Poker Combination Calculation Exercise — My Answer
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Two days ago I posed a poker-related math question. Here’s the question again and then my answer.
What percentage of all possible five card boards put the nuts on board? By “put the nuts on board” I mean that every possible two card hand will split the pot with every other possible hand.
There are two board types where the nuts is on board. First, you have Broadway straights where a flush isn’t possible. Royal flushes are obviously also the nuts. Second, you have quads with the highest possible kicker.
So the following boards are examples of nut boards:
- A
K
Q
J
T
- A
K
Q
J
T
- 4
4
4
4
A
Total Boards
To get started, we need to calculate how many total five card boards are possible. There are 52 boards, and we need to choose 5 cards per board, so the answer is 52c5 = 2,598,960 boards. If you aren’t familiar with the “choose” notation, read this article. Also useful to know is that Google will solve this problem for you by typing “52 choose 5″ into the search box.
Next, we need to count how many nut boards there are.
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Tags: Broadway straights, combinations, google, nut boards, poker, Poker Math, probability

Hello Ed,
Very interesting exercise, thank you for it.
Just something I think about moving all-in with a 5 cards board which is the nuts. In a theorical way, of course it is an EV+ move, even if fold equity is very low. But in a practical way we should consider what we almost always neglect : rake. In that case there is a little computation to do with rake percentage and fold equity. And not sure it is an EV+ move in high limits.
Best regards,
Zeuwan