# What are the 5 card hand probabilities

Of all the 5 card poker hands what are the probabilities?

And how are probabilities derived?

I had this in Excel and could not find it on this site so posting it.

This is 5 card hands:

``````hand          count      pct       cum     1/
straightFlush    40  0.0015%     0.00%  64974
quad            624  0.0240%     0.03%   4165
boat           3744  0.1441%     0.17%  694.2
flush          5108  0.1965%     0.37%  508.8
straight      10200  0.3925%     0.76%  254.8
trips         54912  2.1128%     2.87%  47.33
two pair     123552  4.7539%     7.63%  21.04
one pair    1098240 42.2569%    49.88%   2.37
high card   1302540 50.1177%   100.00%   2.00
sum         2598960 100.000%
``````

These numbers can be solved by statistics (combinations) or by dealing all the 5 card hands.

This would be good for evaluating a flop as 5 cards.

Holdem is best 5 of 7 so the numbers are different. Below is best 5 of 7:

``````                count        pct       cum    1/
straightFlush   41584    0.0311%     0.03%  3217
quad           224848    0.1681%     0.20%   595
boat          3473184    2.5961%     2.80%  38.5
flush         4047644    3.0255%     5.82%  33.1
straight      6180020    4.6194%    10.44%  21.6
trips         6461620    4.8299%    15.27%  20.7
two pair     31433400   23.4955%    38.77%  4.26
one pair     58627800   43.8225%    82.59%  2.28
high card    23294460   17.4119%   100.00%  5.74
sum         133784560
``````

I ran both of these brute force all hands as I use them in a simulator. I could not get the 7 card fast enough to be a phone app.

If you look me up on codereview you will find some of my poker tools.

• I will add a link with an old-but-good Java source code I created long time ago to calculate this and the full brute strength of a hand when back home <3. Apr 12, 2018 at 19:26
• @LuisMasuelli If you can do this in code then you should be able to do the badugi. I did it in like 30 minutes. Apr 12, 2018 at 19:47
• Trust me - I tried the formulae-based version for badugi and failed. With this one you tell, I could use the fornulae-based approach. Apr 12, 2018 at 20:25
• With Badugi, I could reach what I showed you in my question, but there is a point where I could not generalize the sum into another function like I could with these regular poker hands. Apr 12, 2018 at 20:27
• dropbox.com/s/m2mz65595iw4upo/ExpressPoker.rar?dl=0 if you download it, go to src/pokerobjects/Result.java, forgive charset and awful lexical conventions, you'll get what did I achieve in standard hands that I could not in Badugi, and was asking for. Apr 13, 2018 at 2:34