This is a poker story with a GQ attached, since its a long story im putting it in MPSIMS
I’m a pretty decent poker player, and good with numbers and probability which no doubt helps me.I play a fair amount online, which means I see a LOT of hands and am among the many not impressed when I hear the sob stories of AA vs KK, 4k beating boats or what have you. Seen it, Seen it Seen it.But today I was the beneficiary of a miracle. And I’d like to know if anyone can calculate how impossible what I just experienced was. Because I’m about to go all Jules from Pulp Fiction and give up the life over this.
ok-
3/6 No limit Cash Game, hold 'em. Im terrorizing the table with (some) good play and (a lot) of good luck. feeling pretty invincible and have turned a $100 buy in into $500. get my KK in the big blind. table folds to SB who has $300 or so. he raises to 12. Ive been a bit of a little punk so i raise it big, another 60, almost sure hell call me… if he has aces he’ll let me know, otherwise hes mine. And just as I hoped, he calls. Flop: 555. yeah, these happen every now and then, but I don’t usually love it as much I was loving this one. and then he actually forced me to think - he IMMEDIATELY went all in. 275 bucks. So I’ll skip my thought processes,all of which made me pretty confident that I had the best had and that he definitely didn’t have aces or a 5. i call. and the nature of cash games at this site kills the drama a little- they dont show the all in hands until after the river. Bottom line- he PLAYED me. he did have Aces and did all the things to make me SURE he didnt (playing like an idiot for the hour before must’ve all been part of his ruse too i guess) ok, so the end of the story is, after i call his all in, everything happens so fast you cant register whats going on, they speed through the turn and river and reveal the hands all in a blur, there’s a pause, and then they award the pot.
so here’s the board: 5 5 5 A 5… i see his aces and throw up a little in my mouth before i register what has actually happened, but as half the pot heads magically in my direction I soon catch on. I immediately leave the table and cash out. and now I’m left to ponder the odds of what just transpired, but I don’t even know how to begin to calculate them. can anybody figure out the odds of 2 people in a table of 9 having AA and KK and splitting the pot with 4 of a kind and an ace on the board? i’ve got a magic number in my head. If the true odds are larger than it, I vow to quit poker for good.
I don’t understand. If there’s a Royal (Flush?) on the board, anyone in the hand will necessarily split the pot, right? So if someone is in a position to bet at that point they’ve been in through several rounds of bidding and if they fold they lose their stake in the pot.
Or do you mean there was a possibiliity of it? If so, why is it foolish to think you’re just blowing smoke?
I’m heads up at the end of a large tournament, stacks are about even at 150K apiece, blinds are 5K-10K. I’m holding K-10os.
Flop comes QQQ. I bet 20K, opponent calls. Turn comes A. I bet 60K, and my opponent calls. Now I’m wondering if my opp. has an ace, or worse, the other queen, but he’s been making weak calls all night, so I didn’t really stress it.
River comes Q. So we both have the board, there’s no possibility that anyone is holding another hand, so on a lark I push all in. My opp. folds.
A couple of second go by, and into the chat window comes:
I think I can tackle this, but let me make sure I have all of the rules straight. There are a total of five cards face-up on the table, right? And each player has two face-down? How many players were there (about six, I’m guessing)? And the value of the 4 of a kind on the table isn’t relevant (so long as it’s not K or A), nor the other players’ hands, right?
In that case, the table is “holding” a four of a kind, at the standard 5-card-stud probability of 1 in 4164. Except it’s actually a little lower than that, since only 11 of the 13 ranks are available, so it’s 1 in 4921.09. Then, the fifth card on the table is an ace. That has a probability of 4 in 48 (since 4 cards of the deck are used up on the quad), or 1 in 12. This brings us to 1 in 59053.09.
Now we look at the players’ private hands. The probability of any given player holding both aces (given the cards already accounted for) is (3/47) * (2/46), but there are n players who could have this, so the chance of a pair of aces in someone’s hand is n0.002775, or 1 in 360.3/n. Finally, we also have someone holding two kings. The probability for any given player holding two kings is (4/45)(3/44), or 1 in 165, but there are (n-1) players who could have this, so it’s actually more like 1 in (165/(n-1)) (this isn’t quite right, but I’m neglecting the possibility that there are two players with a pair of kings).
Putting it all together, the chances of this happening are 1 in (3.51e9/(n*(n-1))). For n=6, this works out to 1 in 117 million. How’s that compare to your magic number?
The question is, I believe, given that 2 players have AA and KK, what is probability that 5 more random cards (don’t know poker terminology) are four of the same number and an A.
The selections of cards come from the 48 unknown cards, one by one, so the denominator of our fraction is 48x47x46x45x44.
The numerator for any one combination, by 55A55, will include the A taken from a set of 2, and the 5’s taken from sets of 4,3,2,1 respectively, giving 4x3x2x2 = 48 total.
There are 11 different types of card (2-Q) that can make up the four-of-a-kind, and 5 different positions the A can appear in, giving 55.
As the numerator and denonimators do not affect each other, this holds for any position of the A.
So, the total probability is (55x48)/(48X…X44) = 1 in 77,832.
I’m convinced that half the reason guys like poker is because it’s an excuse to talk like a character in a bad detective story. “I slammed him at 3/5, and I slammed him good”. Yeah, whatever, Mickey Spillane.
Absolutely…if you added up conversations between my friends and I, I’d wager that AT LEAST 50% of our conversations start with the words, “So I had AK in the big blind…right…”
Worst Beat Taken: 66 multi-way pot. Flop comes 654 rainbow. Checked around, I push I get two callers…and NOBODY HAS THE STRAIGHT! Guy turns over 54, and A6 suited. :dubious:
A6 suited goes runner runner to take down a 300BB pot.
Worst Beat Given: Three handed tourney. AQs I raise, get re-raised, I push all in. He calls with AA. Flop comes about as bad as I could hope T-4-3 rainbow. I go runner runner flush. I make $150, he only gets his money back.
Best Laydown: First hand of a $40 buy-in I get KK. Raise to 225 (blinds 25/50). MP caller and BB calls. Flop comes J-9-6 two diamonds. Pot is already big so I put in 525. MP pushes all-in :dubious: . BB CALLS! :eek:
I stand up and do a little Phil Hellmuth, “NO!” Both were VERY solid, after a preflop raise, what would I get a re-raise with, and then a CALL of the re-raise? I discounted AA since I didn’t get the re-raise preflop. Someone might have had J9 suited. Either way, the CALL tells me that there is NO WAY one pair is good in this situation.
So I turn over my KK and muck 'em. BB doesn’t even look at me…“THAT…was a MONSTER…LAYDOWN.” BB turns over 66 for a flopped set (MP had AJ).
I was in such disbelief, I honestly never considered how much egg I’d have on my face if I mucked them face up and was wrong. But as it were, I was right and came out looking like a poker pimp.
thanks, and to chronos too, for calculating this. my number in my head was 1 in 10 million… however i was wondering the odds of the whole situation happening as it did, not giving that theres AA and KK… what would the total adds be then, figuring in the odds of AA and KK being dealt to 2 players at a table of 9
