There are 47 unseen cards, and you draw 3, so there are 47 choose 3 or 16,215 total possible redraws.
Of these, there are 6 cards (4 deuces, 2 tens) that you're looking for, and you need two of them. That means there are 6 choose 2 or 15 ways to get the cards you need. Then the third card can be any of the other 41 cards. So there are 15*41=615 ways to make 4-of-a-kind. That makes the chance to draw exactly 4-of-a-kind 615/16,215 ~= 3.8%
Ed
On Wed, Mar 26, 2014 at 8:50 AM, <melbedewy1226@hotmail.com> wrote:
If you are dealt a given pair (10's say) along with three "garbage" cards what are the odds of getting a 4 of a kind on the redraw?
I believe it is something around 1 in 500 on non-deuces games but I can't come up with deuces number-and I've been profitably playing the game for 25 years .
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