Trips to Win

[MikeyEdge]

If you are playing 5 card draw, Three-of-a-kind to win, and you are dealt 2 Pair, is it better to break it up and draw 3 or go for the full house and draw 1?

[Homer]

I don't exactly know how this game works, but I'll assume you simply want to know which action will be more likely to give you trips or better.

Option 1: Draw one to two-pair

P(Trips or better) = 4/47 = .085

Option 2: Draw three to one-pair

P(Trips or better) = P(Trips of the pair you kept) + P(Three drawing cards match for trips)

I'll assume the probability of drawing three matching cards is negligible, so it is just the probability that you draw one or two of the remaining rank of your pair. This is the same as 1 - P(drawing none of the paired rank)

P(Trips or better) = 1 - [(45/47)*(44/46)*(43/45)] = .1249

So...it looks like dropping three and drawing to one pair is better, if you are only interested in the odds of obtaining trips or better.

-- Homer