OT: MATH PEOPLE NEEDED. Slim Pickens, Sheets, etc... help answer! Theo

[j00hndayton]

I'm trying to figure out what affect other players have on the profitability of sng's. My hypothetical situation:

There is a 9 person SNG with players A, B, C, D, E, F, G, H and I. After a statistically significant number of SNG's are played between these players it is determined that:

A) Players A-G are break even in this game
B) Player H has a -10% ROI
C) Player I has a +10%ROI
D) There exists a player, J, who if substituted for player I, would also have a 10% ROI and would not affect the ROI's of the other players.

What happens to everyones ROI if one of the break even players was replaced with player J?

I don't know if I'm asking the right question or if this question is even answerable but any in depth analysis is welcome.

[DannyOcean_]

I don't know if this is entirely answerable. How much ROI is J gonna steal from the breakevens as opposed to player I? I would think he'd steal more from player I, because he'll be likely to last longer than others, and he and I will end up HU or 3 handed more often that any other pair, thus having a greater effect on each other than other breakeven players.

Interesting question, im not sure it has an answer that is provable.

[Insty]

[ QUOTE ]

What happens to everyones ROI if one of the break even players was replaced with player J?


[/ QUOTE ]

[ QUOTE ]

D) There exists a player, J, who if substituted for player I, would also have a 10% ROI and would not affect the ROI's of the other players.


[/ QUOTE ]

So Nothing.


a) What is the question you are trying to ask?
b) Why?

[DevinLake]

Insty, you are confused.

This is an interesting question. But, as stated there is obviously no one mathematical answer.

This is a problem with ten unknowns, so you 10 relationships to close the system.

But how do you get those ten relationships? It is hard to say what affect this new 10% ROI player will have on each individual. This style may make one player adjust more poorly than others and various other unknowns.

[billxo1b]

my guessitmate:

8.5,8.5,-1,-1,-1,-1,-1,-1,-11

[pifhluk]

[runhot]

42

[Slim Pickens]

There's no rake in your system. Rake is usually really important when looking at these sorts of ROI calcs.

Every player i has their ROI change by some amount, call it deltaROI_i when player i=J turns into the 10% player.

1) ROI'_i = ROI_i + deltaROI

You can make some assumptions about how all the deltaROI's relate, like they are all the same or they are all the same fraction of a player's previous ROI or something... whatever makes the most sense. Keep making assumptions until you can solve the system equations formed by...

<ul type="square">[*] all the equations from 1[*] a money balance on the system[/list]

[cougar62]

I've thought about this sort of thing too. For example, lets say there's $100 in the prize pool and 10 players (just to ease the calcs). If we don't know anyone's skill level we assume that each player has $10 of equity before the tourney starts.
But let's say player A is a 10% roi player, and the rest are -10% as they break even over time and lose the rake (in other words, what the entire poker population does as a population). Everyone's equity must always add up to 100%, so would we say at the beginning of the tourney that player A has $12.10 of equity, assuming a $1 rake and his 10% roi? I guess what this rambling is getting at is that, IMO, a 10% roi player has 12.1% equity and the others divvy up the other 87.9% if the opponents were selected at random.
Is this kind of what you are asking? And to folks like Slim am I right, and how do you then adjust for other known roi's in the tourney?

[Gramps]

I think there was a long thread ~3 years ago started by Dali on the subject of how much your ROI is affected by one or two extra good players sitting in your game. Not quite what OP is asking about, but anyone interested in the general topic might want to pull that up from the archives.