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

[Freudian]

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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.

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ICM is telling you it is wrong because once you are ITM, getting into 3rd is worth $0. So if you take plays where you end up in 3rd a vast majority of the time, you are giving a lot of EV to the other players at the table.

[kamrann]

Yep, it's pretty simple really. The decisions you make at this point are based on making money from your current situation, which means finishing 2nd or 1st. If it was winner take all, then forgetting the overlay of the blinds you would call with 50%+ favourite hands, since if you were 50% to double up/bust in the case your equity doesn't change. 0.5 * E(3rd) + 0.5 * E(HU) = 1/4 of the prizepool, since E(3rd) = 0 and E(HU) = 1/2 the prizepool. And this is the same equity you already have with 1/4 of the chips.

What I forgot before was the payput structure affects this. With a 60/20/0, doubling up does not quite double your equity, so you need more than just 50% to make a call correct.

Go here and play around with the stacks with the payouts adjusted to 0.75, 0.25, 0. That should help you understand the situation better.

[pergesu]

I have a few problems with that.

First, that suggests that no matter how many times you get third, you can never make up for a single first place finish. Each time you finish third, you make $0. Each time you finish first, you make $58. So if I played a million tourneys and finished third, I wouldn't have made a penny. In fact, you'd have made more than me if you finished first one time. Which obviously isn't true.

Second, I think that idea would lead to "one more spot" thinking, where you basically are just trying to move up one more spot. When you're on the bubble, you're just trying to make it ITM. When you're ITM, you're just trying to make it to second. And when you're heads up, you're just trying to win. But we always say "play for first" when you're on the bubble and ITM. Because that maximizes EV. Why? Because of the payout structure. I'm just not going to take "because of the payout structure" as an acceptable answer - I want to see it quantified.

For what it's worth, I'm not trying to be argumentative or stubborn at all. I just had an idea, and it doesn't match up with the common (and correct, I believe) ideas that we use to help make decisions. I just want to know why.

[Freudian]

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First, that suggests that no matter how many times you get third, you can never make up for a single first place finish. Each time you finish third, you make $0. Each time you finish first, you make $58. So if I played a million tourneys and finished third, I wouldn't have made a penny. In fact, you'd have made more than me if you finished first one time. Which obviously isn't true.

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Thats an argument for getting ITM, not for getting into 3rd while ITM. If your starting point is when three players remain, getting into 3rd often sucks. If your starting point is when ten players remain, getting a lot of 3rds is ok.

[Moonsugar]

You already have a lock on 3rd. If you win this hand do you automatically win 1st?

Also, as Freudian stated your analysis of prize structure is suspect.

[pergesu]

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You already have a lock on 3rd. If you win this hand do you automatically win 1st?

Also, as Freudian stated your analysis of prize structure is suspect.

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No, you don't automatically win first. Which is why I said when you get heads up, your expected profit is $58, or 40% of the prize pool.

Here's the best way to think about my analsis of the prizepool. Let's say that Freudian and I are both exceptionally good players. So exceptional, in fact, that we both finish ITM 100% of the time. The difference is that Freudian always finishes in 1st, and I always take 3rd. If he plays 100 tourneys, he'll make $7800. But if I play 100 tourneys, I'll make $1800. If I want to make as much as he does in 100 tourneys, I need to play 433 of my own.

That's what I was saying I didn't like about his idea that you make nothing by finishing third. It's simply not true. I can make the same amount of money by playing 4.3x as many tourneys as he does.

[Freudian]

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That's what I was saying I didn't like about his idea that you make nothing by finishing third. It's simply not true. I can make the same amount of money by playing 4.3x as many tourneys as he does.

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The $40 you get for finishing third isn't created when you bust in 3rd, but when you avoid busting while players 4-10 bust.

So I don't see how it is important once you get ITM. The only money up for grabs is the extra money you get for winning or coming second.

[pergesu]

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That's what I was saying I didn't like about his idea that you make nothing by finishing third. It's simply not true. I can make the same amount of money by playing 4.3x as many tourneys as he does.

[/ QUOTE ]

The $40 you get for finishing third isn't created when you bust in 3rd, but when you avoid busting while players 4-10 bust.

So I don't see how it is important once you get ITM. The only money up for grabs is the extra money you get for winning or coming second.

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I just can't make sense of that, cause if I play 4.3x as many tourneys as you, then you and I have the same bankroll. Yeah, you're way more efficient than me, but we earn the same amount of money.

Anyway, that's not even the point of all this. The point is WHY is the 77 call so clearly correct? I was playing around with some math and fell flat on my face. People are telling me it's wrong, but as I said in my first post and nearly every response since, I already know that. But nobody has shown me why it's wrong yet, which is what I want to learn.

[Costanza]

I don't have an ICM calculator handy but I think I can tell you how to set up this problem. Let me make sure I have the situation correct:

Button: 4000
SB: 2000
BB (you): 2000
Blinds 100/200
Button folds, SB flips up AK and pushes, you hold 77

Because of the stack sizes you have 2 options: fold or call

Calling: on average, the chip stacks will change to:
BB 4000
SB: (4000)(0.48) = 1920
BB: (4000)(0.52) = 2080

Folding: chip stacks will change to:
BB: 4000
SB: 2200
BB: 1800

So, in this specific situation calling is +chipEV.


Of course, this isn't what's really important. What you want to know is whether or not the call is +EV from a tournament equity standpoint. That's where the ICM calculations come into play. If you plug the average results into an ICM calculator it will tell you which play, on average, has the best expected EV.

As a step toward understanding the results you'll get, think of is this way:

The $22 you paid to enter the tournament is gone.

If you call, 48% of the time you win $40, and 52% of the time you'll be even with the other stack HU and therefore have a tournament equity of $80 [(0.5)(60)+(0.5)(100)]. So calling gives you an average tournament equity of $60.80.

If you fold, your tournament equity is [(chance of 3rd)(40)+(chance of 2nd)(60)+(chance of 1st)(100)]. If this works out to more than $60.80, you should fold. If it's less, then it's a call according to ICM.

Someone let me know if this makes sense because I want to know I'm thinking about this correctly.

[pergesu]

That makes sense, but it's not the issue at hand. We know that calling is +$EV according to ICM, so folding isn't even a consideration here.

What I'm saying is that you stand to profit 3.2x as much by finishing 1/2 than you do by finishing third. So you're basically getting odds of 3.1-1 on a call, thus you'd be we willing to accept a gamble as a 3-1 dog.

But it changes if we think of the payout rather than profit. 3rd gets $40, taking 1/2 gets $80. You'd still be willing to take a gamble as a 2-1 dog.

So according to my math, you should be able to profitably call with WAY more hands than just the 6% according to ICM. And I think it's wrong...I just want an explanation why.