Theoretical final table tourney question....

[SplawnDarts]

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But again, to repeat the original question:
"so if the payout is [literally] 1,000,000$/900,000$/0 is it still a push?"
[img]/images/graemlins/wink.gif[/img]

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Yes - the math is exactly the same. Just multiply all expected EVs as a fraction of prize pool by 18/19 and the logic is unchanged. I just wanted to keep that gawdawful fraction out of my post since there was no need for it.

[schroedy]

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so if the payout is 1,000,000/900,000/0 its still a push?

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Absoloutly. Not even close. First, to simplify things, let's just make the top two payouts the same, which is what you were getting at anyways I believe.

Now, before this hand, your expectation was well less than 1/3 of the prize pool given your small stack. It's basically a race to see who A eliminates first. If B goes out first, you get about 1/2 of the pool. If you go out first, you get nothing. So your expectation is only slightly more than 1/4 of the pool. Where exactly your expectation is between 1/3 and 1/4 is pretty irrelivant to the analysis that follows.

Now, let's look at what happens if you play all in. If A wins, you get paid.

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If A wins your strategy doesn't matter at all, and in fact if you KNEW A was winning your optimal strategy would be to fold.

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If you win, you get paid.

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The question being, how different is your situation as a result of having risked everything to pick up T3,000 more in chips.

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If B wins but you beat A, you're about where you started, roughly 1/4 equity.

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Flatly wrong. B has tripled to $9000 while you remain static at $6000.

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If A and B both beat you, you're out.

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Unless you don't push and then you are still in and a new analysis of the new situation must be made.

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So, assuming all three hands had an equal chance of winning, your expected value here would be somthing like 9/24ths of the prize pool. Which is already better than 1/3, let alone 1/4.

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You are not comparing the situations that matter -- the before the hand situation is not what needs to be compared. What needs to be compared are the various different after the hand situations.

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But in reality, the QQ is much stronger than A's range here, which in turn is perhaps a bit stronger than B's range here. So the "good" cases where you get a payoff become more likely, and the only case where you lose very much, where both A and B beat you, becomes far less likely. So the real EV for this play might be more like 5/12ths of the pool(1/2 is the upper bound because that what you would get if B just quit). Given that this play has an expected value right up on the upper bound of what's possible, I can't see any way you could possibly turn it down as the situation really couldn't get much better.

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Again, turning down the offer could leave you in close to as good of a situation with ABSOLUTELY NO RISK of elimination. That's what matters.

[SplawnDarts]

The above post has numerous errors, but I don't have time to address them now. Maybe tomorow.

[indianaV8]

I wasn't talking about the math here. Question was, if you personally was in that table playing for 1m$ - will you call? Goes a little bit along Doyles intro, will you bet all your money that you have + all assets, on a 50-50 bet given you are 60/40 favourite.

But back to the math.
You came out with 9/24ths, right?
Why you stared with 1/4-1/3? I would say you should start from the current situation. The other two guys are already heads up. If you fold, let's say the big stack is 40/60 underdog. That is 40% + 50/50 (as if small stack win, it's 50-50 vs you) 3/5th of the prize already?

[SplawnDarts]

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I wasn't talking about the math here. Question was, if you personally was in that table playing for 1m$ - will you call? Goes a little bit along Doyles intro, will you bet all your money that you have + all assets, on a 50-50 bet given you are 60/40 favourite.

But back to the math.
You came out with 9/24ths, right?
Why you stared with 1/4-1/3? I would say you should start from the current situation. The other two guys are already heads up. If you fold, let's say the big stack is 40/60 underdog. That is 40% + 50/50 (as if small stack win, it's 50-50 vs you) 3/5th of the prize already?

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If I'm personally at the table, I play for +EV and thats the raise here. You are correct though that my post should have compared to what you would have gotten if you folded, as B entering a pot all-in with A is a +EV scenario in an of itself so you're already better than 1/3

That said, I don't know where the number 3/5 in your post came from. No mater what happens, you can't own over half the prize pool.

[indianaV8]

3/5th of the second place prize I meant?
Wouldn't you working with that?
I.e. in 40% of the cases you get that second prize.
If you don't (the small stack wins the headsup) - then you have roughly equal stacks, so you have 50% of winning the 2nd place.

[indianaV8]

OK, I can't count ;-)
again 0.4 + 0.6*0.5 = 0.7
So 7/10th, even better than 3/5th

[SplawnDarts]

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3/5th of the second place prize I meant?
Wouldn't you working with that?
I.e. in 40% of the cases you get that second prize.
If you don't (the small stack wins the headsup) - then you have roughly equal stacks, so you have 50% of winning the 2nd place.

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Ok, my post is in units of fractions of the total prize pool, whereas yours is in fractions of one payout. So you're saying that your baseline is 3/10ths of the prize pool, which is between 1/3 and 1/4 which is the range where I said the baseline falls. If you raise all in, you end up well ahead of all those numbers.

[indianaV8]

Ok, then the best I can get with my fold is the same as you. And I should withdraw to your assumption (of 50/50 hand between the big and the small stack).
Then it's 0.5 + 0.5*0.5 = 0.75 i.e. 9/24, so the same.
Maybe it comes to a really tricky calculation?

[PantsOnFire]

If hero goes all-in here, he could lose to Player B but he could beat Player A and double up. And in the unlikely event he does fold, you still have 4000 left.

So Player B losing would be the best result but doubling up is a pretty good result too. As a matter of fact, Player A is your main concern since he is the one that could knock you out.