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Comment by jessaustin | Hacker News Reader

When you think you'll win 2% of the time, those are good odds.

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

More relevantly (IMO), see: https://en.wikipedia.org/wiki/Kelly_criterion

There's a +EV (long run, even with finite starting bankroll) strategy readily available under the stated conditions.

"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

Agreed, suboptimal but only slightly at practical sizes of bankroll.

The Kelly criterion is about optimizing the speed of growth of your bankroll when betting with an advantage, so it's still "safe" to round down.

My trading account is "nowhere near the size of Taleb's" (to put it mildly) and I don't use his strategy, but I've never found that I wished for fractional optional contract sizes. (I don't even use the mini-S&P options.)

Those are still good odds and given enough bankroll you will win. Which of the cases in the article do you think disproves that?

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.

Who said anything about raising bets?

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

Sure. But you said "This is not true at all and a common fallacy". In fact, it is quite possible to reliably win when the odds offered are better than the actual odds.

I guess we're just talking over each other - you made an assumption that I don't believe was clear from the context.

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