straight flush question

[DaBusiness]

On one site in particular i've had an astonishing amount of straight flushes. Now i'm not complaining, but my poker tracker stats say i would have had 14 straight flushes in 94,127 hands... of which i've only taken 5 to showdown (which i think is irrelevant). Now i'm led to believe the odds on a straight flush is 65,000-1 once seeing all cards.

Is there any maths whizzes out there that can find out the chances of getting 14 straight flushes in 94,127 hands?

EDIT: maybe a better question is the odds of more or equal to 14 straight flushes from any 2 random cards seeing all 5 community cards in 94,127 hands.

[BruceZ]

[ QUOTE ]
On one site in particular i've had an astonishing amount of straight flushes. Now i'm not complaining, but my poker tracker stats say i would have had 14 straight flushes in 94,127 hands... of which i've only taken 5 to showdown (which i think is irrelevant). Now i'm led to believe the odds on a straight flush is 65,000-1 once seeing all cards.

[/ QUOTE ]

Those are the odds for 5-card poker. For 7-card poker, the odds against a straight flush if you go to the river are

4*[8*C(45,2) + 2*C(46,2) + 7*44 + 2*45 + 8] / C(52,7)

=~ 3216-to-1.

The total number of 7-card hands is C(52,7). For each of the 4 suits, there are 10 5-card str8-flushes, 8 of which have C(45,2) ways to choose the other 2 cards, and 2 of which (with an A) have C(46,2) ways to choose the other 2 cards. There are 9 6-card str8-flushes, 7 of which have 44 ways to choose the 7th card, and 2 of which (with an A) have 45 ways to choose the 7th card. There are 8 7-card straight flushes.


[ QUOTE ]
Is there any maths whizzes out there that can find out the chances of getting 14 straight flushes in 94,127 hands?

EDIT: maybe a better question is the odds of more or equal to 14 straight flushes from any 2 random cards seeing all 5 community cards in 94,127 hands.

[/ QUOTE ]

The probability of 14 or more is given by the Excel function:

=1-BINOMDIST(13,94127,1/3217,TRUE)

=~ 99.937%.

So you would almost always expect to see more than you actually got in this many hands. Perhaps Poker Tracker only tells you about the ones where you use both hole cards. This would be C(5,2)/C(7,2) =~ 47.6% of all str8-flushes, and you would get 14 or more of these 57.8% of the time, so this seems more likely.