Probability and Poker
Index | Odds | Royal Flush | Straight Flush | Four of a Kind
Full House | Flush | Straight | Three of a Kind
Two Pairs | One Pair | High Card

Probability of Getting No Hand

A high card hand means that you cannot make any other combination that qualifies as a hand.You can bet on anything. You can even bet on the worst hand possible, 2,3,4,5,7 of mixed suits. (The odds of being dealt this particular combination are 1/2548 by the way). To calculate the high card hand we can simply take all of the hands we have dealt with already and then subtract them from the total possible hands. Below is a list of the total possible combinations for each type of hand:

Straight Flush 40
4 of a Kind 624
Full House 3744
Flush 5108
Straight 10,200
3 of a Kind 54,912
Two Pairs 123,552
One Pair 1,098,240
Total 1,296,420

Now we must subtract this total from the number of possible hands:

2,598,960 - 1,296,420 = 1,302,540

Now it is a simple matter of dividing our high card hands by the total possible hands:

1,302,540/2,598,960 = 1 in 2

This gives us about a 50% chance of getting nothing. But this also tells us that we have an even chance of getting at least a pair.

Improving a high card hand can be tricky. The best strategy is probably to keep your two highest and hope for a pair or better. Alternatively keep whatever cards you have of the same suit and hope for a flush. Any close runs are also a possibility, however, going for the inside straight is questionable if the raises are high.

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