JJ all in raise EV question.

[thylacine]

I encountered the following playing in a tourney.

Suppose you are in a NLHE multitable tourney. (Actually this works with any NLHE, but this is where it arose.)

Suppose you are at a 9-handed NLHE table. Blinds are 1000/2000 antes 100. UTG player limps in making 5900 in pot. You are UTG+1 and you have JJ, and you move ALL IN with your stack of X chips.

Suppose all your opponents have you covered. Also assume that each opponent will call if and only if he has AA, KK, QQ, AK, or AQ and will fold otherwise. (No-one has folded yet so any of your 8 opponents could potentially call.) So you might win the pot uncontested, or you might have a showdown and win or lose depending on the 5 board cards.

What is your EV in the case you have X=10,000 chips.

What is your EV in the case you have X=250,000 chips.

For which value of X is this a break even play (and when is EV positive, and when is EV negative).

Feel free to make approximations.

Also say if you have access to some computer simulation and how you did it.

[akh911007]

Interesting. Will more than one opponent call you if they have the hand requirements, or once someone else has called, will they fold?

[thylacine]

[ QUOTE ]
Interesting. Will more than one opponent call you if they have the hand requirements, or once someone else has called, will they fold?

[/ QUOTE ]

That's an extra complication. Some simplifyimg assumptions might not change the answer much, but I'm not sure. Approximate answer is better than none.

[TableCaptain]

The probability that one opponent is holding AA, KK or QQ is ~1 in 74 (if my calc's are correct).

You now have eight opponent wich makes it ~1 in 9.
9 * 5900 (the pot pf) = 53,100.

since you win some times against an overpair. And overcards is only a slight dog,
I would estimate that you break eaven if you push with about 64,000 - 67,000.

[thylacine]

The calling hands are not only AA, KK, QQ, but also AK and AQ (s or not). Thanks tho for this approx.

[Indiana]

Let's build a prob. dist for Y= 'Amount Gained from pushing with JJ'...The prob that someone has one of AA,KK, QQ at your table is about .11, and here u win 20% of the time and lose 80% of the time...The prob that someone has AK or AQ is about .20 and here u will win about half the time and lose about half the time...Finally, there is .69 prob left and here you will pick up what is in the pot....Thus, the variable Y has the distribution (approximately):

Prob(Y=y)= { 5900 with probability p=.69

1180-.6x with probability p=.11

2950 with probability p=.20
}

Thus, E(Y)=.69*5900 + .11*(1180-.6x) + .2*2950 =

4790-.07x....Thus, if you have x=10,000 chips, your EV is
+4090....If you have x=250000 chips then your EV is -12710...Thus, you decision really depends on how much you have left and are risking...When is the break point? Well, just set 4790-.07x to zero and solve...Your answer is at x=68428...What does this mean?

It means that it might not be a great idea if you are in a healthy position, but probably a good one if you are getting shortstacked...If you are healthy, just raise enough to see if you are contested...If you are reraised you may just lay it down...

Later ,

Indiana

[thylacine]

Thanks.

It is surprising to me how big your stack can be relative to the blinds for this to be a +EV move. Intuitively I would have thought a 34XBB all in shmove with JJ in EP was nutty, but the numbers show it is solid.

It is high variance tho, so I guess that counts against it in tournaments.