1 hand vs one player with 2 hands

[Xhad]

My point was that playing this scenario like a 10-handed game (assuming no other players) means you are going to be folding so much that you can't possibly keep up with the blinds.

[ QUOTE ]
Any hands that has an equity edge vs 2 random hands.

[/ QUOTE ]

The difference here is that your opponent has additional knowledge about 2 of the cards in the deck.

So, for example, lets say he is dealt JJ into one hand and JJ into the other - he now knows that he has lost his 2 outs to the set.

Similarly, lets say one hand of his is 4 [img]/images/graemlins/club.gif[/img] 4 [img]/images/graemlins/spade.gif[/img] and the other is 7 [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/spade.gif[/img]

The flop comes 8 [img]/images/graemlins/spade.gif[/img]9 [img]/images/graemlins/spade.gif[/img]T [img]/images/graemlins/spade.gif[/img] - assuming he chose to play the 44, he now knows that 2 of the cards needed for the straight are gone, as are 3 of the cards needed for the flush - those are 4 extra outs that he has knowledge of.

I don't know how you quanify that as a basic principle - because it will affect you differently on different hands - sometimes the discarded hand will have no value whatsoever.

[Kaeser]

[ QUOTE ]
Any hands that has an equity edge vs 2 random hands.

[/ QUOTE ]

I don't think that's right. The problem is that when you are up against 2 random hands you are assuming that 2 opponents are contributing money to the pot.

yea, i'd take the two hands. the knowledge of the outs is important too. interesting topic

First, some statistics theory.

Assuming for a moment that you could list in order aof value all 2 card poker hands, and that these are roughly evenly distributed, then your average hand would be worth 0.5 on a scale from 0 to 1. Your oppenent's average hand will be worth about 0.667 on a scale from 0 to 1. I don't have any theory to back up the 0.667 number, it's based on a quick computer simulation. Furthermore, your standard deviation would be about 0.29 and his 0.23. So not only are his hands considerably better on average, they are somewhat tighter. Also, he will have a better than average hand 75% of the time, and a better hand than you 67% of the time.

Another way to look at it is that, assuming he goes with his highest card or pair most of the time, your opponent will have the following hands:

pocket pair = 12%
A high = 28%
K high = 19%
Q high = 14%
J high = 10%
other = 17%

His median hand will be something like K9 or KT.

I'm therfore tempted to say that you should play hands that are worth calling a raise with heads up.

[ QUOTE ]
I don't think you guys understand me. I think there shouold be a way of calculating the exact hand group that is a favorite in this case.
I did some calculations, and I came to the conclusion that the top 50 "all-in-heads-up-race-hands" shod have an +EV, when the other player can chose to play the best out two seprate hands.

+EV:
[4[img]/images/graemlins/spade.gif[/img] 4[img]/images/graemlins/diamond.gif[/img]],
[A[img]/images/graemlins/heart.gif[/img] 2[img]/images/graemlins/heart.gif[/img]], [A[img]/images/graemlins/club.gif[/img] 4[img]/images/graemlins/spade.gif[/img]],
[K[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/heart.gif[/img]], [K[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/diamond.gif[/img]],
[Q[img]/images/graemlins/diamond.gif[/img] 9[img]/images/graemlins/diamond.gif[/img]], [Q[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/club.gif[/img]],
[J[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/spade.gif[/img]] or better.

But I'm not sure if my numbers are right

[/ QUOTE ]
I think my analysis leads me to a very similar result. Your range above pretty much equals your opponent's expected range.

[Moozh]

I think a more interesting question would be to ask people how much they'd be willing to pay per hand to get an extra hand.