empirical equity study

[eastbay]

[ QUOTE ]
I understand ICM.

It's your study. I'll step aside for now.

[/ QUOTE ]

I'm interested in constructive criticism. It's just not clear that you're understanding the question.

Here's a relevant example:

I have two data points each from two tournaments:

1000 2000 1000 0.3
1000 1000 2000 0.3

1000 2000 1000 0.2
1000 1000 2000 0.2

I want to calculate the expectation of (1000,2000,1000) and (1000,1000,2000). Are you contending that I cannot use all four data points - two for each of the two distributions - to do so? If not, why not?

Edit: make example clearer that distributions are about other stacks, not mine.

eastbay

[jcm4ccc]

[ QUOTE ]
I'm interested in constructive criticism. It's just not clear that you're understanding the question.

Here's a relevant example:

I have two data points each from two tournaments:

1000 2000 1000 0.3
1000 1000 2000 0.3

1000 2000 1000 0.2
1000 1000 2000 0.2

I want to calculate the expectation of (1000,2000,1000) and (1000,1000,2000). Are you contending that I cannot use all four data points - two for each of the two distributions - to do so? If not, why not?

Edit: make example clearer that distributions are about other stacks, not mine.

eastbay

[/ QUOTE ]

Independence of observations is an assumption of most statistical procedures. Some assumptions can be violated and the results can still be interpreted (for example, the normal distribution assumption). But that one can't.

If I understand your variables, they are:

Variable 1: Chip count of Player 1
Variable 2: Chip count of Player 2
Variable 3: Chip count of Player 3
Variable 4: Your results in the tournament

The problem is that your method may actually obscure your findings. Take a look at your first two observations. In observation #1, player 2 has 2000 chips. In observation #2, player 3 has 2000 chips. And yet the outcome is the same: you ended up in 2nd place. So if we just went by the first two observations, we would have to say that it makes no difference whether player 2 or player 3 has the most chips. But I think that's a mistake in your method, not an actual finding.

I may still be misinterpreting your study, but that doesn't really matter. If you are violating the independence of observations assumption, you are creating problems.

If you are interested in chip count distribution and its effect on your outcome in the tournament, I would pick one particular spot in a tournament (say, the first hand of the bubble, or the last hand of the bubble). Use the variables above, plus your own chip count (you have to include your own chip count, since that will have the most effect on your outcome). Do a regression analysis. The variable with the most effect, without a doubt, will be your own chip count. But what you could find is whether the chip count distribution has an effect, beyond the effect of your chip count.

You could even do multiple, separate studies. Look at the findings at different points in the tournament:

1) first six-handed hand
2) first five-handed hand
3) first four-handed hand

etc. You may find that chip count distribution is important when it is four-handed and five-handed, but not when it is six-handed. Or something interesting like that.

Again, I may be misinterpreting what you are trying to do. But nonetheless, you can't violate the assumption of independence of observations.

[eastbay]

[ QUOTE ]

If you are interested in chip count distribution and its effect on your outcome in the tournament, I would pick one particular spot in a tournament (say, the first hand of the bubble, or the last hand of the bubble). Use the variables above, plus your own chip count (you have to include your own chip count, since that will have the most effect on your outcome). Do a regression analysis. The variable with the most effect, without a doubt, will be your own chip count. But what you could find is whether the chip count distribution has an effect, beyond the effect of your chip count.



[/ QUOTE ]

Comment 1: Are you sure you understand ICM? This discussion implies you don't.

The whole point of an equity model like ICM is to find deviations from chipEV, which considers your stack only, and $EV, which considers all stacks. Of course you'll find that bubble play has the largest deviations, with chipEV approaching $EV as you move away from the bubble. We already know this.

eastbay

[eastbay]

[ QUOTE ]
[ QUOTE ]
I'm interested in constructive criticism. It's just not clear that you're understanding the question.

Here's a relevant example:

I have two data points each from two tournaments:

1000 2000 1000 0.3
1000 1000 2000 0.3

1000 2000 1000 0.2
1000 1000 2000 0.2

I want to calculate the expectation of (1000,2000,1000) and (1000,1000,2000). Are you contending that I cannot use all four data points - two for each of the two distributions - to do so? If not, why not?

Edit: make example clearer that distributions are about other stacks, not mine.

eastbay

[/ QUOTE ]

Independence of observations is an assumption of most statistical procedures. Some assumptions can be violated and the results can still be interpreted (for example, the normal distribution assumption). But that one can't.

If I understand your variables, they are:

Variable 1: Chip count of Player 1
Variable 2: Chip count of Player 2
Variable 3: Chip count of Player 3
Variable 4: Your results in the tournament

The problem is that your method may actually obscure your findings. Take a look at your first two observations. In observation #1, player 2 has 2000 chips. In observation #2, player 3 has 2000 chips. And yet the outcome is the same: you ended up in 2nd place. So if we just went by the first two observations, we would have to say that it makes no difference whether player 2 or player 3 has the most chips. But I think that's a mistake in your method, not an actual finding.


