Fun Hand, Odds Approach?

[LetYouDown]

Fun Hand

Just messing around in a $10+1 Omaha 8OB Limit Tournament. Generally limping/raising UTG with ANY A-2 is effective...as you get 6-9 callers most of the time and even if you get 3/4'd you can profit. Regardless, was just messing around anyway trying to kill time.

Got me to wondering, how would you express the odds of this happening? The math isn't overly challenging but it's really a question of whether it's more accurate to think of its rarity in terms of "pre-cards" or "pre-flop". Obviously there are a lot of hands where a 7 card straight flush isn't even possible.

Random sidenote for those considering playing Omaha. It was capped on the river and no one folded. I scooped. No one even had an A-2.

[BruceZ]

[ QUOTE ]
Fun Hand

Just messing around in a $10+1 Omaha 8OB Limit Tournament. Generally limping/raising UTG with ANY A-2 is effective...as you get 6-9 callers most of the time and even if you get 3/4'd you can profit. Regardless, was just messing around anyway trying to kill time.

Got me to wondering, how would you express the odds of this happening? The math isn't overly challenging but it's really a question of whether it's more accurate to think of its rarity in terms of "pre-cards" or "pre-flop". Obviously there are a lot of hands where a 7 card straight flush isn't even possible.

Random sidenote for those considering playing Omaha. It was capped on the river and no one folded. I scooped. No one even had an A-2.

[/ QUOTE ]

nh

Any 7 cards:
4*[(6*C(43,2) + 2*C(44,2)) + (5*42 + 2*43) + 6] / C(52,9)
= 120,830-to-1.

4 in hand, 3+ on board:
4*[(6*C(43,2) + 2*C(44,2))*C(7,4) + (5*42 + 2*43)*C(8,4) + 6*C(9,4)] / C(52,4)/C(48,5)
= 417,886-to-1.

The 3 summed terms are for 7,8 and 9 card str8-flushes of which there are 8, 7, and 6 respectively in each suit. For the 7 and 8 card cases, the 2 with an A are separated since the number of remaining cards is 1 more.

[LetYouDown]

Thanks for that breakdown. My friend was sitting next to me and I said "how funny would it be if the 4 of hearts came on the turn?". Sure enough, there it was. My plea for the 8 of hearts on the river went unheard. Oh well, still a fun hand. I fully expected to 3/4 someone...which is disappointing when you have such a ridiculously good hand.