Re: Tough question???
Is the first question, what are the chances of flopping a
set or having a pair dealt in your hand? The first
(including quads) is 1-C(48,3)/C(50,3) and the last is 1/17
(pick first card; second can only be 3 of 51 of the
remaining). By the way, the first number is about 0.117551
and C(n,r) = the number of combinations of n objects chosen
r at a time (or the number of possible sets of size r
chosen from a set of n>=r objects). It is just
n!/((n-r)! x r!) where k! = k x (k-1) x...x 1.
If the board reads XXY then for a two card hand to have one
of the two remaining Xs (or more), the combinations are 1
(XX) + 2 x 47 (Y on flop excluded) = 95 out of C(49,2) =
1176 hands. I suppose you also should note that there are
C(3,2) = 3 hands that flopped a full house without an X.
Altogether, the chances of a specific hand being trips or
better is 98/1176 = 1/12 = 0.083333, a very simple number
to remember. On the other hand, obviously if a specific
action (or lack of action) has occurred, these odds don't
necessarily help you in the play of the hand. Also, hands
containing an ace tend to get played.
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