# Poker Combination Calculation Exercise

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This is just a little math problem, but I think it’s good exercise for your poker math muscles.

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. Answer to come in the next post.

Tags: combinations, poker, Poker Math, probability

I think it’s 1745 .

The lowest possible nuts-on-the-board is the broadway straight.

There are 13 quad combinations and 4 straight flush combinations.

There are no full house combos because quads are always possible if the board is paired, and no other flushes besides the four straight flush combos.

That’s the easy part.

For the broadway straights, there are two basic suit patterns where no flush is possible: xxyyz, and xxyzw.

For xxyyz, there are 16 ways for the suits to distribute across it and 27 ways for the ranks to distribute across of each of those. That makes 432 combinations.

For xxyzw, there are 24 ways for suits to distribute across it and 54 ways for the ranks to distribute across each of those. That makes 1296 combinations.

So summing it all together:

4 straight flushes

13 quads

432 xxyyz broadway straights

1296 xxyzw brodway straights

—————————–

1745 nuts-on-the-board

Did I get it right?