[/ QUOTE ]

The issue here is that we are computing several different things from the same pool of data which has some non-independent data. The question is, does the data have to be independent for each quantity that we are computing, or does it have to be independent between quantities as well. Do you see? I think I am going to have to do an experiment to settle it.

eastbay

[jcm4ccc]

[ QUOTE ]
Comment 1: Are you sure you understand ICM? This discussion implies you don't.

[/ QUOTE ]

i barely understand it. probably not very well. but i understand statistical research very well.

[jcm4ccc]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I'm interested in constructive criticism. It's just not clear that you're understanding the question.

Here's a relevant example:

I have two data points each from two tournaments:

1000 2000 1000 0.3
1000 1000 2000 0.3

1000 2000 1000 0.2
1000 1000 2000 0.2

I want to calculate the expectation of (1000,2000,1000) and (1000,1000,2000). Are you contending that I cannot use all four data points - two for each of the two distributions - to do so? If not, why not?

Edit: make example clearer that distributions are about other stacks, not mine.

eastbay

[/ QUOTE ]

Independence of observations is an assumption of most statistical procedures. Some assumptions can be violated and the results can still be interpreted (for example, the normal distribution assumption). But that one can't.

If I understand your variables, they are:

Variable 1: Chip count of Player 1
Variable 2: Chip count of Player 2
Variable 3: Chip count of Player 3
Variable 4: Your results in the tournament

The problem is that your method may actually obscure your findings. Take a look at your first two observations. In observation #1, player 2 has 2000 chips. In observation #2, player 3 has 2000 chips. And yet the outcome is the same: you ended up in 2nd place. So if we just went by the first two observations, we would have to say that it makes no difference whether player 2 or player 3 has the most chips. But I think that's a mistake in your method, not an actual finding.


[/ QUOTE ]

The issue here is that we are computing several different things from the same pool of data which has some non-independent data. The question is, does the data have to be independent for each quantity that we are computing, or does it have to be independent between quantities as well. Do you see? I think I am going to have to do an experiment to settle it.

eastbay

[/ QUOTE ]

your observations have to be independent. no ifs, ands, or buts, regardless of my poor understanding of ICM. your variables do not have to be independent.

[mistaken]

[ QUOTE ]
Ok, I thought of one. Consider HU match. Strategy A is to push when you have half or more of the chips, and fold if you have less than half. Clearly equity distribution is a step function for two players both playing this strategy.

[/ QUOTE ]

Is this a generally accepted strategy?

I usually apply the "Q higher or better in the SB = push against the average heads up player when blinds are 250/500 or higher... BB play varies"

[mistaken]

Please disregard this post...
I must have been high or daydreaming when writing it [img]/images/graemlins/tongue.gif[/img].

Mistaken

[PrayingMantis]

Interesting post.

I'm thinking however that this kind of empirical $EV model, might create some paradoxical implications. I'm not a mathematician, so please forgive me for the language and terms in which I'll make my point.

Let's assume you're on the bubble with whatever stacks and blinds, you're on the BB and button pushes. Folded to you. Now you put button on a specific range of hands, and lets say you use normal ICM to decide whether this is a call or not with your hand. This is a common pratice for you in such spots.

Now, let's say you have played enough SNGs to come out with your "true" empirical $EV (which is obviously higher than the what ICM tells you). Now you find yourself at the same spot described about. But instead of using the normal ICM to make your decision, you now base it upon your "empirical EV" model. Not surprisingly, your decision is now different. with the same range of hands you put button on, you now probably need a somewhat better hand to call with. Suppose you fold, where you used to call earlier, based on pure ICM.

Do you see the paradoxical side of this? Your $EV for this situation was based upon making moves which now you will not do (or do differently), and therfore your equity might actually go down from now on.

This brings to mind, in a way, the way Helmuth plays in the last few years. His big success in the past ("empirical equity") made him feel he is able to pass up on situations in which he is a big favorite, in order to "preserve" his equity. It is probably not a mistake to assume that his true equity has really dropped down because of this.

Any thoughts about this problematic side of what you call empirical equity?

[Slim Pickens]

I'm sorry. I walked in late and I need a clarification. Why do you argue in this thread that your data points within the same tournament can be treated as independent trials, but in The Shadow's recent thread, you seem to make the opposite argument?

[ QUOTE ]
Intuitively I agree that only one data point is permissible on independence of observations grounds. I'm not sure how to prove it, but I'm not sure that it needs proving.

[/ QUOTE ]

This case is four-handed, so there is a chip distribution, and the other is two-handed, so only your chip count is variable. Is that it? If so can you explain why?

Slim