Probability question

[Derelique]

Say in a hand, you are holding, A10, with a flop that comes 7-7-A. What is the probability of someone having a 7, and how hard should you push your top two pair in this kind of situation.

[jogger08152]

The raw probability is simply = 2x(players to the flop-1) / 48. Thus, if 4 players (including you) took the flop, and assuming they will play any two cards, the chances that at least one of them has at least one 7 is simply 6 in 48, or 7-to-1 against.

The "game" probability is more determinable: if you raised preflop, any decent player behind you most likely didn't call with a 7, unless he held two of them. If you didn't raise, go with the above probability, bet the flop, and see what happens. If the flopped A is offsuit relative to the sevens and you get callers (especially if you raised preflop) you've probably got some trouble, especially since a better ace beats you just as surely as a 7 does. If you do get a caller, you could consider betting the turn and folding to a raise. You could also consider check-calling and check-folding (even check-raising, but only against a strong player and only if nobody raised preflop).