# Short deck probability

Short deck is remove 2-5 so 36 cards left. A6789 is a straight.

What is the hand order and probability.

For example a flush is harder to make but a straight is easier.

Ideally post the equations for probability.

Number of possible 5 card hands 376,992

``````               count    fraction  cumulative
straight flush    24  0.00006366  0.00006366
flush            480  0.00127324  0.00668449
boat            1728  0.00458365  0.00541126
straight        6120  0.01623377  0.02291826
trips          16128  0.04278075  0.06569901
2 pair         36288  0.09625668  0.16195569
1 pair        193536  0.51336898  0.67532468
high card     122400  0.32467532  1.00000000
total         376992
``````

A flush becomes harder than a boat.

Some sources say trips become harder than a straight but that is not what my numbers conclude.

I just ran these equations. Please don't ask me to post the calculations. They are in that link. This site does not support Latex. There is a meta asking for support of Latex that I encourage you to up vote.

• @RaymondTimmermans Straight flush count of 24 is correct. If you want to run 7 cards the please do so. – paparazzo Feb 4 '18 at 12:00
• You are correct my apologies. I am trying 7 cards right now, but for me it is really difficult :/ – Raymond Timmermans Feb 4 '18 at 12:18
• Trips are harder than straight when you use 7 cards, but mostly because they turn into full houses very often. – Bogdan Alexandru Aug 24 '18 at 22:48
• @BogdanAlexandru Turn into a full house has not germane. There is a be nice policy so I will leave it here. – paparazzo Aug 24 '18 at 22:53
• @paparazzo Not sure what you mean. I explained that when you add two more cards you see less trips because the new cards will pair the first five, in addition to adding more straights. – Bogdan Alexandru Aug 24 '18 at 22:57