I flop a boat she makes quads

[yoursmine]

I have a pocket pair she does as well

What is the probability I flop a boat and she makes quads?

I figured it as this but please check my math

Prob of flopping a boat is 1/136
Prob of flopping wuads is 1/407

1/36 * 1/407= 1/55352 or .0018% of the time

Is this correct?

[SamIAm]

You can't just multiply any two probabilities and get their intersetion. The probability that I flip this coin and it comes-up heads is 1/2. The chance that it comes up tails is 1/2. Therefore the chance that it lands on both at once is 1/4...

If you have XX and she has YY, you need a board with XYY in it. (It's up to you whether you want to count a board like XXYYZ as "giving you a boat".) Count those up and divide by the total number of boards.
-Sam

[yoursmine]

Well in the hand I had 99 and the board came 988. She had 88. So how do I figure that one out? Sorry for the confusion (on my part)

[jay_shark]

Suppose you have pocket 9's and you estimate that there is a 33.3% chance that she holds a pocket pair given the range of hands she would have played this way . So one third of the time you know she has a pocket pair if she decides to see the flop with you . Lets Say she is equally like to have any of the ranks of pairs from 2's, 3's all the way to aces .

The probability you flop a set and she flops quads is :

1/3*[2*1/48c3] = 0.0000385

[yoursmine]

thanks Jay

I need to seriously revisit my probability notes

[mykey1961]

[ QUOTE ]
I have a pocket pair she does as well

What is the probability I flop a boat and she makes quads?

I figured it as this but please check my math

Prob of flopping a boat is 1/136
Prob of flopping wuads is 1/407

1/36 * 1/407= 1/55352 or .0018% of the time

Is this correct?

[/ QUOTE ]

Prob = (72/73)*(2*2*1)/(48*47*46) = 0.00380%

[BruceZ]

[ QUOTE ]
[ QUOTE ]
I have a pocket pair she does as well

What is the probability I flop a boat and she makes quads?

I figured it as this but please check my math

Prob of flopping a boat is 1/136
Prob of flopping wuads is 1/407

1/36 * 1/407= 1/55352 or .0018% of the time

Is this correct?

[/ QUOTE ]

Prob = (72/73)*(2*2*1)/(48*47*46) = 0.00380%

[/ QUOTE ]

You need to multiply that by 3 since your expression gives the probability of the 3 flop cards coming in the order XYY, but the X can come in any of 3 positions. I see that you allowed for the possibility that she has the same pair as you, since we are only told that she holds some pair, and since there are 73 total pairs and 1 way to make your pair, the probability is 72/73 that she has a different pair. Including this, the solution should be:

(72/73)*(2*2*1*3)/(48*47*46) =~ 0.0114%

OR

(72/73)*2*1/C(48,3) =~ 0.0114%

In the second solution we are not concerned with the order of the 3 cards. The denominator counts the total number of flops without regard to order C(48,3) = 48*47*46/(3*2*1). The numerator counts 2 cards that give me a full house times 1 pair of cards that gives her quads.