What are the odds?

[suzanne]

I havent figured out how to get a hand history on ipoker yet but just wondered what the odds were in this case and should i have got out early?

6 handed mtt only on the second level, 1 guy is aggressive and been lucky and trebled, another has doubled and the rest of us are still on starting stacks. UTG (aggresive guy) has min raised to 120 i call next with 9Td another guy also called. Flop is 4? UTG puts 120 in the pot i call, 1 goes out another calls. Turn is 3? but not same suit as the 4.
UTG puts 240 in the pot, I decide to gamble and call as does 3rd guy. River is so ive made my flush but not a good one. Ive put UTG on face cards of some kind with 2 pair or trips and was more worried about the guy behind me. Then UTG goes allin, he had done this previously with top pair so i take a chance, guy behind goes allin too....eeeekkkkkkk.

UTG has A?d and matey boy had q?d

I dont think to be honest (unless I had folded preflop) I would have played it different coz im a fish but i just wondered what the odds are of 3 people on a 6 handed table all having diamonds with 3 diamonds on the board?

[AlexMartin]

erm, long...................

[Rookie (Rodney)]

erm, long...................

Took me a while to work out but alex has got it spot on.

[Smart Money]

...but i just wondered what the odds are of 3 people on a 6 handed table all having diamonds with 3 diamonds on the board?

p(3 players all having diamonds) = 13/52 * 12/51 * 11/50 * 10/49 * 9/48 * 8/47 = approx 12,000/1

There are 20 combinations of 3 players from 6, so divide 12,000 by 20 --> p(at least 3 players on 6-handed table all holding diamonds) = 600/1

p(flop all diamonds, given 3 players have diamonds) = 7/46 * 6/45 * 5/44 = approx 430/1

so p(3 people on a 6 handed table all having diamonds with 3 diamonds on the flop) = approx 600 * 430/1 = approx 250,000/1

Of course there's nothing special about diamonds, so you should divide that answer by 4 to allow for all the suits.



*The precise answer would be very slightly higher than the one above because we haven't taken into account the decreased probability of the flop being all diamonds if more than 6 diamonds are out in the hole cards, but it's close enough.



Of course, this information is pretty worthless at the table and it certainly shouldn't be used to make incorrect assumptions about the likelihood of your opponents' holdings!

[kinboshi]

Of course there's nothing special about diamonds...

Tell my missus that!!

[thetank]

Slightly more than 250,000 to 1.

Diamonds are rarer now Sheila's Wheels seems to be hogging all the the action.