AA cracked twice in one hand--how bad is this beat?

[feelixthegreek]

Playing the 1-2 NL at Foxwoods, I'm dealt AA in the cutoff. Before it gets to me, there's been a raise ($10), a reraise($20), and a cold call($20). I've got about $95 in front of me, and go all-in. Original raiser calls with the rest of his stack (around $45), reraiser folds, cold-caller calls me and has me covered.

Original raiser shows KK. Cold caller shows 88.

Flop brings a K, so the main pot goes to KK. Competing for the side pot, I lose when an 8 hits the river.

These things happen. But I wonder what the odds were against such a scenario taking place. It's probably easy math for most of the folks on this forum. Thanks in advance.

[Cobra]

In this situation you need to have a board that has one K, one 8, and no Ace. Also the board cannot pair or you would have multiple full houses.

Total Boards for 46 unknown cards

=combin(46,5) = 1370754

Boards with the above combinations

=2*2*combin(10,3)*power(4,3)= 30720

Probability of this occurring =30720/1370754 = .0224 or
1 in 44.6 times.

Cobra

[KegNog]

Are you sure the possible hands for this board is 46 nCr 5, or 1370754? You know that a K and 8 must be present w/o any ace, therefore 2 cards are already on the board (the K and 8) and the other 4 aces are removed as well, leaving only a randomized 3 card draw from a deck of 42 cards (taking into account that 3 K's, 3 8's and 4 aces are already used).

I'm not the best at these calculations just yet, but I think the total possible hands would be 42 nCr 3, or 11480.

Please confirm

[Cobra]

As you can see from my number of posts I am new to the probabilities area as well. That said I do believe I did the math correctly. Hopefully one of the other guys will confirm which one of us is correct. In order to find out the probability of his situation to occur you must take the number of boards that has his specific requirements and divide by the total number of boards that are available from the unseen cards. Like I said hopefully someone else will look at this and tell us if it was done properly.

Cobra

[gaming_mouse]

[ QUOTE ]
Are you sure the possible hands for this board is 46 nCr 5, or 1370754?

[/ QUOTE ]

Yes, Cobra is correct about that. Your objections don't apply because we are concerned with ALL possible boards -- thus there are no constraints. You are describing the conditions of the boards in which this rare event occurs, which would therefore affect the answer of the numerator, not the denominator, of Cobra's calculation.

Also, I'm not sure why you guys added the constraint of the board not pairing. The OP's aces would still lose in this case (just to a boat instead of to trips).

Finally, a question a interpretation. Cobra answered the question "What is the chance of getting beat, given the original starting hands?"

It seemed to me that the OP might also have been asking: "What is the chance of my getting aces, someone else getting kings, a third person getting another pair (eights or better?), and then me still losing?" Just another possibility.

HTH,
gm

[MortalWombatDotCom]

i just hacked my hand calculator code to allow me to figure out how often a hand comes in last place (instead of first). running A/images/graemlins/club.gifA/images/graemlins/spade.gif against K/images/graemlins/heart.gifK/images/graemlins/diamond.gif and 8/images/graemlins/club.gif8/images/graemlins/diamond.gif i get

.56% a tie for last (which players tie for last isn't specified)
4.78% the aces come in last (this is the situation you had)
19.12% the kings come in last
75.54% the 8s come in last

this doesn't care if the Ks and 8s beat the As by each hitting their set, or (in this case) by catching four diamonds to make the flush, or 9TJQ to make a straight, or anything else i may have overlooked. it just sees who comes in last for every possible board if all three hands stay to the river (as they will when two are all in before the flop). so almost one time in twenty, AA vs KK vs 88 will lose both the main and side pots. assuming i have no bugs in my code.

also, changing 8/images/graemlins/club.gif to 8/images/graemlins/heart.gif bumps the losing % up to 5.16%, so suit selection is non-trivial.

if you want to know how often both players will beat you specifically by hitting their set, or something else even more specific (like the K hits on the flop AND the 8 hits on the river), then i concede that combinatorial counting is a better approach, but it's not clear to me that people agree on what it is they should be counting.

[feelixthegreek]

Thanks for the calculations. I needed some cold numbers to offset the burning sense of injustice I felt when it happened.

[Blackjack]

What a great game! 88 calling an all in preflop.

I never find great games like this at Foxwoods - mostly because I play the 5-5 which is filled with chip spewers or supertight aggressive sharks.

Yee haw,

Blackjack

[feelixthegreek]

I was plenty happy to get the call, believe me. I was looking to get paid over 3-2 on a hand where I was a ridiculous favorite. Oh well, the next nineteen times I get called like that maybe I'll win.

[other1]

I had AA double cracked last night myself.

All in preflop. 2 callers (both covered me).

Main pot goes to a guy who pulled out a one card flush (4 diamonds on the board, I had AhAs).

Side pot went to someone who flopped 2 shitty pairs like 7s+10s.

C'est la vie.