

What's the odds of this happening? Only happened twice to me





It happened, so by definition the probability is 100%.
. The probability of 7s and Jd hitting the board after the flop is the same as 2c and 7h hitting. Allin preflop you win 45% of the time. Most of them won't be this dramatic. But, other than having something to talk about it is 100% meaningless. You had the villain with 7 bbs out stacked by 3:1 and you are ~even stacks if he wins. Nothing but super standard play here. 




Hi MCFISHY6,
Without any information about the opponent and tournament stakes. It looks like your are heads up in a 6max game, level 50/100 and the villain has 7bb behind and you have them well covered. A close call... just maybe! There are far better HA peeps than can help. 




I'm not sure but it's huge. I tried to work it out and came up with 270.6 million to 1 which seemed a bit much so I don't know. Maybe someone that's more into poker math can work out what it really is.





Although Fadyen's calculation seems highly accurate, I did some poker math.
If you are referring to hitting a straight flush, they are something like 72.193 to 1. Now four of a kind odds are like 4.165 to 1. So I guess that we have to multiply them (that's what I always like to do with big numbers). And the results for the odds of this exact situation are 300.683.845 to 1. Or I am completely wrong, not sure yet. 




I'm unsure how to do the maths but I think those numbers are off. I don't think you can multiply them because they are 2 unrelated events. Or if they are related then its a much lesser number.
Pokerstars has dealt over 100,000,000 hands but by your reckoning a straight flush v 4 of a kind has been dealt just 3 or 4 times on the site? I'm sure it's a helluva lot more than that imo. Probability theory really interests me, can anyone suggest a good poker book on the subject? Bracelet Winner





The odd should change depending on the number of players at the table but tbh I have no idea how to work that out. But the fact it's a heads up should mean it's less likely? hence the huge number. And it would have happened about 407 times on the site by that math.
I think we need to find a math wiz. 




Look what I stumbled upon (looking for an entirely unrelated question)
http://wizardofodds.com/askthewiza...m/probability/ What are the odds of having two four of a kinds and a straight flush dealt to the same player in a Texas hold 'em game with ten players in 50 hands? — Paul from Toronto, Canada The probability of a four of a kind in seven cards is 0.00168067, the probability of a straight flush is 0.00027851. If x is the probability of a four of a kind and y is the probability of a straight flush then the probability you ask for is combin(50,2)*48*x2*y*(1xy)47. The answer comes out to .0000421845, or 1 in 23,705. Bracelet Winner





Quote:
Not necessarily. As question was phrased, the only mathematically correct answer to the question is the first one in my initial response. Any other answer assumes what the OP may have meant with their question. Probabilities are based on the information at hand. So as the information changes so do the probabilities. It terms of poker analysis, this hand is essentially a coin flip with neither player making a mistake in absence of reads. So the question comes down to the drama here and the answer depends on what point to begin. Since there is no drama until after the flop, let's start there. There are two outs for the OE strait flush. With 45 unknown cards one hits on the turn 4.4% of the time. No drama here. The probability of the case J hitting is 2.3%. Again not dramatic. The probability of those two events occurring in either order is just over 0.2% so the odds are ~500:1 against. Situations analogous to this happen several times daily on Stars alone. The answer to that flop hitting the board is a bit more time consuming. If someone asks I'll outline the path to the answer. 




The number will be monstrously large, but it depends on how you frame the question.
If the question was something like "What is the probability that on the next hand dealt, one of us makes a straight flush while the other makes four of a kind without a pocket pair in his hand?" then you can get fairly close to the right number by multiplying the odds against making a SF and the odds against making quads. Straight flush odds are roughly 3600 to 1. Quad odds are 594:1 (I think Gambling Prop based his odds on 5card poker, but in Holdem we use 7 cards). Multiplying the two numbers is roughly the probability that both hands are made, and that's 2,138,400 to 1. The true odds for these particular hands would actually be (much) higher, because it's a lot harder to make a straight flush if there are three cards of the same rank on the board. To calculate the true probability, you'd have to count all the possible board textures that don't make quad jacks and don't make a straight flush for 98s (around 130 million boards), and calculate how many that do. I'd estimate that this situation occurs about once every 3 million hands. Bracelet Winner





I've been playing poker for like 1 month now (I'm pretty new) and I've dealt with this situation. Too bad that I had the 4 of a kind card





Well going by Arty's calculations I think I may have been on the right track but made a mistake somewhere and got 270mil rather than 2.7mil. Slightly higher than his first answer but the off of quads are higher for nonpocket pair hands.
And I still think the real odds do change based on number of players at the table as the more players the less likely suited connector hands are played and so on. I know you shouldn't really count that but really these things do become a factor in the real world. 




Fayden,
If you use PT, HM or another similar program please do this exercise: Look for the % of hands you are dealt a pocket pair by the numbers of players dealt. If you don't use on, deal out 200 hands each headsup, 6 players and 10 players and keep track of the pocket pairs. The expected value is just shy of 6% by either method. 




I don't deny that Joe. However I would be playing small pockets and suited connectors a lot less in full ring but every time heads up. The shorter handed you get the wider range of hands will be played by all players therefor the more opportunities for hands to be made. The point I'm trying to make is people fold hands so in reality the calculation will be off from the real result so in fact empirical data would be better. I guess that's a whole other story though.





Why are you bringing hand value relative to table size into the discussion. Those two are as different as apples and cattle. That hand values change as the number as players change pretty basic and has no relevance to the OP.
Would you care to try another diversion? BTW, speculative hands played cheaply are generally more profitable against more opponents as there are more opportunities to be paid off when properly played. 




You're right it's not relevant to the OP and I did say "I guess that's a whole other story though." I was simply trying to defend my earlier point by explaining more what I meant. And my earlier point about odds being different for different number of players I think is relevant as I was wondering whether we should, if even possible, consider such factors. But that's probably getting far too complicated and since in this case it's a heads up anyways I suppose it doesn't matter.





Relative hand values are necessary components of the situational analysis/awareness. I hope I did not lead anyone to think they were not important. You're not a complete poker player with out that knowledge.



