[BeatingBaseball]

Kelly theory has always made sense to me and I do respect it - but would like to raise one question regarding it that has been in the back of my head for a long time.

Since Kelly theory implies that even in a +EV dynamic, one can be virtually certain to lose one's entire bankroll by "overbetting" - should it not conversely be theoretically possible (since we control the amount of the wager) to, let's say in the face of a small -EV, turn a virtually certain profit at some point in a run, simply by forcing the action beyond the "optimal" bet of an "opponent."

I ask this as a firm believer that -EV means dead in the long run and in full recognition of all the inviolate mathematics of gambling (the consraints of the "house limit," the virtual unlimited bankroll of the house and all the fallacies re chase systems, Martingale-type systems, etc.) But if Kelly says that it's so easy to turn +EV into being dead at some point in the run if you overbet - should there not by the same token be some subtle method to stucture one's betting to some advantage within the rules of a game (e.g., pass line on the dice table) that may present a slight -EV on any given wager in a series, but gives one control of both the wager amount and the length of the run (i.e., one can quit any time one is ahead).

[NunyaBidness]

Since Kelly theory implies that even in a +EV dynamic, one can be virtually certain to lose one's entire bankroll by "overbetting" - should it not conversely be theoretically possible (since we control the amount of the wager) to, let's say in the face of a small -EV, turn a virtually certain profit at some point in a run, simply by forcing the action beyond the "optimal" bet of an "opponent."

No, this is obviously untrue.

[NunyaBidness]

I ask this as a firm believer that -EV means dead in the long run and in full recognition of all the inviolate mathematics of gambling (the consraints of the "house limit," the virtual unlimited bankroll of the house and all the fallacies re chase systems, Martingale-type systems, etc.) But if Kelly says that it's so easy to turn +EV into being dead at some point in the run if you overbet - should there not by the same token be some subtle method to stucture one's betting to some advantage within the rules of a game (e.g., pass line on the dice table) that may present a slight -EV on any given wager in a series, but gives one control of both the wager amount and the length of the run (i.e., one can quit any time one is ahead).

If I'm understanding you, and I'm not sure that I am; if you're saying in a -ev game of chance where your opponent has a limited bankroll that you exceed and you can set the amount that is bet as well as choose to quit at any point in the future, can you turn it into a +EV situation?

No, you cannot. You will win his entire stake much more often than not, but you will have sessions with large losses. If your stop-loss is set at your entire stake, and say you will quit at a win of one unit, you will win one unit almost every session, with an incredibly rare session where you lose everything. Over time this will approximate the neg. expectation of the original wager.

[BeatingBaseball]

Thanks for responding, Nun. I certainly understand and agree that everything you say is true. We can never turn a -EV game of chance into +EV no matter what we do.

It simply intrigues me that since Kelly implies that it's not in our financial best interest to overbet even when we have a series of +EV propositions, it might also be in the financial disinterest of the house if we could take advantage of that same dynamic by making the house overbet their edge. I realize they have a virtually unlimited bankroll and that bankroll is key to Kelly betting - but if we were shooting for a set win goal for a series the amount of our goal would in effect serve as the house bankroll for that given session. Kelly says there is an optimal bet size for them to maximize their edge in defending that bankroll. Of course, the last thing we would want to do is bet their optimal amount, so if we were to wager amounts exceeding that optimal bet size it should per Kelly be to our advantage to some degree as the increase in variance would offer a better shot at getting over the top at some point in the action. I agree, however, that we'd ultimately and inevitably run into the nightmarish blood bath session that would take us out.

[Carl-Haakon]

It simply intrigues me that since Kelly implies that it's not in our financial best interest to overbet even when we have a series of +EV propositions, it might also be in the financial disinterest of the house if we could take advantage of that same dynamic by making the house overbet their edge.

I recall Taleb writing something about this as a riddle somewhere on his webpage or in one of his books; I think it went something like

"If you have to bet with the odds stacked against you, bet as much as possible on as few occasions as possible"

Basically, if you have a statistical edge you'll want to bet small amounts of your BR over many occasions in order to get as much of that edge as possible without losing your BR (which is what Kelly wagering is about), so if your EV is negative you'll want to increase your bet size and lower the number of times that you bet (if you have to bet).

The statement did intrigue for a long time, but I can't remember exactly where I saw it. I'll post the exact quote here if I find it again.

EDIT: I forgot that this was about profitable betting with -EV; the quote I mentioned is only about how to bet if you have to bet with -EV

[BeatingBaseball]

Thanks, Carl. When you say it like that it makes perfect sense.

The key is IF you have to play a given amount (bankroll) into neg EV propositions, there's no way to make it +EV, but you mitigate the odds against you if you fire the highest percentage possible of that bankroll as few times as possible. The shorter the run, the more the +EV opponent is gambling as well.

Certainly a casino exec would rather a tourist with 3K to blow in Vegas put that stake across the table in $100 increments than as one single shot on the pass line at the dice table. In the latter case, even though he has +EV, he's gambling almost as much as you are. Also the reason you'l never get comped playing like that.

This also relates to another current thread on this forum re a +EV proposition to pick a marble out of a bag. In the prop you can only do it once. It's not a good move to offer that proposition at all, but you'd have to be really crazy to let someone do it all day:

http://www.sportsbookreview.com/forum/handicappe...tion-quiz.html