[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?

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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.