Odds of 8 Pocket Pairs in 25 hands, plus 3/3 with 2/3 being sets?

[Spaggy]

I just played a heads up SNG, and got pocket pairs 8 out of 25 hands. I'll have to add these in, but during the other SNG I was playing I got 6 more pocket pairs during the 25 hands in the heads up, two of which matched exactly what I had on the other table.

Also, I had 44 followed by 44 (which hit a set on the flop), followed by 77 (which hit a set to lose to a turned straight). I've never had 2 sets in a row.

Not claiming rigged or fixed at all, but I've never seen anything like this. I have the hand histories that go along with this, but I'd rather just find out the odds of this before I post them.

[pococurante]

I had a run like that last week... maybe not quite as many pocket pairs in rapid succession, but I was flopping sets like crazy. Unfortunately I didn't get a lot of payoffs, but it was just insane seeing so many sets in a short period of time.

The formula for calculating "what are the odds of this happening in this # of hands" isn't that hard once you get used to it... here's how you find the standard deviation

sqrt(#ofHands x Odds x ReverseOdds)

which in this case is sqrt(25 x 1/17 x 16/17)
sqrt(1.384)
std deviation = 1.18

Your expected number of pocket pairs is 25/17, or 1.47. Then to find the odds of what happened, count the number of standard deviations you're off by, and use the chart at http://en.wikipedia.org/wiki/Standard_deviation

So for instance, you're about 68% to be in the range of 0.29-2.65 pocket pairs. 95% of the time you'll be between 0 and 3.83.

With 8 pocket pairs out of 25, you are 6 standard deviations away from the expected number. The odds of this are around 1 in 5,000,000. Guess you should have played the lottery instead that day...

[jay_shark]

The probability of getting 8 pocket pairs in 25 hands is :

(78/1326)^8*(1248/1326)^17*25c8=0.0000553 or 5.53 in 100 000 trials .

[jay_shark]

Also , the probability of hitting two sets in a row regardless of the outcome is :

a) The probability you've just hit a set on your previous hand : (78/1326)*2*48c2/50c3 = 0.00677 or about 6 in 1000 trials .

b) The probability you specifically hit 2 consecutive sets at any fixed point in time is : 0.00677^2 = 0.0000458

In other words , you are slightly more likely to get 8 pocket pairs in 25 trials than you are to hit two consecutive sets on your first two hands .