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Poker Probabilities

NLHE - Probabilities
This page was created for the purpose of providing useful poker probabilities. This area of the site will grow in the future. If you have any comments/suggestions, be sure to speak up in our forum area.

* All percentages are rounded to the nearest tenth of a percent
Starting Hand Probabilities

Hold'em Starting Hands - Probability of being dealt: HIT CHANCE
Pocket Aces 0.45%
Any Pocket Pair 5.9%
Ace - King suited 0.3%
Ace - King offsuit 0.9%
Ace - King suited OR unsuited 1.2%
Any two suited cards 24.0%
Pocket Aces OR Pocket Kings 0.9%
Pocket Aces, Pocket Kings OR Ace-King 2.1%
Any Pocket Pair OR two cards ten or higher 18.0%
Any Pocket Pair of Sevens OR higher 16.0%
Taking a pocket pair to the river, to make a set or better 19.0%
Turn and River Probabilities

Turn Card
1 2.1% Quad Draw
Gutshot Straight Flush Draw
2 4.3% Set Draw
3 6.4% Two Pair Draw
4 8.5% Inside Straight Draw
5 10.6%  
6 12.8%  
7 14.9%  
8 17.0% Open Ended Straight Draw
9 19.1% Flush Draw
10 21.3%  
11 23.4%  
12 25.5% Flush and Inside Straight Draw
13 27.7%  

River Card
1 2.2% Quad Draw
Gutshot Straight Flush Draw
2 4.3% Set Draw
3 6.5% Two Pair Draw
4 8.7% Inside Straight Draw
5 10.9%  
6 13.0%  
7 15.2%  
8 17.4% Open Ended Straight Draw
9 19.6% Flush Draw
10 21.7%  
11 23.9%  
12 26.1% Flush and Inside Straight Draw
13 28.3%  

Turn OR River Card
1 4.4% Quad Draw
Gutshot Straight Flush Draw
2 8.4% Set Draw
3 12.5% Two Pair Draw
4 16.5% Inside Straight Draw
5 20.3%  
6 24.1%  
7 27.8%  
8 31.5% Open Ended Straight Draw
9 35.0% Flush Draw
10 38.4%  
11 41.7%  
12 45.0% Flush and Inside Straight Draw
13 48.1%  

The Math

The math to figuring out the probability of 'hitting' an out is really quite simple. Let's begin with The Turn.

At the turn you have seen 5 cards, the 3 on the flop, and the 2 in your hand. There are 52 cards in the deck, making 47 UNSEEN cards (52- 5=47). With me so far?
Once you know how many outs you have, let's say 9 (you are shooting for a flush draw), to find out the chances of hitting an out, we simply do 9/47 (47 unseen cards remember) which gives us 19%. So if you have:

...and the flop is:

... then you know you have a 19% of catching a heart on the turn.

So the turn comes... no heart. Damn. Fortunately you still have a shot of completing your nut flush on the good old River. To calculate this we simply do 9 (your number of outs) / 46. We saw one more card on the turn, giving us 6 known cards total, and thus 46 unseen cards, so we do 9/46 and get 19% again (it's 19.1 and 19.6 on the turn and river respectively if you want to be very specific).

Now - to calculate your chances of catching your outs on EITHER THE TURN OR THE RIVER, this is a very different procress. I did a fair bit of research on this, and contrary to what you might have heard elsewhere, the following equation is the way to work this out. I'm not very good at math to know exactly how this works, but I do know that it works:

1 - 38/47 * 37/46 = 35.0%

Replace the 38 with the result after you subtract your number of outs from the number of unseen cards on the turn, and do the same with the 37.