odds of getting a pocket pair 3x in a row

[BruceZ]

[ QUOTE ]
Now, using your formula, the chances of Ichiro having a 55 game hitting streak in a 162 game season (not missing any games) would then be 0.001106131, or, a little less than 1 in 900. Is that correct?

[/ QUOTE ]

No, I get 0.005815 or about 1 in 172.

P(1) to P(54) = 0
P(55) = (0.866636)^55
P(56) = P(55) + (1 - 0.866636)*(0.866636)^55
P(n) = P(n-1) + [1 - P(n-56)]*(1 - 0.866636)*(0.866636)^55, for n > 56
...
P(162) = 0.5815%

[mtgordon]

Here's one that'll blow your mind. Earlier today I got KK 3 times in a row on bodog. And after the first hand I got KK on Pacific as well. I don't feel like doing the math again, but it was something like 0.000093% chance of getting KK 3 times in a row.

[DougOzzzz]

[ QUOTE ]
[ QUOTE ]
Now, using your formula, the chances of Ichiro having a 55 game hitting streak in a 162 game season (not missing any games) would then be 0.001106131, or, a little less than 1 in 900. Is that correct?

[/ QUOTE ]

No, I get 0.005815 or about 1 in 172.

P(1) to P(54) = 0
P(55) = (0.866636)^55
P(56) = P(55) + (1 - 0.866636)*(0.866636)^55
P(n) = P(n-1) + [1 - P(n-56)]*(1 - 0.866636)*(0.866636)^55, for n > 56
...
P(162) = 0.5815%

[/ QUOTE ]

Okay, I had an error in my formula. For some reason I was multiplying by (1-.86636)^2.
In other words, my formula was: P(n) = P(n-1) + [1 - P(n-56)]*(1 - 0.866636)^2*(0.866636)^55, for n > 56
I get the same answer now.