theoracle101

How does this compare to grape ? Interested in mainly REST API's for things like mobile API

The optimal betting strategy would be to "invest" a fractional percentage of your bankroll. See the kelly criterion from above.

Not doing so is suboptimal

"The original meaning is that a gambler who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually go broke, even if he has a positive expected value on each bet."

When you're selling deep out of the money puts you can't just assume there will be a buyer to satisfy the fractional betting condition mentioned by the author in the (theoretically correct) kelly principle.

"The original meaning is that a gambler who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually go broke, even if he has a positive expected value on each bet."

Yep, that is correct, but the kelly criterion requires fractional betting, which at some point in the real world is not possible, especially with options.

This is because there is a limited amount of options you can sell/purchase, so the fractional bet will always decrease as your bankroll increases. And there is also a floor where you cannot purchase below if your bankroll falls below (though your investors would have wiped you out by than).

That is suboptimal

This is not true at all and a common fallacy. See the gamblers attrition problem (or double knockout options for this who want to see the only closed form solution).

Essentially your wealth is path dependent. Though the expected value may be positive, once you are ruined you cannot continue to play (or in this case) invest anymore.

In math you could theoretically always bet (or invest) a fractional value of your wealth, but not in the real world.

https://en.wikipedia.org/wiki/Gambler%27s_ruin