XY, XY, XY, ZZ, flop comes XYZ - odds?

[btetreau]

Hey All,

Ran into this recently in a MTT, table was full (10 heads) and I got AK, raised, and 3 callers came along. Flop was AK5, everyone went allin, and the 4 hands were AK, AK, AK, 55.

So, what are the chances that the flop will come XYZ if 3 of the 10 people hold XY and a fourth holds ZZ?

Thanks in advance.

[MickeyHoldem]

There are only 1 X&Y left and 2 Z's so there are only 2 flops out of the 44c3 possible flops left.... so

= 2/13244 = 1 in 6622 or .000151012

Presto! there's your answer!

<sorry - couldn't resist>

[mtrubo]

just curious; did the turn and/or river help?

[schafdawg]

[ QUOTE ]
just curious; did the turn and/or river help?

[/ QUOTE ]

It would be crazy if one of the AKs hit a flush during that. If no AKs, then turn and river help no one. (Can't tell if you were asking a serious question or not)

[spaminator101]

1 xy left two z left
1/50*1/49*1/24=1/58800

[BruceZ]

[ QUOTE ]
1 xy left two z left
1/50*1/49*1/24=1/58800

[/ QUOTE ]

1/44 * 1/43 * 2/42 * 6 = 1/6622

There are 44 cards left not 50, and the 3 cards can come in 6 different orders.

[spaminator101]

sry y is order important

[BruceZ]

[ QUOTE ]
sry y is order important

[/ QUOTE ]

If we don't multiply by 6, then we are computing the probability of XYZ in exactly that order. We don't care about the order, so we multiply by 6 to allow any possible order.

[spaminator101]

ok thank you