STT - How will ROI change if I increase my ICM edge?

[Rambling Wreck]

I apologize if some one has already done all this analysis and there is already plenty material available.
I had posted this in STT but I thought it is more appropriate here.

Question 1:
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Is payout directly proportional to prize equity?
That means if I will pass up 0.2% edge and make decisions that have 0.5% edge will the increase in payout be proportional to this additional edge?
I am assuming the answer is yes since the prize equity accounts for the pay structure.
If the answer is no then my model in Question 2 is invalid. You may point me to the correct analysis.

Question 2
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Assuming the statement in Q1 I computed increase in ROI if I start making decisions that have greater edge. By that I mean I will pass up 0.2% edge and make decisions that have 0.5% edge. According to the assumption I made in Q1, I say that my payout increase by an amount proportial to the edge% I increased.

Another assumption is that I have my opponents figured out (calling ranges) and I make perfect decision every time and play infinite games.

Here are my computations-
On a N person table E% increase in prize equity means increase of N x Buyin x E/100$ payout (Using the statement in Q1)

If the rake is K% and my current ROI is R% (based on buyin+rake) then the new ROI is
ROI(old) + 100*((N * E)/(100+K))

Question 3
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If you agree with model in Q2 would you agree with following statements?
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.

[plexiq]

Short answer: Passing up small +EV spots will not automatically increase your ROI. It may as well lower your ROI.

Trivial example: If you set your min-edge to 100%, you will not play a single hand, and your ROI will probably be very close to -100%.

[Rambling Wreck]

I agree this is true but only in an imperfect world where you and your opponents are "trading mistakes". You might push all in with slight edge (push-fold diff) (which is a small mistake) but your opponent might call with negative call-fold diff (huge mistake). These opponent mistakes are the #1 reason behind our ROI (Thank God for the fish!).

But in a perfect world where everybody makes right decisions I think the edge you choose represents your ROI.

I am not sure about the example you gave. If I play infinite games I should have +ve ROI (in perfect world) if I make 100% edge decisions.

What about if I increase my edge from 0.2 to 0.3?
Should that increase my edge automatically?

[pzhon]

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But in a perfect world where everybody makes right decisions I think the edge you choose represents your ROI.


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No.

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I am not sure about the example you gave. If I play infinite games I should have +ve ROI (in perfect world) if I make 100% edge decisions.


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If you wait for AA, you will be a big favorite when you play. You will also lose money extemely rapidly when you fold hands like AQ and JJ that pay for the blinds.

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What about if I increase my edge from 0.2 to 0.3?
Should that increase my edge automatically?

[/ QUOTE ]
No.

A very good player, who wins on average on other hands, may prefer to give up some +EV but high variance gambles which are less advantageous for the variance than playing normal poker.

You do not become a good player by giving up advantages.

It is more questionable to give up a marginal push than to give up a marginal call. First, the push has less variance, since you don't know that you will be called. A smaller edge will have a good edge-to-variance ratio. Second, while you don't know that your opponent is pushing or calling with a good range, you can often count on larger errors from your opponent on his calls. This means your edge on pushes in practice is significantly greater than what the programs indicate.