Bubble dilemma

[McBandit]

4 people left in a 55+5 single-table PP tourney.

UTG: 200
Hero (button): 1300
SB: 4300
BB: 4200

blinds 250/500

UTG folds to me, I have AKo. Raise or fold?

I really thought about this one and ended up folding. The short stack ended up winning his BB and I ended up third. Was I right to hold back on this one?

[DrSavage]

No. You'd be happy to pick up the blinds and you are very likely to get called by any ace/ any king. If you get called and win you'll have over 3000 chips which would put you in contention for the first place. You need a much smaller stack to consider a fold here.

[rachelwxm]

Using independent chip model here is the equity for different situations:
1. you fold AKo equity=23.5 close to 3rd payout
2. you push and they both fold equity=27.4
3. you push and win the all in assuming sb call, this should not make a big diff. equity=31.8

if you push and only get called by 25% of the hands either by sb or bb, you are 1.7:1 favorate, there is roughly 46% of chance either sb or bb has that hand. There fore, your average equity if you push is
54% * 27.4+46%*1.7/2.7*31.8 = 24

So it’s marginal, but push is slightly better. I would also just flat call bb just hope to slow play when you hits the flop but if you are push against, you have to call all in.

[tallstack]

It is interesting how marginal of a benefit that pushing with AK has from the button here. Since the ICM does not take into consideration the fact that the small stack is all-in on the very next hand, this marginal benefit may be eroded by the likelihood that the small stack busts out next hand.

Analysing the bust out potential requires a lot more assumptions, but if we put in some plausible numbers for the small stack winning the next hand (say 25% chance he doubles up, 15% chance he triples up, and 60% chance he busts out), then what does that do to our numbers?

I have evened out the two big stacks here because we are not sure what happened on the AK hand. If we assume equal stacks for them then:

Short stack doubles up
Player Chips 1st 2nd 3rd 4th Equity
A 400 0.040 0.063 0.166 0.732 0.07195
B 1300 0.130 0.190 0.472 0.208 0.21637
C 4150 0.415 0.374 0.181 0.030 0.35584
D 4150 0.415 0.374 0.181 0.030 0.35584

Short stack triples up
Player Chips 1st 2nd 3rd 4th Equity
A 600 0.060 0.091 0.213 0.637 0.09971
B 1300 0.130 0.185 0.410 0.275 0.20251
C 4050 0.405 0.362 0.189 0.044 0.34889
D 4050 0.405 0.362 0.189 0.044 0.34889

Short stack busts out
Player Chips 1st 2nd 3rd 4th Equity
A 0 0.000 0.000 0.000 1.000 0.00000
B 1300 0.130 0.200 0.670 0.000 0.25902
C 4350 0.435 0.400 0.165 0.000 0.37049
D 4350 0.435 0.400 0.165 0.000 0.37049

With these assumptions, we would have a $equity of .25*.216 + .15*.203 + .60*.259 = .240.

I think that my assumptions here are open to a lot of uncertainty, but it may be that there is as much gain in $equity by waiting for the next hand to bust the small stack as there is in pushing here.

Prior to looking at your analysis and the bust out estimation above, I would have thought that pushing with AK would be the better move. I still think it is pretty weak to fold it here, but the numbers show it has merit. Even if my assumptions here are out to lunch, you don't gain that much pushing in this situation. Very interesting.

Dave S

[rachelwxm]

If we assume sb will call all in with any two, then a fold is in order since AK is not even 2:1 favorate against any random hand and the equity for push drop to 20.8. /images/graemlins/cool.gif