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

There is at least one factor which is not taken in ICM.
The "Dynamism of the game" . I would imagine a line as this one. D=0,35 would mean there is 35% tourney where the other short stack will be broken while you fold all your hands.

An idea like that. I know it's not enough but we can't ignore that.

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

The two main problems are, you have already paid the $22 and you have already won at least 3rd place.

You have a certain chance of half of the remaining equity, which is $80, and a certain chance of none of the remaining equity. You have to weigh this against the equity you have if you fold.

If you wanted to, you could phrase the question like this:

I have won $1 million dollars playing poker in my life. If I win this hand, I will have won $1,000,058. If I lose this hand, I will have won $1,000,018.

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

Just got home from church and will try to clarify:

Payouts are as follows:

1 = 30
2 = 10
3 = 0

(These are pool% numbers less the floor all players have of 3rd place money.)

Your EV right now is 10.83 (for simplicity lets say 10). Ignore blinds (for simplicity) and assume that if you win you have EV of 20. Since if you fold you have EV of 10 and if you call you have a binary payout of EV0 or EV20 (with our assumptions) then your hand has to win more than 50% v. AK for this call to be profitable.

What hands beat AK more than 50% of the time? Any pair. You call with any pair and you fold all others.

Our assumptions are not too out of line and I think the math gives the correct answer here.

Does this help?

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

Now that I think about it, what you seemed to be leaving out of your reasoning was that if you fold you can still win 2nd or 1st. I think you were only thinking that you could get 3rd.

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

The problem with all your math is that you are ignoring what your stack is worth when you fold. As you say, you are in a coinflip situation, and then will be HU with a chance at another coinflip (even stacks) to win. So you win a little more than 25% of the time and get HU a little over 50%.

If you were to fold you still have 1800 chips and should by conventional wisdom finish first just under 25% of the time and get HU a little under 60% of the time

If you are suddenly taking 2-1 the worst of it here, now you will only win about 16% and gets HU 33%. Obviously a much worse situation.

Note: You logic is pretty good if you ever end up on "Who Want's to be a Millionaire"

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

I edited this post a bit, but my original reply is that if you fold your EV is a little less than $20, and if you call and win your EV is $40, and so, assuming equally skilled players, the math is very easy.

Numbers are for a $22 SNG.

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

OK -- I think I understand your question a little better now. So, what range of hands should you call with in this situation if your opponent flips over AKo?

As a rough guess, let's say your current equity is [(0.375)(40) + (0.375)(60) + (0.25)(100)] = $62.50

We already decided that your equity if you call and win is [(0.5)(60)+(0.5)(100)] = $80. If you call and lose it's $40. You can then figure the winning percentage you need to make this call correct: 62.50 = 80x + 40(1-x) ==> x=0.56

So if these were the real numbers, you'd need a hand which is 56% against AKo in order to increase your tournament equity. [edit: this would mean you could only correctly call with AA or KK]

But, folding is an option. Maybe not the best one, but it is an option. So the real question is what percentage of the time do you need to win for calling to be better than folding.

I can't see my last post, but I think I remember gettting something like $60.20 in tournament equity if you fold. With this number, you need a hand that is 50.5% against AKo to make calling better than folding. AKs or any pair should do.

I'll run it with some real numbers when I get home this evening but I bet these are close.

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

[ QUOTE ]
OK -- I think I understand your question a little better now. So, what range of hands should you call with in this situation if your opponent flips over AKo?

As a rough guess, let's say your current equity is [(0.375)(40) + (0.375)(60) + (0.25)(100)] = $62.50

We already decided that your equity if you call and win is [(0.5)(60)+(0.5)(100)] = $80. If you call and lose it's $40. You can then figure the winning percentage you need to make this call correct: 62.50 = 80x + 40(1-x) ==> x=0.56

So if these were the real numbers, you'd need a hand which is 56% against AKo in order to increase your tournament equity.

But, folding is an option. Maybe not the best one, but it is an option. So the real question is what percentage of the time do you need to win for calling to be better than folding.

I can't see my last post, but I think I remember gettting something like $60.20 in tournament equity if you fold. With this number, you need a hand that is 50.5% against AKo to make calling better than folding. AKs or any pair should do.

I'll run it with some real numbers when I get home this evening but I bet these are close.

[/ QUOTE ]

If you are aware of doing it and being consistent with it, it doesn't matter much, but usually when you talk about EV, it's easier and makes more sense to ignore the money already won (here, for instance, the share of the prize pool that was already distributed to all 3 ITM players, is not part of your *expected* value). And you're not the only one doing it here. I think it's a source for a lot of confusion.

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

Now I think I'm confused with semantics. I agree there is some confusion here, and purposefully didn't talk in terms of EV in my last post for just that reason. It's a lot easier for me to think of these situations in terms of what I call "tournament equity" which is the amount of the prize pool I can expect based on my chip stack and the stacks of the remaining players.

If there was a problem with that in my last post please let me know. I think this is a pretty fundamental aspect of understanding tournament play, I think I finally am starting to understand it, and I want to know if I'm getting things mixed up.

If we're going to talk about EV in this situation, I think we need to be careful to explain if were talking about a play being +EV in terms of adding chips to your stack or being +EV in terms of increasing your, well, what I would call "tournament equity." Because the two are definitely not always the same thing.

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

You essentially have it right. The first calc where you got .56 isn't right because keeping 2000 chips isn't an option. The second equation is right. The things to equate are equity if you fold vs. expected equity if you call.

In the previous example I don't see where you worked out the equity if you fold. Your procedure (guessing how likely you are to come into each place, multiplied by the prize amount) is reasonable, but hard to justify the numbers you pick. (say, when stacks are 4000,2200,1800) ICM is just a way of estimating the value of those complicated stack arrangements.

It's not just a coincidence that you come up with the right answer (IMHO), which is basically call if you are the favorite.

This is different than a cash game, where you should call as a slight dog because of the dead money in the pot.