Likelihood of a better hand????

[malfaire]

This should be pretty complex and I'm pretty sure that nobody has done work on this, or at least published it (correct me if I'm wrong).


Scenario: I have AcTs UTG. There are 6 other players in the hand. What is the likelyhood that I have the best hand preflop at this moment? We will define a "better" hand as being ATs, AJo+, 77+ AND ATo (they'll have position advantage, and we'll assume this advantage for SB and BB as well to keep things simple).



Can anyone answer this question to an accurate degree (say +/- 1%).

[kev]

There are 4 ATs, 12 AJo, 12 AQo, 12 AKo, 4 AKs, 6 AA, 6 KK, 6 QQ, 6 JJ, 6 TT, 6 99, 6 88, 6 77.

50*49/2=1225 combinations for the next player
48*47/2 combinations for the next player etc
you do the sums

[MCS]

Kev, I'm not sure I understand your post, but I think it's wrong. [img]/images/graemlins/frown.gif[/img]

[kev]

It's easy to work out. Just work out the probability of the first opponent having a better hand (which we call a1). Then the probablity of the second guy having a better hand (a2) etc
The likelyhood that you have the best hand preflop is
(1-a1)*(1-a2)*(1-a3)*(1-a4)*(1-a5)*(1-a6)

[SamIAm]

[ QUOTE ]
It's easy to work out. Just work out the probability of the first opponent having a better hand (which we call a1). Then the probablity of the second guy having a better hand (a2) etc
The likelyhood that you have the best hand preflop is
(1-a1)*(1-a2)*(1-a3)*(1-a4)*(1-a5)*(1-a6)

[/ QUOTE ]Except the way in which you satisfy a1 matters for a2. For instance, if Opp1 had A9, there are more ways for Opp2 to be bad than if Opp1 had 79.

[ QUOTE ]
This should be pretty complex and I'm pretty sure that nobody has done work on this, or at least published it (correct me if I'm wrong).

[/ QUOTE ]Another thread with the (almost) exact same question is currently right next to this thread in the list. [img]/images/graemlins/smile.gif[/img]
-Sam