Quote:
Originally Posted by David Sklansky
Nope.
They'll all go broke, and a trillion years is plenty of time for that to happen. Adding a googolplex losses together does not equal a combined profit.
IRL, there is a minimum wager, so there is a RoR even when kelly-betting (not that this is the reason you're wrong, but it might help you see that you are). Define the ruin point as some small fraction y of your initial bankroll where you're no longer able to place another wager.
There is a formula for the probability of ever reaching y when betting x*f. When x=1, you're kelly-betting and the formula simplifies to p = 1/y.
The formula is P(reach y) = y
(2/x - 1)
Notice that when x=2, the probability is 100%. The formula returns >100% for x>2, which really means 100%.
So if each of the googolplex participants has a 100% chance of going broke, that means every single one will go broke.
But even if there were no minimum wager (meaning no such thing as "broke"), they'd all be approaching 0 forever, which still isn't profit. They'd reach y, then they'd reach y^2, and so on until the universe ended.