Odds of set over set occuring?

[Unarmed]

Heads-up.
You put your opponent on a pocket pair and you have one as well. What are the odds of, given you hit your set on the flop, that your opponent will hit his by the river.

I'm looking to adjust my 7.5-1 hands odds for hitting sets with low PPs.

[stinkypete]

1-(45/47*44/46*43/45*42/44) = 1-((42*43)/(47*46)) = something

this factors in the possibility that he also hit his on the flop

[aloiz]

Not including the times that one of you hits four of a kind, the odds that your opponent makes a set by the river given that you made a set on the flop and your opponent has a pocket pair = 2 * C(44,3) / C(47,4) =~ 14.9%

As far as adjusting the odds heads-up for hitting a set with a low pocket pair, I think you're just wasting your time. First you can never be 100% sure that your opponent has a pair. And second, if you have a low pp and you think your opponent has a higher pair you shouldn't even play the hand, as you are about a 4:1 dog.

aloiz

[Unarmed]

[ QUOTE ]
if you have a low pp and you think your opponent has a higher pair you shouldn't even play the hand, as you are about a 4:1 dog.


[/ QUOTE ]

Really?
So if your opponent flips over AA preflop and you have TT, he raises 2% of your stack and has you covered, you're folding?

Not being sarcastic here, I would call that hoping to make the set of Ts and double up. Perhaps I need to adjust my thinking. But then perhaps you were thinking limit and I NL?

[aloiz]

Yes, I was thinking of limit and not no-limit. Your're right, in NL you have much greater implied odds so that call would obviously be correct.

aloiz

[Unarmed]

Thx aloiz.

Re: your initial 14% figure. That would be the probability of opp having the set on or after the flop correct? Wasn't sure by your post whether it meant that or the prob that opp hits his set on the turn or river. (i.e.: 4 cards not 2)

Really need to dig up my stats books.... [img]/images/graemlins/grin.gif[/img]

[aloiz]

Yup, on or after the flop.


aloiz

[DcifrThs]

[ QUOTE ]
Heads-up.
You put your opponent on a pocket pair and you have one as well. What are the odds of, given you hit your set on the flop, that your opponent will hit his by the river.

I'm looking to adjust my 7.5-1 hands odds for hitting sets with low PPs.

[/ QUOTE ]

http://www.math.sfu.ca/~alspach/mag86/

go there... dr. alpsach is a genius for combinatorics and he gets 1/167 assuming a few things...check it out.

-Barron

[Unarmed]

Thanks for the link Barron,
The 14.9% figure was the exact number I was looking for (prob given opp and you holding a PP that you both make the set by the river) but an interesting read nonetheless.

[smartalecc5]

THe odds that you are HU and you both have pocket pairs that both hit the flop is so minimal that I dont think it even really matters....