What are the odds of hitting 2 pair on the flop?

[pendragon]

What is the probability of hitting 2 pair on the flop with unpaired hole cards?

[DiamondDog]

Suppose you hold 85.

To flop precisely two pair you need to flop one of the other three 8's, one of the other three 5's, and one of the other forty four cards which are neither 8 nor 5.

All together there are 50 cards not yet seen.

So the probability you're looking for is (3 x 3 x 44)/(50C3)

= 396/19600
= 0.020204

which is roughly 49-1 against.

Someone please tell me if I've got that wrong.

When I say precisely two pair, I'm excluding the possibility of flopping better than two pair (trips, boat, quads).

[jay_shark]

Thats correct Diamond .

Sometimes people may also be interested in flopping two pair where you don't use both of your hole cards .

ie , you have 85 , flop comes 8 xx where x is not a 5 .

Then you would add (3*66 + 3*66)/50c3 for 8xx and 5xx.

[pendragon]

Thank you [img]/images/graemlins/smile.gif[/img]

2% to hit 2 pair with two unpaired cards.

[BradleyT]

[ QUOTE ]
Suppose you hold 85.

To flop precisely two pair you need to flop one of the other three 8's, one of the other three 5's, and one of the other forty four cards which are neither 8 nor 5.

All together there are 50 cards not yet seen.

So the probability you're looking for is (3 x 3 x 44)/(50C3)

= 396/19600
= 0.020204

which is roughly 49-1 against.

Someone please tell me if I've got that wrong.

When I say precisely two pair, I'm excluding the possibility of flopping better than two pair (trips, boat, quads).

[/ QUOTE ]

How about a flush draw when holding 2 suited? I can't seem to get 10.9% that I see all over the web.

Edit - 11 * 10 * 39 = 4290/19600 = .2188
If you divide that by 2 you get 10.9% but why are we dividing by two?

[jay_shark]

11c2*39/50c3 ~ 10.943%

or , [11*10/2*39]/50c3 =10.943% .

You forgot to divide by two .

ie 10h 8h is the same as 8h 10h so we don't want to overcount . If you notice that for each two cards ;ie, xy , we can always find yx.

[BradleyT]

So to flop 3 flush - ABC, ACB, CBA, CAB, BCA, BAC are all the same so....
((11*10*9)/6)/50c3 = .841% AMIRITE?


quads when we hold 88

88x, 8x8, x88
((2*1*48)/3)/50c3 = .163% - that's not right...sigh.

[jay_shark]

Quads when you hold 8's is 48/50c3~0.00244 since there are 48 cards other than 2 8's .

Or 2/50*1/49*48/48 + 2/50*48/49*1/48 + 48/50*2/49*1/48 ~0.00244

[mykey1961]

My question is what are the odds of flopping two pair, and not having it hold up.

Every friggin time based on my experience.