Re: Variance
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You cant just put % on one of the axes.
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I know, I didnt suggest only using it one axis.
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Linear means that for each 1 unit increase in one axis, there is a fixed amount of increase or decrease on the other axis. (As an aside, this comparison should probably be win rate vs risk of ruin instead of win rate vs required bankroll). For this example, for the relationship to be linear the additional amount of bankroll required for a decrease in win rate from 2.0 to 1.5, for example, should be the equal to the additional amount of bankroll required for a decrease in win rate from 1.5 to 1.0. That isn't the case here.
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Well duh, no one should ever consider that to be what anyone is referring to if they said there was a linear relationship between WR and Bankroll required. Obviously, the scenario you describe for any poker scenario since the BR required will be infinity for all WR <0, thus it will be assymptotic as x->0. Percentage are clearly implied in this conversation (or use natural logs if u like).
The interesting question is, does variance increase with a decrease in WR.
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