Long-term ROR with resizing

**Optimus Prime** · 04-01-2019, 10:18 AM

The ROR formulas assume that you never change your betting scheme as your bankroll shrinks and grows. The expected growth formulas make the same assumption. If you're resizing every time your BR shrinks or grows, your actual chance of ever hitting zero should be much lower than your calculated ROR and your expected growth in bankroll should be exponential.

Is there a way to calculate your real ROR, assuming a given betting scheme and further assuming that you'll resize bets in proportion to your new BR after some given amount of BR fluctuation?

Hoping maybe CVData does this...

**DSchles** · 04-01-2019, 10:57 AM

Originally Posted by Optimus Prime

Is there a way to calculate your real ROR, assuming a given betting scheme and further assuming that you'll resize bets in proportion to your new BR after some given amount of BR fluctuation?

It's a valid question, but one not easy to answer. Of course, if you bet pure Kelly and constantly resize (in theory only), your ROR is zero.

To accomplish what you're looking for, you need to specifically enunciate exactly where the thresholds will be for rescaling your bet sizes, and, even then, I'm not sure of a precise formula. I expect that simulation would be easier.

But, there is a principle that can help, at least a little. If you bet Kelly, without resizing, the probability that you will lose x% of your bank at some point is (100 - x)%. So, far example, there is an 80% chance that, at some point, you will be down 20% of your starting bankroll. This is without any time constraint or goal.

So, for example, suppose you said that if you lost 20% of your bank, you'd resize to 80% of original stakes but then, from that point on, you would continue to play until you were ultimately ruined ... or not. In that case, your first probability would be that you would have an 80% chance of having to cut back, and then you'd have the customary 13.5%, non-resizing, ROR from that point on. So, ultimate ROR, from the very beginning, would be 80% of 13.5%, or 10.8%.

But, you can see how quickly such a manual calculation would get out of hand and much too complicated with multiple thresholds.

Don

**Optimus Prime** · 04-01-2019, 11:12 AM

I would think that this could be simulated. You provide your ROR, etc. from CVCX, your thresholds for resizing, how you'll resize when you do, and bet minimums and maximums you may run up against. Does that sound like it would give valid results?

If no one has coded something for this, I may do it myself. Are there variables I would need other than the above?

I think where it might get sticky is if rules change on you as stakes go up or down. For example, during a BR downturn, you may not be able to sit at the $100 min table that has the good rules.

**DSchles** · 04-01-2019, 01:34 PM

Originally Posted by Optimus Prime

I would think that this could be simulated. You provide your ROR, etc. from CVCX, your thresholds for resizing, how you'll resize when you do, and bet minimums and maximums you may run up against. Does that sound like it would give valid results?

If no one has coded something for this, I may do it myself. Are there variables I would need other than the above?

I think where it might get sticky is if rules change on you as stakes go up or down. For example, during a BR downturn, you may not be able to sit at the $100 min table that has the good rules.

When you do studies like this, you don't complicate your life by introducing too many variables at the first pass. I would keep all the limits and rules identical. Solve one problem at a time.

Don