8% 4% Pocket pair Set
3 13% 7% Drawing to 1 Overcard
4 17% 9% Gut Shot Straight, Two Pair Full House
5 20% 11% One Pair Two Pair or Set
6 24% 13% No Pair Pair
7 28% 15%  
8 32% 17% Open Straight Draw
9 35% 19% Flush Draw
10 42% 22%  
11 42% 24%  
12 45% 26% Open ended straight and flush
13 48% 28%  
14 51% 30%  
15 54% 33% Flush plus Open Draw
16 57% 34%  
17 60% 37%  

How are these odds calculated?

Most people calculate these odds incorrectly. If on a flush draw most people calculate their odds by simply dividing the number of outs by the cards remaining after the flop and multiplying this by the number of outs after the turn divided by the number of cards remaining after the turn, as follows:

(9/47)*(9/46) = 38.7 per cent.

However this overestimates your chance of winning and is not correct. The correct way to calculate your odds are as follows.

Flop = 1 - [ ((47 - Outs) / 47) * ((46 - Outs) / 46) ]

River = (46 - Outs) / 46

Using the above method, you are basically working out the probability of your cards not hitting twice in a row and then subtracting one to obtain the probability of hitting your hand. However, you don't need to worry about any of this becuase the odds are all summarised in the table.