[Octopus]

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A greater edge doesn't mean your variance will change. It just mean your winrate will be higher.

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Gotcha! Your variance is simply a measure of short-term luck (for both you and your opponents), right? The edge you have over your opponents would not change that. That would simply change the fact that you're going to win more. Is it more complicated than that or am I right on?

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You are right on and it is more complicated than that. The two things are not unrelated.

For example, if your edge over your opponents came from them betting/raising everytime it was their turn to act, regardless of their holdings, then both your winrate and your variance would be much higher than it they are now.

In other words, how your opponents play has a direct effect on your own variance.