Poker Math Question

[The Sweeney]

Can someone please provide a solution and, hopefully, win me a pint. Playing a home game the other night, my friend and I were both dealt AA when heads up. He claimed the odds of this were 48,840 to 1, whilst I believe them to be 270,274 to 1. Who is correct?

[Moskvich]

270,724 to 1 is the correct answer to a question that you aren't asking and which probably isn't the right question anyway... 1,224 to 1 is the right answer to a better question. Other possible questions would need to factor in stuff like how many hands you played heads-up. Which question are you asking..? 

He's not right though, whatever the question...

[kinboshi]

50/50 is the correct answer.

[TheChipPrince]

52/4 /3 x51 /2 x50 /1 x49

[The Sweeney]

270,724 to 1 is the correct answer to a question that you aren't asking and which probably isn't the right question anyway... 1,224 to 1 is the right answer to a better question. Other possible questions would need to factor in stuff like how many hands you played heads-up. Which question are you asking..? 

He's not right though, whatever the question...

Sorry, to be precise, I am referring to one heads-up hand in isolation, the odds of both players having pocket rockets? Does that help? 1,224 to 1 refers to?

[Moskvich]

Well the point (which comes up endlessly) is that you only choose to ask the question once you've already noticed that it's happened. So yes the chance of it happening on that hand was 1 in 271k. But you would presumably still have asked the "omg what are the chances" question if it had happened on a different hand in your game, so maybe a better question would be what the chances were of it happening in your game. But then you could extend that to any time you played ever. Which would make the chances much higher again. Or you could ask what the chances were of him having aces once you've already been dealt aces, which is what needs to happen for you to be surprised that he has aces, and that would be only 1,224 to 1.

[MereNovice]

Can someone please provide a solution and, hopefully, win me a pint. Playing a home game the other night, my friend and I were both dealt AA when heads up. He claimed the odds of this were 48,840 to 1, whilst I believe them to be 270,274 to 1. Who is correct?

As has already been stated you are correct, i.e. before a card is dealt, the odds of two heads-up players both being dealt pocket aces in Texas Hold 'Em (from a standard randomised 52 card deck) is 270,724 to 1.

48,4840 to 1 would be the odds of you being dealt pocket aces on two consecutive hands (before any cards are dealt).

[Jon MW]

fyp

[gatso]

Well the point (which comes up endlessly) is that you only choose to ask the question once you've already noticed that it's happened. So yes the chance of it happening on that hand was 1 in 271k. But you would presumably still have asked the "omg what are the chances" question if it had happened on a different hand in your game, so maybe a better question would be what the chances were of it happening in your game. But then you could extend that to any time you played ever. Which would make the chances much higher again. Or you could ask what the chances were of him having aces once you've already been dealt aces, which is what needs to happen for you to be surprised that he has aces, and that would be only 1,224 to 1.

yeah, this. there's a thread that's about 3000 pages long somewhere with me trying to explain this concept

[SuuPRlim]

Moskvich yet to see a disappointing post from you lol
 
 

[Moskvich]

Er, thanks lol ... I'm sure there are plenty of shit ones though, maybe just running good. I ain't no thetank...

[SuuPRlim]

Er, thanks lol ... I'm sure there are plenty of shit ones though, maybe just running good. I ain't no thetank...

no modesty please im sure you'll say something stupid eventually lol just bask in the compliment till then :p

[George2Loose]

How did the hand play out?

[sovietsong]

fyp

this