Question about risk of ruin

There's a concept I can't quite get my head around. Let's say you determine a bankroll that will give you a RoR that you consider acceptable. Now you play +EV video poker--and the usual result in the short term is that your bankroll diminishes. If you "complete" one royal cycle, just before you hit that royal, you'll be down something like 0.95 royals. This might mean that your RoR has dropped to unacceptable levels, which by definition means that you should stop playing. But this result--significant short-term losses--is the rule, not the exception. So what kind of safety margin do you actually need? If you had a 5K bankroll (with a resultant acceptable RoR), but the RoR for a $4K bankroll would be too high, isn't that 5K bankroll in reality insufficient to keep you in action?

Quote: Eaglesnest

There's a concept I can't quite get my head around. Let's say you determine a bankroll that will give you a RoR that you consider acceptable. Now you play +EV video poker--and the usual result in the short term is that your bankroll diminishes. If you "complete" one royal cycle, just before you hit that royal, you'll be down something like 0.95 royals. This might mean that your RoR has dropped to unacceptable levels, which by definition means that you should stop playing. But this result--significant short-term losses--is the rule, not the exception. So what kind of safety margin do you actually need? If you had a 5K bankroll (with a resultant acceptable RoR), but the RoR for a $4K bankroll would be too high, isn't that 5K bankroll in reality insufficient to keep you in action?

RoR is a useless measure, IMO. You need to use Kelly Criterion and re-evaluate as your bankroll drops, and drop down in stakes when your bankroll can no longer support the level that you are playing.

The reason that it is useless is exactly for the reason that you point out. The RoR is only accurate up until you make your first bet. After that it rises if the lose the bet, and drops if you win it. You can't just do one calculation and then stick your head in the sand and start playing until you hit it big or run out of money.

Unfortunately, Kelly isn't all that useful for VP. Usually, a given opportunity only exists at one denomination--that overwhelmingly being .25. Also, you can't drop down to .20 or .15 when your BR diminishes; the next available lower increment is usually .10, at which point you might as well not bother. Likewise, if you had been playing at $1 or .50 denoms (assuming you could even find a decent play), your next drop-down would be to halve the stakes at which you're playing. So at that point, assuming you made the Kelly adjustment soon enough, you're now underbetting Kelly (if, for instance, the proper Kelly bet would now be $4 instead of $5, you can't play four coins, and to drop down to halves would mean you're only betting $2.50).

Furthermore, Kelly isn't very useful by itself. It only identifies the optimum bet given a certain +EV and variance. If you play VP at a professional level, you'll be playing games of low (JOB, etc.), medium (FPDW, JW) and high (DB, DDB) variance. A bankroll more than sufficient for one game may be grossly inadequate for another, even at the same denomination. There is also the question of whether one should reduce to, say, 1/2 Kelly when minimizing RoR is paramount, even at the expense of optimum bankroll growth. If you're playing with an advantage, volatility is your enemy.

Quote: Eaglesnest

Unfortunately, Kelly isn't all that useful for VP. Usually, a given opportunity only exists at one denomination--that overwhelmingly being .25.

Kelly is useful for everything.

If you can choose how much to bet, it tells you how much to bet. If not (so your only choices are either play or don't play) then it tells you if you have the bankroll to play.

Never bet more than double Kelly. This is critical. Betting 0 is equivalent to betting double Kelly, and is superior to betting more than double.

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Also, you can't drop down to .20 or .15 when your BR diminishes; the next available lower increment is usually .10, at which point you might as well not bother. Likewise, if you had been playing at $1 or .50 denoms (assuming you could even find a decent play), your next drop-down would be to halve the stakes at which you're playing. So at that point, assuming you made the Kelly adjustment soon enough, you're now underbetting Kelly (if, for instance, the proper Kelly bet would now be $4 instead of $5, you can't play four coins, and to drop down to halves would mean you're only betting $2.50).

But it tells you which of those choices is best for you. You don't have to be able to make the exact optimal bet. When you can't make the one that is as close as possible to optimal. This mean (repeating myself from above) that 0 is superior to 2x Kelly.

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Furthermore, Kelly isn't very useful by itself. It only identifies the optimum bet given a certain +EV and variance. If you play VP at a professional level, you'll be playing games of low (JOB, etc.), medium (FPDW, JW) and high (DB, DDB) variance. A bankroll more than sufficient for one game may be grossly inadequate for another, even at the same denomination.

Yes, exactly. That's why you need to use the Kelly Criterion. It takes variance into account. The optimal Kelly bet for JoB will be much, much (much much much) higher than the optimal bet for TDB if you have the same edge in both.

If you are just multiplying your edge by your bankroll, you are not using the Kelly Criterion. There is, unfortunately a common misconception that that's what the Kelly Criterion is.

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If you're playing with an advantage, volatility is your enemy.

Yes, exactly, which is why the Kelly Criterion takes all this into account.

This seems to be one of the most misunderstood concepts in advantage play that there is. I've been meaning to write a simple paper about it (which I hope would be easily accessible) but I've been way too busy and lazy.