table selection calculations, thoughts wanted

[Paul2432]

I've been giving table selection more thought lately. I've kicking around some numbers and assumptions to try to quantify the effect of having good players at my table.

Suppose a player has a 15% ROI. On average, the other players at his table will have a -11.8% ROI. Now suppose one of those average players is replaced with another 15% ROI player. If we assume the bad players stay constant at -11.8%, the two good players will now have an ROI of 1.6%. If a third 15% ROI player sits down, the three good players will now have an ROI of -3%. (note that 10 equally skilled players will have an ROI of -9.09%)

Of course the assumption above that the bad players hold there ROI constant when another good player sits down is probably false. If we assume the good players hold ROI constant, then with two good players, the bad players ROI needs to decrease to -15.1%. With three good players, the bad players ROI needs to decrease to -19.4%.

My questions then are:

1) What is the best way to model the impact of a good player taking a seat at your table?

2) If you sit down for a SNG, how many known good players would need to take a seat before you get up?

Paul

[Apathy]

[ QUOTE ]
1) What is the best way to model the impact of a good player taking a seat at your table?

2) If you sit down for a SNG, how many known good players would need to take a seat before you get up?

Paul

[/ QUOTE ]

A few things about your post in general:

It is a poor assumption that either the winning or losing players would have a consistent roi given the inroduction of more positive roi players. It is more likely everyone will do a little worse.

Also In terms of how mnay good players, that depends. I know people that are winning players (probably not by much) who I have notes on but love to play with if I can get the right seat because they have highly exploitable weaknesses.

You can't make assumptions like 15% roi players play identically to acheive those results...that just isnt the case, the odds are that one will fair better then the other becuase of their playing style, or the fact that they can better adjust to the introduction of a skilled player.

I have other thoughts but I'll let others get into it.

[uphigh_downlow]

It would be an interesting possibility to assign a vector (x,y,z...) to each player such that you could compute your tournament equity, before the first hand is dealt. (something like ICM)

The sad part is that again it would require some empirical avalidation, that seems near impossible.

I wonder if there is any related work around. That would be able to answer this question in any accurate way.

A simplifying assumption would be to limit the vector to 1/2 dimensions.

Neway

[lorinda]

I would simplify by working out how much each player returns on average.

For instance a -10% ROI player in a $11 returns $9.90

Add all the values together for the total prize pool and then work out what % of the new prize pool each player wins.

so if all the players are -10% ROI, the total is $99 so they all have $9.90 from $99 in the prize pool, which returns them $9.90 = 0% ROI
You then subtract 9.09% for rake, and they are all -9.09%

Lori

[e_fermat]

Some valid thoughts here. I think the best way to approach this would be to use past results and run a regression analysis based on table averages of completed SNG's using poker prophecy. If you have the time then take a sample of a few hundred recent SNG's and calculate the table average ROI of the other 9 players and then plot that against your results. The obvious hypothesis is that your ROI is negatively correlated the other player's ROI. Even still, you can perhaps find the cutoff point at which your ROI is diminishes to a point where it is not worth your time based on the table average ROI.

From a practical point of view, I try to leave if I recognize 3 or more names as strong players but often it's too late by the time I notice.

[johnnybeef]

[ QUOTE ]
It would be an interesting possibility to assign a vector (x,y,z...) to each player such that you could compute your tournament equity, before the first hand is dealt. (something like ICM)

The sad part is that again it would require some empirical avalidation, that seems near impossible.

I wonder if there is any related work around. That would be able to answer this question in any accurate way.

A simplifying assumption would be to limit the vector to 1/2 dimensions.

Neway

[/ QUOTE ]

player vector? what direction would we measure this in?

[johnnybeef]

[ QUOTE ]
I would simplify by working out how much each player returns on average.

For instance a -10% ROI player in a $11 returns $9.90

Add all the values together for the total prize pool and then work out what % of the new prize pool each player wins.

so if all the players are -10% ROI, the total is $99 so they all have $9.90 from $99 in the prize pool, which returns them $9.90 = 0% ROI
You then subtract 9.09% for rake, and they are all -9.09%

Lori

[/ QUOTE ]

i think that this would be a great way to quantify table selection as it is simple and effective.....but how does one assign these values (i.e. -10% roi)

[Paul2432]

[ QUOTE ]
[ QUOTE ]
1) What is the best way to model the impact of a good player taking a seat at your table?

2) If you sit down for a SNG, how many known good players would need to take a seat before you get up?

Paul

[/ QUOTE ]

A few things about your post in general:

It is a poor assumption that either the winning or losing players would have a consistent roi given the inroduction of more positive roi players. It is more likely everyone will do a little worse.

[/ QUOTE ]

I agree with this. My figures were just given as starting point for further discussion.

Another question: What is the ROI of a bad player?

Paul

[uphigh_downlow]

the vector can be something like (%First place finish, %2nd place finish,.....) or another suitable combination of parameters that can determine tournament equity, before play can start, or atleast approximate it.

well, I'm assuming that RoI does'nt provide an accurate enough estimation of tournament equity.

But maybe it does. Or maybe it is a close enough approximation.

You could simply add everyones RoI, and divide your RoI with the sum. That could be your potential equity in this trny.

However such an analysis is disjoint from the payout structure or other similar factors. Assuming consistent payout strutucture, maybe there is something to this hypothesis, but its far from a rigourous validation.

Anyway, what I was curious about is if anyone had attempted any such characterization in the past. Or anything close to it. Or maybe there is a similar problem in another field, which has a solution that can be adapted with some modifications.

[shejk]

The roi of many bad players is way way worse than -12%.