Some math that's supposed to help me figure out SNGs

[pergesu]

Okay so Bones and I have been talking about that 77 ITM hand I posted a little while ago. Here is a hypothetical situation that we're using to try and figure it out.

You: 2000
SB: 2000
Button: 4000

Blinds 100/200


SB shows AKo and pushes. You look down and see 77. ICM says a call here is correct (+1.3%).

The main reason the call is correct because of the payout weights.

So here's what we were thinking. In a $22 SNG, your profit for finishing 3rd will be $18. Winning this hand will give you a 50% chance of winning the tourney, ignoring difference in skill level. So when you go heads up, you have a profit EV of $58 ((78 + 38) * .5).

45% of the time you make $18, and 55% of the time you make $58.

58/18 = 3.22, so you need to finish 3rd place a little more than 3 times to equal the profit you gain from getting heads up once.

So that means to me that you only need to be 1-3.22 or better to win the hand, because getting heads up gives you the same expected profit as three third place finishes. So you ought to only need a hand that wins ~24% of the time to make the call.

That would be a massive range, but in fact you need 22+,AKs to make this call profitable. That's a range that wins 57% of the time, only 6% of hands.

I have to be looking at this all wrong, simply because SNGPT is slapping me around. I'd really appreciate it if someone could tell me what I'm missing, cause I think whatever it is may be the next big step towards me understanding SNGs.

[Freudian]

All three of you already have $40. What you are playing for now is a prize structure of $60/$20/$0.

The reason you don't take a 24% call now is that you can no matter what you have push the next hand for even more value. And if you call with a 24% hand, you will miss out on that opportunity 76% of the times. So instead of just having two outcomes (calling and winning/calling and losing) there is a third, folding, which means you get to play on.

Might add that I don't use ICM or SNGPT. So I don't think in terms of +1.4% etc. Mostly because I think we are often so poor at guessing the other guys range that the numbers is at best slightly inaccurate.

[pergesu]

No, the correct play according to ICM is to call here. So there are two outcomes - winning or losing.

You're talking about folding against ICM because we can have a bigger edge later on. But our edge increase with 77 vs AKo is 1.1%, which is just far too big to pass up.

[Freudian]

[ QUOTE ]
No, the correct play according to ICM is to call here. So there are two outcomes - winning or losing.

You're talking about folding against ICM because we can have a bigger edge later on. But our edge increase with 77 vs AKo is 1.1%, which is just far too big to pass up.

[/ QUOTE ]

With the 77, calling is correct.

But once you introduce hands that have 24% against his range, surely folding is an option.

[pergesu]

[ QUOTE ]
With the 77, calling is correct.

But once you introduce hands that have 24% against his range, surely folding is an option.

[/ QUOTE ]
According to ICM, it's not that folding is an option - it's that calling ISN'T an option.

Which is what I'm trying to figure out. If you need 3 3rd place finishes to make up for one heads up finish, you'd be willing to call with a hand that's a 3-1 dog, because you're getting an overlay.

[Freudian]

[ QUOTE ]

According to ICM, it's not that folding is an option - it's that calling ISN'T an option.

Which is what I'm trying to figure out. If you need 3 3rd place finishes to make up for one heads up finish, you'd be willing to call with a hand that's a 3-1 dog, because you're getting an overlay.

[/ QUOTE ]

But why would you call with a hand thats 3-1 dog when you the next hand, no matter what cards you have, will have a more +EV situation?

Are you working against a time limit here?

Are you really aiming for a finish distribution where you have twice as many 3rds as 1st and 2nds?

I might add that I have gotten much more patient when ITM and HU lately. I have learned to fold hands I might have called with/pushed in the past. And my 1sts have gone up. Of course I still play aggressive but not uncontrolled.

[kamrann]

[ QUOTE ]
If you need 3 3rd place finishes to make up for one heads up finish, you'd be willing to call with a hand that's a 3-1 dog, because you're getting an overlay.

[/ QUOTE ]
This is where you're going wrong, you don't need 3 3rd places to make up for one heads up. What you did wrong is you used expected profit in your calculations rather than expected payout. The $22 you invested is no longer yours, it's part of the prize pool. Using the payouts, you get E(3rd) = $40, E(HU) = ($100 + $60) * 0.5 = $80. So E(HU) = 2 * E(3rd). So 2 3rd places equates to 1 Heads Up, therefore you need to be even odds to make a call a break even play, as you'd expect.

In reality, due to the overlay of the blinds, it should be correct, by ICM, to call here as slightly less than 50%. I'm not sure why this doesn't quite fit with your calculations.

[pergesu]

According to what you said, you need to finish 3rd twice to make up for a single first place finish, so you can be at worst a 2-1 dog to make this break even.

[pergesu]

Of course I'm not aiming for more thirds than firsts.

What you're saying is to pass on a hand where you're a big dog because you can get a big edge later on. That makes perfect sense. Simple gambling concept to maximize EV.

What I'm saying is you'd be WILLING to take a gamble where you're 3-1 against winning. Sure, you can have a bigger edge later on, but taking this gamble still isn't bad.

But what I'm also saying is that's wrong. The reason I'm saying it's wrong is because ICM is telling me it's wrong. I'm trying to understand WHY it's wrong.

[kamrann]

Yeah, I messed up. It's a bit confusing. But basically it's to do with what Freudian said about the remaining payouts. You're all guaranteed 3rd place money, so you're playing for 60/20/0. As such it doesn't make sense to apply any sort of valuation to finishing third, because it currently has zero value. I've just woke up and my head isn't working too well. I'll have a think about it...