Math Wiz Help

[jah0550]

I think that I made the correct call in folding, but was it mathmatically correct to fold? I was getting better than 4-1. Any math experts help me out with this one? Any comments are appreciated.

Party Poker No-Limit Hold'em Tourney, Big Blind is t300 (5 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

SB (t4380)
Hero (t900)
UTG (t890)
MP (t715)
Button (t1115)

Preflop: Hero is BB with T/images/graemlins/heart.gif, Q/images/graemlins/heart.gif.
<font color="#CC3333">UTG raises to t890 (All-In)</font>, MP calls t715 (All-In), <font color="#666666">1 fold</font>, SB calls t740, <font color="#666666">1 fold</font>.

Flop: (t2795) 9/images/graemlins/diamond.gif, 6/images/graemlins/spade.gif, 5/images/graemlins/club.gif <font color="#0000FF">(3 players, 2 all-in)</font>

Turn: (t2795) T/images/graemlins/spade.gif <font color="#0000FF">(3 players, 2 all-in)</font>

River: (t2795) 7/images/graemlins/diamond.gif <font color="#0000FF">(3 players, 2 all-in)</font>

Final Pot: t2795

[LaggyLou]

Down to t415 you will have no fold equity. Push and hope to get lucky.

[gumpzilla]

I'm pretty sure folding is correct here. If you were up against three random hands, then QTs is good enough to make calling a chip +EV play. But, you've got 5 people left, the two shortstacks are all-in, and the SB is calling them. I'm not expecting three random hands here (the second shorty calling the all-in bet looks potentially strong), and QT stops looking so good then.

So my guess is that calling might be marginally positive chip EV (and even that seems kind of iffy), but negative $ EV. It's quite likely that both of the shortstacks in here could bust to the SB, in which case you're in the money. It's very likely that at least one will bust out. If one triples up, then hope you can get lucky and double up in the next couple of hands. I think your chances will be better getting in with one other hand instead of three.

I fold this. This seems like a good spot for ICM analysis, but I've yet to learn about that, so perhaps somebody else can illuminate you there.

[jcm4ccc]

There are seven different scenarios, I think (I simplified it a bit, by not considering sidepots):

You fold, UTG wins
You fold, MP wins
You fold, SB wins

You call, you win
You call, UTG wins
You call, MP wins
You call, SB wins

FOLDING
If you fold, you will have 600 chips. Let's assume that there's a 1/3 chance that UTG will win, a 1/3 chance that MP will win, and a 1/3 chance that SB wins. Here is your percentage of the prize pool if you fold:

UTG wins: 11.61%
MP wins: 11.03%
SB wins: 25.12%
Percent of prize pool if you fold: 15.92%

CALLING
If you call and win, you will have 3405 chips. If you call and the SB wins, you will get into 3rd place, with 20% of the money.

If you lose and one of the other small stacks wins, I am assuming that you will have 0 chips. Let's assume that there is a 25% chance you will win if you call, and a 25% chance that the SB will win if you call. Then the percentage of the prize pool you will get is: (0.25 * .3673) + (0.25 * .20) = 14.18% of the prize pool if you call

CONCLUSION
This is pretty close. If you include some of the complications in this analysis (sidepots, etc), it's probably a toss-up as to whether you should call or fold. I think I would call, though. There's a 25% chance that you will end up the big stack, basically, and a 25% chance that you will end up in 3rd place.

If you fold, the best scenario is that you are in 3rd place with a very short stack. The other two scenarios put you in 4th place with the short stack. I think ICM prefers the fold because you get a percentage of the prize pool 100% of the time, as opposed to 50% of the time under the calling scenario. In this instance, I would go against the ICM.

[UMTerp]

You can't really ignore the sidepots here. For one, the most important scenario you left out is if you call and the big stack wins - you get 3rd place money.

Also, if either of the other two stacks win, you still may have chips left, which are not insignificant, especially with another pretty short stack still in the game.

I also think it's fairly safe to assume that on average, UTG will have a worse hand than MP and SB here.

I don't think it's as clear-cut as you suggest, but I'm still not sure what the correct play is.

And FWIW, The math is ridiculously complex for a 4-player all-in situation. Nobody's going to be able to give you accurate numbers on it.

[jcm4ccc]

[ QUOTE ]
You can't really ignore the sidepots here. For one, the most important scenario you left out is if you call and the big stack wins - you get 3rd place money.


[/ QUOTE ]

Wow, I am an idiot, aren't I? That's a huge consideration, and probably pushes it towards a call.

Maybe this afternoon I'll try to do a more sophisticated analysis like you suggested, and see what I come up with.

[ QUOTE ]
This math is ridiculously complex for a 4-player all-situation. Nobody's going to be able to give you accurate numbers on it.

[/ QUOTE ]

I don't agree with this. You can simplify the problem, I think, and get some good numbers to guide your decision. They won't be perfect, but they'll be better than just relying on your intuition. My problem was that I simplified it too much.

[jcm4ccc]

I edited my original post, based on your comment. Changes the conclusion completely.

[gumpzilla]

[ QUOTE ]
You can't really ignore the sidepots here. For one, the most important scenario you left out is if you call and the big stack wins - you get 3rd place money.

[/ QUOTE ]

I hadn't considered this detail. It clearly makes calling more attractive. I guess it's just an issue of whether it makes it attractive enough. It's very hard to put people on a useful range of hands here - the only person who to my mind is showing strength is MP. The big stack is getting enough in the way of odds that he could be calling with all sorts of hands. So it's pretty hard to make good estimates of the likelihood of winning.

Call: 3rd if SB wins - 20% of prize pool
almost guaranteed loss if UTG, MP win - assume 0%
of prize pool, though you certainly have some chance at it
tie for chip lead if you win - worth about 37% of prize pool

Fold: SB wins - ICM gives about 25% of prize pool in this circumstance, but given that you are about to be in SB with the other short stack with 2x your chips on the BB, I think it's probably slightly worse than that.
MP/UTG wins (neglecting smallish side pots) - 11% of prize pool, as an approximation

Looking at this, I think calling actually starts to look pretty good, particularly since the ICM numbers are probably a little optimistic in the folding case given that you're immediately in the SB, have basically no folding equity, and have enough to exactly pay one more orbit following this. It surprises me how much currently being in third affects this.

[curtains]

I have no idea what to do!!!!!! First instinct was easy fold, but I'm not so sure anymore. Fortunately this isn't a situation I grapple with every day, otherwise I'd have been living a confused life.

[jah0550]

Thanks for the replies fellas, but what range of hands, if any, do you have to have to call here? What if I had A /images/graemlins/heart.gifK /images/graemlins/heart.gif or Q /images/graemlins/club.gifQ /images/graemlins/diamond.gif? Would that change anything?

[curtains]

Yes it does change things, I believe these hands are easy calls.