Betting the flop

You and your friends play texas hold em and you decide to place a side bet on the combination of the 3 card flop. Player A choose A-10-3, player B choose 7-4-K, player C choose 9-3-3 and player D choose 5-5-5. Suits are not considered and the order of the flop does not matter. What is the probability of each players flop hitting?

Quote: mrxpink

You and your friends play texas hold em and you decide to place a side bet on the combination of the 3 card flop. Player A choose A-10-3, player B choose 7-4-K, player C choose 9-3-3 and player D choose 5-5-5. Suits are not considered and the order of the flop does not matter. What is the probability of each players flop hitting?

If I've done my math correctly, there are 64 possible flops of A-10-3 (if suit doesn't matter) out of 22,100 possible flops, so it's about a 0.29% probability.
Same goes for the 7-4-K flop. The 9-3-3- flop can happen 24 ways, so it's about a 0.11% probability. The 5-5-5 flop can happen 4 ways, so it's about a 0.03% probability. Of course, this is all assuming that the "pre-flop" bet is made prior to any cards being seen by any players. Once that happens, these probabilities change.

Quote: mrxpink

You and your friends play texas hold em and you decide to place a side bet on the combination of the 3 card flop. Player A choose A-10-3, player B choose 7-4-K, player C choose 9-3-3 and player D choose 5-5-5. Suits are not considered and the order of the flop does not matter. What is the probability of each players flop hitting?

All flops with three different ranks would be equally likely, flops with a pair would be less likely, and flops with three of a kind would be less likely still (MUCH less likely than the other flops).

Quote: mkl654321

All flops with three different ranks would be equally likely, flops with a pair would be less likely, and flops with three of a kind would be less likely still (MUCH less likely than the other flops).

I humbly bow to your much deeper analysis. :)

Quote: bruski

I humbly bow to your much deeper analysis. :)

Yeah, I was too lazy to actually quantify the proabilities, since the real question the OP seeming to be posing seemed to be which of the three possible bets was best, and which was worst. I often do that in my own gambling/poker adventures, when "not bloody likely" is good enough to steer me away from a given course of action/bet, without needing to quantify it: What are the chances that that hot, scantily dressed blonde sitting alone on the barstool will want to go out with me? I don't need to quantify the odds: "not bloody likely" is good enough to determine my appropriate action (and I realize that in this case, the terrific payoff may justify bucking very heavy odds).