How low would you go...

[Lloyd]

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My ICM calculations puts the value of your stack at ~550K if you fold and ~650K if you call and win. Obviously you win 250K if you call and lose.

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There's no way your value goes up by only 18% if you double up. That just intuitively doesn't make sense.

[locutus2002]

I got about the same numbers.

Hero risks 250K to win 100K in EV or 2.5:1 and has to be 72% in the hand.

Somewhere around JJ is EV+ considering villain is tossing out the bottom range of his hands.

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What's the lowest hand you'd call with, if any?

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Haven't read the other posts, so apologies if this is a re-run.

Call me crazy but why would anyone call with anything less than KK or AA? Maybe the player even has to consider folding QQ and JJ here.

The button is going all in on the BB next hand with the average hand being T-8 offsuit, I have to like that chances that he is going down, as it is 2-1 that someone gets dealt a better hand.

If button gets lucky and doubles or triples, then I'll cross that bridge when I come to it. Last thing I want to do is tangle with the chip leader when the only remaining player is on life support, especially for that prize differential.

[adanthar]

Lloyd,

Your equation *is* flawed, because the assumption is that the short stack will bust first. While you can't really count on it, it will happen ~90% of the time (as he'll be forced into at least 3 all ins by pot odds as a random hand) and therefore the hero has 500K locked up, not 250. You can consider it 450K if you'd like, but you still need waaaaay more than 40.9% to call.

BTW, this is from one of the, like, two WPT events I've ever seen on TV and the guy's call was *horrible*.

[Saborion]

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Lloyd,

Your equation *is* flawed, because the assumption is that the short stack will bust first. While you can't really count on it, it will happen ~90% of the time (as he'll be forced into at least 3 all ins by pot odds as a random hand) and therefore the hero has 500K locked up, not 250. You can consider it 450K if you'd like, but you still need waaaaay more than 40.9% to call.

BTW, this is from one of the, like, two WPT events I've ever seen on TV and the guy's call was *horrible*.

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Yes, this was from a WPT event that I re-watched the other day. Personally I think the guys call was very interesting, not something I would do. Hence this post. The numbers may not be 100 % accurate, but they are close enough. If the BB would've had a little smaller stack I think the call would've been a must, but with 1M I think I'd want a bit better hand than the one he had. With more than 1M I'd want an even better hand since we're so much more likely to survive the short stack. But 1M is starting to get borderline with those blinds, since it's not impossible that the short stack will double/tripple up on the next hand, although unlikely, it will still suck big time.

Anyway, thought it would be interesting to know what the "math" says that we should do. For those interested it was from the Doyle Brunson blah blah, I think it was season 3? The BB called the SB (Carlos Mortensen) A5o push with TT without too much hesitation, if any at all, and doubled up.

[Dan Mezick]

The #3 to #2 diff is 250K.

The Button has 150K left and he's allin on the Big next hand.

If you assign a probability of 90% that the T150 goes away on the next 6 hands, why call with ANY hand here? If SB is that wild right now, he will take care of the T150K Button.

And you'll be 250K richer.

The fact that SB has you outchipped 5:1 has everything to do with this decision to fold just about everything until Button is eliminated.

[Lloyd]

Okay,

So let's say the value of folding equals $250,000 (the difference between the guaranteed 3rd place money and 2nd place). And what we are really playing for is the $500k difference between 1st and 2nd.

If we call and win we'll have 2,015,000 chips out of 6,150,000 total. That's 32.8%, multiplied by 500,000 equals 164,000. That makes sense. Essentially if we call and win we'll have 1/3 of the total chips and use that as an approximation of equity.

If we call and lose, we're LOSING $250,000 (what we have essentially locked up).

So the value of calling where "x" equals the percentage of the time we call and win:

x($164,000)+(1-x)(-$250,000) = 164000x -250000 +250000x
414000x = 250000
x=250000/414000
x=60%.

So we need to win 60% of the time for it to be a neutral decision. Let's say we need to win 70% of the time for it to be profitable enough.

We're then calling (versus my previous range) with AA-QQ. JJ would be slightly +$EV and TT would be neutral (and thus increasing variance with no reward).

I do agree that without taking into consideration the blinds my previous calc was flawed.

Edit: If we change his range of hands to any 2 cards (which I think is certainly reasonable) then a +$EV range would be 99+ so in that sense it could have been correct to call with TT.

[Piers]

Playing with http://sharnett.bol.ucla.edu/ICM/ICM.html assuming the stack sizes are after posting blinds (not clear form post). Prize fund is (.57,.286,.144)

If you fold stack sizes are (524,100,15) giving a EV of 312.5.
If you call and win stack sizes are now (400,224,15) giving an EV of 377.8.

You should call if you chance of winning is grater than p against his range where

p = .3125/.3778=.82715. or nearly 83%

Aces will always be worth a call.
If you reckon he is rasing more than two thirds of the time, which he probably is, then you can call with kings. Also calling with queens would only be a small mistake. Calling with anything else would be a big mistake.

[Lloyd]

Usually when people post stack sizes they are before blinds/antes. While I'm not sure that's the case here (and the stack sizes are approximate in any case) that's what I based my numbers on. So folding actually leaves him with 835k, not 1M.

[locutus2002]

the ICM model does not account for position, blind or stack size. All very important in this situation.

Short stacks equity in the pot is irrelevant.
Hero has about EV 550K if he folds, $ 250K if he loses and EV 650K if he wins. (according to ICM).

Betting 300K to win 100K is a terrible bet. Short stack is all in next hand, hero should probably fold everything other than AA. The chips won are worth much less than chips lost because of the preponderance of chips held by the big stack. If you make the stacks more similar, the EV goes up substantially. In other words the match is already over (in the most likely case).