Re: UB $5.50 - Non-Results-Oriented Push Check
 

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Math, please. This cannot possibly be correct. TT is 3:1 over any 2. The bubble is over.

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To quote Tigerite, ITM is like a mini-bubble.

If Hero folds, stack sizes look like this:
6420
3030
5520 (Hero) (34.77%)

If Hero calls and wins, stack sizes are
3030
11940 (Hero) (45.95%)

Hero needs to win 75.67% of hands when he "calls the all-in" to break-even. Calling a push of any two with TT doesn't get him there. Is my math off?

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I think it is. Check mine and see if it makes sense.

You're ignoring the fact that hero has 20% of the prize pool if he calls and loses. It's a bit complicated here b/c hero has villain covered by 100 chips (and the chip amount adds to 14970), but let's use the OP's numbers.

Possible results:

Hero folds: 34.77% of prize pool, as you calculated.
Hero calls and wins: 45.95% of the prize pool, as you calculated.
Hero calls and loses: (V-11640),(SB-3030),(H-100), Hero has 20.47% of the prize pool. I'm rounding this to 20% for sanity purposes

Hero's total equity from calling is (%win)*(.4595) + (%lose)*(.2).

Since %lose = (1-%win), for calling to break-even,

.3477 = (W)*(.4595) + (1-W)*(.2)
.3477 = (.4595)W -.2W + .2
.1477 = (.2595)W
.5692 = W

So, hero has to win 57% of the time when he calls. If Villain is pushing any 2, we're talking about something like the top 20%: 55+,A7o+,A3s+,KTo+,K8s+,QJo,QTs+ that we need to call. Of course, we need a bit more hand than this, b/c V's not pushing any 2, but we need a bit less than that b/c V will fold to our push fairly often here. Going the other way, unless V is raise/calling all in with about his top 17% (66+,A5s+,K9s+,Q9s+,JTs,ATo+,KTo+,QTo+), we have the necessary equity here. Hopefully this bit of handwaving suffices b/c I think it's pretty clear that if the 57% number is correct, then TT is plenty of hand here.

Re: UB $5.50 - Non-Results-Oriented Push Check
 

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You're ignoring the fact that hero has 20% of the prize pool if he calls and loses.

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That's all you had to say. I'm used to doing the math on the bubble. Sorry for the trouble.

I feel a lot better that my insticts (and OPs') were right. Thanks again, parappa.

Re: UB $5.50 - Non-Results-Oriented Push Check
 

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You're ignoring the fact that hero has 20% of the prize pool if he calls and loses.

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That's all you had to say. I'm used to doing the math on the bubble. Sorry for the trouble.

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Yeah, I figured that when I got about halfway through my post, but by then I was having too much fun to stop. It's been a while since I worked one of those through. [img]/images/graemlins/smile.gif[/img]

Re: UB $5.50 - Non-Results-Oriented Push Check
 

[ QUOTE ]
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[ QUOTE ]
Math, please. This cannot possibly be correct. TT is 3:1 over any 2. The bubble is over.

[/ QUOTE ]

To quote Tigerite, ITM is like a mini-bubble.

If Hero folds, stack sizes look like this:
6420
3030
5520 (Hero) (34.77%)

If Hero calls and wins, stack sizes are
3030
11940 (Hero) (45.95%)

Hero needs to win 75.67% of hands when he "calls the all-in" to break-even. Calling a push of any two with TT doesn't get him there. Is my math off?

[/ QUOTE ]

I think it is. Check mine and see if it makes sense.

You're ignoring the fact that hero has 20% of the prize pool if he calls and loses. It's a bit complicated here b/c hero has villain covered by 100 chips (and the chip amount adds to 14970), but let's use the OP's numbers.

Possible results:

Hero folds: 34.77% of prize pool, as you calculated.
Hero calls and wins: 45.95% of the prize pool, as you calculated.
Hero calls and loses: (V-11640),(SB-3030),(H-100), Hero has 20.47% of the prize pool. I'm rounding this to 20% for sanity purposes

Hero's total equity from calling is (%win)*(.4595) + (%lose)*(.2).

Since %lose = (1-%win), for calling to break-even,

.3477 = (W)*(.4595) + (1-W)*(.2)
.3477 = (.4595)W -.2W + .2
.1477 = (.2595)W
.5692 = W

So, hero has to win 57% of the time when he calls. If Villain is pushing any 2, we're talking about something like the top 20%: 55+,A7o+,A3s+,KTo+,K8s+,QJo,QTs+ that we need to call. Of course, we need a bit more hand than this, b/c V's not pushing any 2, but we need a bit less than that b/c V will fold to our push fairly often here. Going the other way, unless V is raise/calling all in with about his top 17% (66+,A5s+,K9s+,Q9s+,JTs,ATo+,KTo+,QTo+), we have the necessary equity here. Hopefully this bit of handwaving suffices b/c I think it's pretty clear that if the 57% number is correct, then TT is plenty of hand here.

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On the ITM "bubble" I actually use 0.75/0.25/0 as the payouts, because everyone has the $20 "tied up". Not sure what difference that would make to these calculations, I guess I'll do them later or something.

Well ok so I decided to now..

Fold EV = 0.3692
Call/win = 0.6488
Call/lose = 0.0118, which is so close to 0, it may as well be 0.

.3692 = (W)*(.6488) + (1-W)*(.0118)
.3692 = (.6488)W -.0118W + .0118
.3574 = (.637)W
.5610 = W

So basically, yeah, you need to be a 56% favourite. If I assume the lose EV is 0, which is the same as yours with 0.2, I actually get 0.5691, which is close enough to say the results are the same.