How low would you go...

[Saborion]

[ QUOTE ]
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*.

[/ QUOTE ]

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.

[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.

[M.B.E.]

[ QUOTE ]
x=% of time you call and win

Total chips = 6,150,000
Total prize money playing for = $1M ($250k already wrapped up for each)

Fold = 825k
825k/6150k = 13.4% * $1M = $134,146

[/ QUOTE ]
I don't quite understand this -- aren't you overlooking second place money?

With a stack of 825k, we'd have a 13.4% chance at first plus an 82% chance (approx.) at second, with let's say a 4.6% chance at third. So our equity on folding is not $134,146 but $555,500.

(13.4% x $1M) + (82% x $500K) + (4.6% x 250K) = $555,500.

[ QUOTE ]
Call and win = 2,015,000
2015000/6150000 = 32.8% * $1M = $327,642

[/ QUOTE ]
Should be more like $658,500.

(32.8% x $1M) + (65% x $500K) + (2.2% x 250K) = $658,500.

So that agrees with Fiskebent's post: because of the prize-payout schedule and the very short third stack, the value of your stack increases by only 18% if you double up.

Here are my complete ICM calculations:

You fold (Stacks are 5M, 1M, 150K)
$EV = 1000000/6150000 * $1000000 + ( you take 1st )
5000000/6150000 * 1000000/1150000 * $500000 + ( BigStack takes 1st, you 2nd )
150000/6150000 * 1000000/6000000 * $500000 + (ShortStack takes 1st, you 2nd )
5000000/6150000 * 150000/1150000 * $250000 + (BS 1st, SS 2nd)
150000/6150000 * 5000000/6000000 * $250000 (SS 1st, BS 2nd)

$EV = $162611 + $353482 + $2033 + $26511 + $5081

$EV = $549718

If you double up (Stacks are 4M, 2M, 150K):
$EV = 2000000/6150000 * $1000000 + ( you take 1st )
4000000/6150000 * 2000000/2150000 * $500000 + ( BigStack takes 1st, you 2nd )
150000/6150000 * 2000000/6000000 * $500000 + (ShortStack takes 1st, you 2nd )
4000000/6150000 * 150000/2150000 * $250000 + (BS 1st, SS 2nd)
150000/6150000 * 4000000/6000000 * $250000 (SS 1st, BS 2nd)

$EV = $325203 + $302515 + $4065 + $11344 + $4065

$EV = $647192

[Saborion]

I don't know how to make the math, but the SB is an aggressive player, capable of raising with a lot of hands. The reason I asked this is because when I played some SnGs I remember that when it's 4 people left and you have a big stack, you can bully them quite a lot. This seems to apply here as well since the short stack is likely to bust soon, especially if they gang up on him on the next hand. The difference of $250k prize money between third and second place is quite a lot, but it's all relative and you've got to draw the line somewhere.

I don't know at which level they were thinking and all that, but I'd like to believe that AA and KK may be slightly less likely due to the push, which makes calling with lesser hand a bit more attractive. Can't be certain though, have to have been there I guess. I just think that I would've been quite tight there, but I wonder how tight "correctly" tight is. If he push with A5o and we call we'll still lose 30 % of the time. Very nice sitaution to get all in, being that big of a favorite. Is it good enough given the situation?

Shorty is all-in next hand. Biggy is correct to push any two here, and you are correct to fold any unpaired hand even knowing this information.

As for pairs, if he's indeed pushing any two, I think you'll find TT+ as +EV. If he's pushing only 75%, then call QQ+. If you think his range is less than that, then stick with just Kings and Aces.

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.

So if we want to find out the chance you need to win (we'll call that P) to break even, we get 0 = P * 100K - (1 - P) * 300K. That translates into P = 75%.

So calling with a dominating hand is wrong, since you're usually only about 70% to win those. You basically need an overpair to his two cards. And without running stuff in Pokerstove, I'd say only AA and KK gives you good enough odds against his range.

[Lloyd]

[ QUOTE ]
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.

[/ QUOTE ]
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.

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

[/ QUOTE ]

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.