Empirical chip equity

[eastbay]

I have half a mind to try something like this:

Sift through my hand histories for every 3-handed hand in, say, $55 SnGs.

Discretize chip counts into 1k bins. I think there are only 14 unique ways to put 3 chip counts into 1k bins.

Get an average actual equity for each chip count possibility.

Compare with ICM range (over bin size).

My guess is that 1k or 2k SnGs might not be enough to converge this result. If there are, say, 10 3-handed hands per SnG, that's about say 15k 3-handed hands. So there will be roughly 1k data points per bin. I'm not sure how to put an uncertainty on that, but it seems low.

eastbay

[Desdia72]

[ QUOTE ]
I have half a mind to try something like this:

Sift through my hand histories for every 3-handed hand in, say, $55 SnGs.

Discretize chip counts into 1k bins. I think there are only 14 unique ways to put 3 chip counts into 1k bins.

Get an average actual equity for each chip count possibility.

Compare with ICM range (over bin size).

My guess is that 1k or 2k SnGs might not be enough to converge this result. If there are, say, 10 3-handed hands per SnG, that's about say 15k 3-handed hands. So there will be roughly 1k data points per bin. I'm not sure how to put an uncertainty on that, but it seems low.

eastbay

[/ QUOTE ]

and the purpose is...........?

[eastbay]

[ QUOTE ]
[ QUOTE ]
I have half a mind to try something like this:

Sift through my hand histories for every 3-handed hand in, say, $55 SnGs.

Discretize chip counts into 1k bins. I think there are only 14 unique ways to put 3 chip counts into 1k bins.

Get an average actual equity for each chip count possibility.

Compare with ICM range (over bin size).

My guess is that 1k or 2k SnGs might not be enough to converge this result. If there are, say, 10 3-handed hands per SnG, that's about say 15k 3-handed hands. So there will be roughly 1k data points per bin. I'm not sure how to put an uncertainty on that, but it seems low.

eastbay

[/ QUOTE ]

and the purpose is...........?

[/ QUOTE ]

To determine if the mathematical equity models like ICM bear any resemblance to reality.

If you don't know the purpose of equity models in general, you'll have to do your own research on that.

eastbay

[Daliman]

[ QUOTE ]
Discretize chip counts

[/ QUOTE ]

Wow. Isn't that illegal in some states?

[ChrisV]

Man, that's spooky. I had this exact same thought, for the first time, last night.

I don't see any reason to restrict it to 3-handed hands. In theory you could do it for every hand of the sng... I'm not sure that's a good idea as it may skew results? Possibly sample once, every time a player is eliminated?

[eastbay]

[ QUOTE ]
Man, that's spooky. I had this exact same thought, for the first time, last night.

I don't see any reason to restrict it to 3-handed hands. In theory you could do it for every hand of the sng

[/ QUOTE ]

You could but there's at least one practical problem with more stacks than three or finer grained bins: the number of stack combinations gets very large, very fast. And if the number of combinations is big, then the number of samples you'll get per combination will be that much smaller.

Anyway, 3-handed was a place to start. 4-handed would be more interesting as a follow-on. There's just only so many hours in a day for this stuff.

eastbay

[zephyr]

I posted on this topic a while ago under one of my very unpopular threads: "the ICM is not all its cracked up to be". I think an empirical equity model would be one of the most powerful tools in an SNG players arsenal. Of course, the results that you obtain will only apply directly to you.

Zephyr

[eastbay]

[ QUOTE ]
I posted on this topic a while ago under one of my very unpopular threads: "the ICM is not all its cracked up to be". I think an empirical equity model would be one of the most powerful tools in an SNG players arsenal. Of course, the results that you obtain will only apply directly to you.

Zephyr

[/ QUOTE ]

The idea was to compute it regarding all players the same, to get a sort of mean result.

Repeating the process for my equity in particular would also be very interesting. Probably moreso.

eastbay

[zephyr]

[ QUOTE ]
The idea was to compute it regarding all players the same, to get a sort of mean result.

[/ QUOTE ]

In that case, I'm sure that there is no shortage of HH's out there if your sample size is too small, which is likely the case if you start analyzing with 4,5, and 6 players left.

Only my opinion,

Zephyr

[rachelwxm]

Sounds like an interesting idea. Couple of questions:

1.Why use bins? If you want to fit a curve from experiment data, does it make sense to fit the whole curve directly Even you believe it's not linear relationship? /images/graemlins/smile.gif

2. more importantly, the only result that you can compared to emperically is final payout, so there would be some correlation among different hands in one tourney. If you have 10 3 handed hand per tourney that is 30 data points per touney, but there are lots of redundent data. /images/graemlins/smile.gif

[eastbay]

[ QUOTE ]
Sounds like an interesting idea. One question, why use bins?

[/ QUOTE ]

How else could you do it?

If you don't bin, you'll get ~1 data point per chip stack combination. Not very statistically useful.

eastbay

[rachelwxm]

I mean if you want to fit data like car distance vs time of travel you are not going to use bin, are you? Since you have a ICM prediction, you can compare with emperical results within statistically acceptable region.

Or maybe I am totally confused myself since it's really late?

[eastbay]

[ QUOTE ]
I mean if you want to fit data like car distance vs time of travel you are not going to use bin, are you?


[/ QUOTE ]

I think it is not analogous.

[ QUOTE ]

Since you have a ICM prediction, you can compare with emperical results within statistically acceptable region.

Or maybe I am totally confused myself since it's really late?

[/ QUOTE ]

I think you are confused. What we want is an ensemble average of many instances of the actual equity of any given chip stack combination. The bigger the ensemble the better.

But it just doesn't happen often enough that stacks are exactly x, y, and z amounts, no more and no less, to get a nice ensemble. So you can cheat by binning stacks which are "close enough" to be considered more-or-less equivalent.

eastbay

[rachelwxm]

OK, bear with me for a moment. I have trouble understand English sometimes. Is the purpose of this try to validate ICM model or something else? And what is your detailed plan?
I am all ears. /images/graemlins/smile.gif

[The Yugoslavian]

Eastbay,

Is there any update regarding this possible project of yours? Seems like this is a great way to see if ICM is off or dead on.

This post is more of a bump in case there are other posters with some skills to help you do this. Unfortunately, I would have no idea how to go about setting up a program to do what you're discussing, /images/graemlins/confused.gif.

Yugoslav