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Message: [QUOTE="Sohmurr, post: 1219425, member: 23211"] My first question is where did the 84 come from? I did the math but came to a different conclusion. Here is what I did: I agree with you post flop. (6/46)*(4/45)*(2/44)=0.000527 Preflop however I see a problem. If you have 9 people, the chance that any one will get a pocket pair is (3/51)*9= 27/51 (which is fairly common, 1.8888 to 1). Once it is established one player has a pocket pair, the chances of a second player is (3/49)*8. Note a few things, because it doesn't matter which order the cards are dealt nothing changes in the math. The 49 represents the deck minus the first pocket pair and the first hole card of the second player. (3/49)*8=24/49. Repeat for a 3rd player where 47 is the deck minus the first two pocket pairs and player three's first hole card. (3/47)*7=21/47. Multiply them all together. (27/51)*(24/49)*(21/47)=0.11586 or 8.63-to-1. It seems correct because the likelyhood of 3 players getting pocket pairs preflop is not uncommon. So if we assume 3 players are dealt pocket pairs and all see the flop then (0.11586)*(0.000527)=0.0000611 or a 16,377-to-1 chance of all seeing the flop and each hitting a set. I think that my method is closest. Your shorthand method makes sense but I think you screwed something up. (3/51)^3 makes perfect sense, but that 84 is what is messing up your results. Again I'm not sure where it came from. If you take (3/51)^3 and multiply it by 9*8*7 (which represents the possibility of remaining players being dealt a pocket pair), then you get [(3/51)^3]*9*8*7=0.1023 which is significantly closer to the 0.11586 that I got. The shorthand method is fine to approximate as you did, but that 84 still doesn't make sense. Could you please explain where you got it from if it wasn't an error? Using my shorthand method, 9*8*7=504 where your 84 would be. [/QUOTE]

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