Hand matchup calculation - multiway pots

[gulebjorn]

I've tried poker theory, I've tried probability, but got no answers.

Prove them ignorant small stakers [img]/images/graemlins/grin.gif[/img]

Here's the post:

I was just in a NLHE tourney where KQo pushed all-in after three limpers. I was sitting in the small blind with AQs and folded. Two limpers called, holding 44 and 33. Now let's say I called as well. What would you guess that the different probabilities of winning are for all four hands?

To get you started, here are some head-up matchups:

cards %win
4s 4c 50.67
Ah Qh 48.85

3s 3c 50.02
Ah Qh 49.44

Qs Kd 23.75
Ah Qh 75.15

4s 4c 78.48
3d 3h 17.83

So far, this is nothing special and most of you know these % by heart.

Now, what happens if we put these hands in a 4-way pot? I'm sure everyone sees that AQs and 44 are the big favorites, and that KQ and 33 don't stand much of a chance.

Before I let twodimes calculate it, I would have guessed that the probabilties of these hands in a 4-way pot would look something like this:

AQs 38%
KQo 13%
44 42%
33 8%

This distribution would mean that AQ and 44 remain a coinflip, with the pair as a slight favorite, AQ vs KQ is still 3:1, and 44 vs 33 remains 5:1.

But the twodimes result says:

cards %win
4d 4h 32.02
3s 3c 17.09
Kd Qh 17.90
Ac Qc 31.84

As you can see, suddenly AQs no longer dominates KQo as badly as it does headsup, and the probability of 33 winning in a 4-way pot remains almost exactly the same as heads-up. Also, I would expect AQ to do worse, because one Q is gone, and the K interferes with some of the straight possibilities.

So, anyone have an explanation for these differences?

And more importantly, does anyone know of an easy way to guesstimate these probabilities preflop? Lets say that in a tournament, there are two all-ins before you. You are holding AK and you assume that you are up against a small pair and some suited big cards. Is there an easy way of calculating the chance of you winning the race, if we know the numbers for the matchup of the individual hands?

Thanks a lot.

[kurto]

I know the value of pocket 3s didn't go down much because its winning percent is entirely based on it hitting a set which is likely to hold up most of the time. So you shouldn't expect too much deviation on that.

AQ still has a large leader over KQ... but both hands now have to face the possibility of losing to sets... so they but go down. Furthermore, the AQs has lost one of its flush outs in the 4 way.

Also, things like 1 card low straights which didn't exist before are now possible.

Finally, The AQ vs KQ... without improving, one of the 2 would win. Now, they both require improvement to beat the 4s.

[ajmargarine]

[ QUOTE ]
I know the value of pocket 3s didn't go down much because its winning percent is entirely based on it hitting a set which is likely to hold up most of the time. So you shouldn't expect too much deviation on that.

AQ still has a large leader over KQ... but both hands now have to face the possibility of losing to sets... so they but go down. Furthermore, the AQs has lost one of its flush outs in the 4 way.

Also, things like 1 card low straights which didn't exist before are now possible.

Finally, The AQ vs KQ... without improving, one of the 2 would win. Now, they both require improvement to beat the 4s.

[/ QUOTE ]

/end thread [img]/images/graemlins/smile.gif[/img]

nh

[gulebjorn]

[ QUOTE ]
I know the value of pocket 3s didn't go down much because its winning percent is entirely based on it hitting a set which is likely to hold up most of the time. So you shouldn't expect too much deviation on that.

AQ still has a large leader over KQ... but both hands now have to face the possibility of losing to sets... so they but go down. Furthermore, the AQs has lost one of its flush outs in the 4 way.

Also, things like 1 card low straights which didn't exist before are now possible.

Finally, The AQ vs KQ... without improving, one of the 2 would win. Now, they both require improvement to beat the 4s.

[/ QUOTE ]

But there's no fast way of estimating these numbers?

Ex. You're at the table with someone who goes all-in on his PP's, and only his PP's. You get AK. You know you are still a small underdog when he goes all-in.

Now this guy is a little shortstacked, there are a few limpers so there is dead money in the pot, and another guy doubles his bet by going all-in as well. For some reason you know that the second guy is holding JTs. What does this mean in EV terms? Has this become a +EV call? If not, how much dead money is required before this becomes +EV?

[gulebjorn]

[ QUOTE ]
/end thread

nh

[/ QUOTE ]

Not until you can answer this:

[ QUOTE ]
And more importantly, does anyone know of an easy way to guesstimate these probabilities preflop? Lets say that in a tournament, there are two all-ins before you. You are holding AK and you assume that you are up against a small pair and some suited big cards. Is there an easy way of calculating the chance of you winning the race, if we know the numbers for the matchup of the individual hands?

[/ QUOTE ]

[gulebjorn]

As for 33, in another forum someone else made the "they need a set to win, and they win when they hit it"-reply. I answered:

[ QUOTE ]
But when you add let's say Kh Qd and AcQc, (opposed to 33 vs 44) suddenly 33 has to dodge a lot more boards: anything with two Q's, A's or K's, any combination of ATJ or AKJ, any three clubs, any four hearts or four diamonds, all 555xA or 555xK flops and stuff like that...

[/ QUOTE ]

Wouldn't this make a difference?