Hold'em poker hands simulation

[Erazman]

you don't even have to know the rules of poker to help me out.. this should be very simple math but i just can't figure it out...

10 players (including me) are dealt 2 cards each.

Of 169 possible starting hands, i only want to play 16 of the best hands (the remaining 153 hands i would fold).

so the setup is simple: my chances of getting a hand that i like is 9.467%.
but the question is: what are my ODDS of me being the only one in the Top 16?

 

[Erazman]

the only thing i know is the obvious: there's a 1:1 chance that ONE of the 10 players will be in the top 16 (if we round off to 10%), but that doesn't give me my answer :(

 

[Hurkyl]

Actually, it can't be done accurately without knowing the actual rankings of the hands -- the fact that person #1 has two cards that make up a top hand affects the odds person #2 can have a top hand (because those two cards aren't available to #2).

The best way to do this, though, is a computer simulation.

 

[Erazman]

can it be done at least semi-accurately without a simulation?

 

[Hurkyl]

Depends on what those 16 hands are.

 

[Erazman]

s = same suit

AA
KK
QQ
JJ
AKs
TT
AQs
AJs
AK
KQs
99
QJs
KJs
ATs
AQ
KTs

 

[Erazman]

would it really matter which hands belong in top 16? theoretically if the rules of poker all of a sudden changed, and different hands became "better" than others, the answer should still be the same should it not

 

[mattmns]

But there are more than 16 hands right? There are 6 ways to get an AA hand, 6 for a KK etc. Also, AKs there are 4 of these. 4 AQs, etc. This makes it a bit more complicated, unless you did something to simplify it that I did not see.

 

[Hurkyl]

Consider, as a hypothetical game, one where all sixteen of the best hands contain the ace of spades. Clearly, in this game, if you have one of these 16 best hands, it's absolutely impossible for anyone else as well.


Even with these sixteen hands, the odds still depend on which one you have -- having an ace and a king in your hand makes it harder for everyone else to have one of these top hands than, say, having a pair of nines.


I'm assuming a finite number of cards, though... probably one deck.

 

[Zach_C]

To further expand on the subject, the probability of 9.467 could only be used in the case of one player. Since you have a game of n number of players each dealt hand changes the probability of the remaining hands. Also in a ten person game the ratio is not 1:1 as probability can not be 100%. If there is a 1:7 chance of winning a pepsi give away will I win? Would I only win once?

To answer your question completely would require more statistics than I know (as I know none). I will look into it though.

 

[Erazman]

But there are more than 16 hands right? There are 6 ways to get an AA hand, 6 for a KK etc. Also, AKs there are 4 of these. 4 AQs, etc. This makes it a bit more complicated, unless you did something to simplify it that I did not see.

yes its all simplified.. ace of hearts mixed with ace of diamonds has the same value to me as ace of clubs mixed with ace of spades.. so i count it as one.. there's 169 total 2 card combinations if you look at it that way.

and Hurkyl, if i have KK, then someones chances of getting KK as well are split in half, but their chance of sitting in the "top 16" that i listed is only SLIGHTLY reduced by an insignificant amount that i really don't care about..

 

[kreil]

There are programs that can calculate the chances of other people having aces if you get dealt one (and it can obviously be expanded to include whatever you want). This information is always useless when playing though because you can get more reliable information by just paying attention to betting patterns and mannerisms.

kreil