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Although ROI is a little more complicated than probability of being in the money, there's no obvious reason to think it changes the relative information based on sample size.

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It pains me to disagree with my personal favorite 2+2 poster, but I think this is wrong. The variance of the r.v. ROI is much higher than the variance of the r.v. ITM. You need significantly more data to put a confidence interval around your ROI than you do for your ITM.

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If you think it might, it's possible to make a more complicated model, that could give you a more precise result (unless the assumptions are wrong, in which case it might do worse).

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I think the best thing to do (provided you have the computing power at hand) is to run simulations for a given probability distribution of finishes and, for each set of n trials, see if you fall within various confidence intervals. This is tedious and not very elegant, but it works!