Still Can’t Believe It

I still can’t believe that I made a four of a kind in a game of five card draw last night.

I took statistics in college, but that was 10 thousand years ago and I don’t remember how to calculate the probability of pulling four of a kind.  So I googled it:

A four-of-a-kind is four cards showing the same number plus any other card.

If we order the 5-card hand with the four-of-a-kind first, we have 13C1 choices for the number showing on the first four cards. Since we will have all four suits, we have only 4C4 = 1 way to choose the suits. The remaining card will be any of the 48 remaining cards:

# 4-of-a-kinds = 13C1·4C4·48C1 = 13·1·48 = 624

Dividing by the number of possible hands gives the probability:

P(4 – of – a – kind) = 624/2,598,960 = 2.401⋅10−4 or 1 in 4165

1 in 4165.

Can you believe it?  I mean it was just a friendly game with my wife and my step kids.  We were betting pennies, but each player’s pennies came out of the same little jar.

But still… four of a freakin’ kind!

It would have been cooler if it was aces instead of twos, but it was still uber awesome.