Agonizing decision:

[EricW]

Hey guys, this is quite the agonizing decision as I do not know what to do. It's a 10+1 sit n go at PStars and I have a significant chip lead, and it's 3 handed so we're all ITM.

PokerStars No-Limit Hold'em Tourney, Big Blind is t200 (3 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

Button (t2825)
SB (t2685)
Hero (t7990)

Preflop: Hero is BB with K/images/graemlins/heart.gif, A/images/graemlins/spade.gif.
<font color="#CC3333">Button raises to t600</font>, <font color="#CC3333">SB raises to t2660</font>, <font color="#666666">Hero ???</font>, Button calls t2060.



First of all, I believe the button calls here so both will be essentially all in. Now the problem here is I don't believe neither of these two players are very good. I have such a large chip lead that once it gets down to heads up, I think I can outplay both of them. However, AK is a great hand and if I call and win, I make short work of the tourney. What would you do and why?

Now what do you do if you believe that the button DOESN'T call? And why?

Thanks all!

[AlphaWice]

Js Jh 0.456
Tc Td 0.183
Ac Kh 0.361

Ac Kh 0.341
Ts Td 0.461
Ad Qh 0.198

Ac Kh 0.538
Ks Jc 0.224
Ad Qh 0.239

Im an idiot, so I'll let those speak.

[junkmail3]

Push if the button's going to call. Push if the button isn't going to call.

you're ITM and have a great hand. There really is no reason not to push. And if you lose, you're still chip leader (almost).

[Onaflag]

I can think of no reason whatsoever for anything other than a push. If you can't push AK, what, then, will you push? You more than likely have the best hand right now and if you don't, its a coinflip. Push.

Onaflag.............

[schlach]

I guessed "Push" and then crunched the numbers, and by my mongoloid math, it came to $42.13 Push vs. $41.79 Fold, assuming he's equal to or a little worse than you. So, perhaps that's why it was an "agonizing" decision -- it was six one way and half a dozen the other.

Your assumption is that the button always calls, but after crunching some more numbers, it looks like 'Push' is always correct, no matter what the button does.

Hero starting EV $39.83
Hero folds, button calls: $41.79
Hero pushes, button calls: $42.13
Hero folds, button folds: $39.53
Hero pushes, button folds: $42.16

The math:

I started with the assumption that they both have Sklansky Group 4 hands or better. Then I decided that T9s is pretty unlikely, so I removed suited connectors lower than KTs. I crunched it (Monte Carlo) using that excellent java app, PokerCalculator, and found that you had about 36.38% to win, and they each had 31.75% or so. Then I figured,

Fold (bar tie):
.5
Sb: 0
Button: 5510
Hero: 7990

.5
Sb: 5370
Button: 140
Hero: 7990

Which, with a little handwaving, worked out to about $41.49 EV.

Push:
.364
Hero: 13,500

.636
Hero: 5165
Button: 8385
Sb: 0

And again I'm simplifying and assuming that one of the other players will end up with all the chips.

.364 x $50 + .636 x ( .382 x $50 + .617 x $30 ) = 42.13

Here's my scratch pad, if anyone wants to check my math.

Starting EV:

Button wins .209
places .405 = (.513 x (1-.209))
shows .385

Sb wins .199
places .390
shows .411

Hero wins .592
places .205
shows .204

Hero starting EV $39.83
Hero folds, button calls: $41.79
Hero pushes, button calls: $42.13

Hero folds, button folds:

Hero: 7790
Sb: 3485
Button: 2225

Button wins: .165
places: .325
shows: .510

Sb wins: .258
places: .453
shows: .289

Hero wins: .577
places: .222
shows: .201

Hero EV: $39.53


Hero pushes, button folds:

Hero wins 57.35%, loses 42.65%

.5735
Hero: 11275
Button: 2225

Ev: .835 x $50 + .164 x $30 = $46.70 x .5735 = $26.78

.4265
Hero: 5305
Button: 2225
Sb: 5970

Button wins: .165
places: .247
shows: .588

Hero wins: .393
places: .428
shows: .179

Sb wins: .442
places: .325
shows: .233

Hero EV: 36.07 x .4265 = $15.38

15.38 + 26.78 = $42.16