Increased prize equity = How much increase in ROI?

[Rambling Wreck]

I apologize if some one has already done all this analysis and there is already plenty material available.
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I was just wondering how a small edge of 0.5% in a game can make a difference.
So I started calculating how much difference this small edge can make.

Okay - here is the biggest drawback of my computations and analysis. I assumed that ROI is directly proportional to prize equity since it represents stake in prize money. Some of you might argue that a small increase in edge% might result in huge increase of ROI because of the nonlinear payout structure. But isn't that already taken care of by the edge% which uses ICM?


Other trivial Assumptions:
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A big assumption I am making is that I have my opponents figured out (calling ranges) and I make perfect decision every time and play infinite games.
I did not check the computations for -ve ROI but I doubt it will matter.


Here are my computations-
On a N person table E% increase in prize equity means increase of NxE/100$ equity
If the rake is K% and my current ROI is R% then the new ROI is
ROI(old) + 100*((N * E)/(100+K))
Please note that the increase in ROI is independent of ROI and is equal to
100*((N * E)/(100+K))

At a 9 players table with 20% rake it would bring
100x9x0.5/(100+20) = 3.75%

My initial guess was 4.5% but the rake changes things because we don't have stake in rake but it is counted toward
ROI computations.

At 10% rake the increase in ROI is 4.1%.

Points to take home:
1. Increase in ROI is independent of current ROI.
2. If some one has low ROI it making these small edge decisions can almost double their ROI.
3. If some one is at medium-high ROI (20-30%), because the increase in ROI is smaller portion of their ROI, they can make decisions that have very little Edge% (0.1-0.2%) without losing too much ROI. Decreasing edge from 0.5% to 0.2% only decreases their final ROI by 2.5% (the increase in ROI is only 1.63% instead of 4.1% with higher edge). But they might be able to play more hands per hour and increase their overall returns.

[Rambling Wreck]

I posted this in Poker Theory after refining my thoughts a little bit.
http://forumserver.twoplustwo.com/showfl...=0#Post13128855