[ryanj247]

i'm almost certain i've seen calculations that say "if you've won $x in the past 100K hands, there is a y% probability that your winrate is between a and b". so it seems to me that we ought to also be able to calculate something like "if your winrate is x, there is a y% probability that you will win $x, a z% probability that you will lose $x, etc". for any given $ amount, positive or negative, we ought to be able to calculate the probability that at the end of, say, one year, a player with a given winrate would end up with that amount of $.

that would give us a "model" of this "investment". once we have that, isn't there a mathematical way to evaluate that against any other investment? aren't other investments analyzed with that same type of modeling? isn't an investment that has shown returns of {7%, 7%, 7%, 7%, 7%} a much different investment than one that has shown returns of {7%, 100%, 7%, -93%, 7%} in the past 5 years? (i understand the total ROI on those two investments is not the same for the past 5 years, but you get the idea...whatever the numbers in years 2 and 4 of the latter investment would have to be for its total ROI to have been equal to the former for the 5 year period) how do you compare and choose between those two investments when you're considering investing for a one year period? isn't there a way to take the returns for the past 5 years on the latter investment and be able to answer the question "what is the probability that the return next year will be 75%"? how would you use the answer to that question in deciding which investment was the better choice?

as for the poker "investment", i am assuming that the winrate is established and constant (same with the standard deviation). i understand that's a big assumption, but i'm trying to calculate probability of any given win/loss in a certain period of time given a certain winrate. once i can do that, then i can estimate best case/worse case with higher/lower winrates...