Odds question when playing deuces.

[PITTM]

A group of friends and i play deuces a lot, i was wondering, if you deal out all 52 cards to 4 people, how often would quads be dealt to one person? Thanks

rj

[donkeyradish]

Revised answer (but maybe still wrong)

I figure the number of ways to deal a 13 card hand is C(52,13)
635,013,559,600

There are 13 ways to pick quads out the deck, and so we don't care what the other 9 cards are in the hand.
So the hands with quads must number 13 * C(48,9)

ie. 13 * 1,677,106,640 = 21,802,386,320

Dividing yields roughly 0.03433 (3.4%)

A 28:1 chance

Can someone who can do maths comment on this logic? I'm just learning.

[DeadRed]

This is exactly how to figure the probability that 1 person gets quads being dealt 13 cards. Dealing all 52 out to 4 people is a little (maybe a lot) more complicated, because the cards dealt to player 1 influence the probability for player 2. e.g. If player 1 holds A,2,...K of hearts, there is no way anyone else can have quads, but if they hold 3 As, 3Ks, 3Qs, 3Js, and a 10, the chance that player 2 has quads is ~ 7%. More on this topic later...

[donkeyradish]

Ah, well if the question is whats the probability of exactly one person having quads... you're right I've no idea how to work that out.

Once one person has quads I'd presume the chance of a second having quads increases a bit.