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"showing that odds based investing can be relatively easy" It depends on what you mean by easy. To maximize the probability of going from $1 -> $1B in 1000 fli

"showing that odds based investing can be relatively easy" It depends on what you mean by easy. To maximize the probability of going from $1 -> $1B in 1000 flips, you need to bet almost everything you have every time (the answer to the problem is > 0.99999). If you do so, you must win at least 917 of the coin flips to get more than $1B. I can't compute the probability of this event, but using the normal approximation to the binomial distribution, the probability of winning at least 615 coin flips is less than 1 in a trillion (10e-12). You can imagine how much lower it is if you need 917 flips. This is under the favorable betting scenario where you get 2x the value of your bet every time you win. EDIT: Ignore everything above. Clearly I solved this a while ago and forgot to check what the actual question was. The probability that you become a billionaire is > 0.99999, the optimal fraction is quite small, of course. Things change drastically if you get the value of your bet when winning instead of 2x (it seems you need 602 coin flips in that case which is about 0.07 in a billion).

taeric 10y ago
That isn't what that answer means, is it? Rather, that is your odds of becoming a billionaire. Which is basically certainly. Now, yes, that is greatly simplified and lets you always divide your current wealth. And always double. That is what I meant about floors and ceilings. I recall playing with the code to toy with more realistic situations. Washing fees out of the game makes it a lot easier to not lose everything. By no means guaranteed. But easier. And it is likely someone could have done really well by the odds. Edit: Just saw your edit. Yeah, it was easy to think it was asking the other question. And yes, realistic scenarios are vastly different. Otherwise, a lot of us would be billionaires. :). Just pointing out that the odds aren't nil. Just small. And don't forget, in real scenarios you can change games once you have won enough.

taeric 10y ago

That isn't what that answer means, is it? Rather, that is your odds of becoming a billionaire. Which is basically certainly. Now, yes, that is greatly simplified and lets you always divide your current wealth. And always double. That is what I meant about floors and ceilings. I recall playing with the code to toy with more realistic situations. Washing fees out of the game makes it a lot easier to not lose everything. By no means guaranteed. But easier. And it is likely someone could have done really well by the odds. Edit: Just saw your edit. Yeah, it was easy to think it was asking the other question. And yes, realistic scenarios are vastly different. Otherwise, a lot of us would be billionaires. :). Just pointing out that the odds aren't nil. Just small. And don't forget, in real scenarios you can change games once you have won enough.