Question about kelly betting

**qhdon** · 12-28-2018, 08:07 AM

I am trying to figure out the best way for me to grow my bankroll.

I understand that kelly betting is the best way to go and want to apply it to my strategy.

Lets say that I play full kelly and adjust my bet sizes for every 10% increase/decrease in my bankroll. If I start at 100k, I would play full kelly until I hit 90k or 110k, then adjust my bet sizes, then that's my new current bankroll, and so on. Assuming that I am considered bankrupt when my current bankroll reaches half of the original bankroll, what would be the risk of ruin of doing this?

How would the risk of ruin be affected If I did the same thing with 2/3 kelly or half kelly? What about if I assumed bankruptcy at 40% or 30% of original bankroll?

Tried to state my question as simple as possible but it's hard

How do other professional gamblers and card counters determine how much to bet?

Please provide explanations.
Thank you!

**DSchles** · 12-28-2018, 09:16 AM

In general, without adjustments, the formula is rather simple about losing x % of your original bank. The probability is 100% - x. So, you have an 80% change of losing 20% of your bank and a 30% chance of losing 70% of your bank.

Note, however, that your rebalancing schemes definitely complicate the situation. Most players don't adjust as frequently as you propose.

Don

**BoSox** · 12-28-2018, 09:35 AM

Originally Posted by qhdon

Lets say that I play full kelly and adjust my bet sizes for every 10% increase/decrease in my bankroll. If I start at 100k, I would play full kelly until I hit 90k or 110k, then adjust my bet sizes, then that's my new current bankroll, and so on. Assuming that I am considered bankrupt when my current bankroll reaches half of the original bankroll, what would be the risk of ruin of doing this?

Sounds like you would be starting out overbetting full kelly by 100% as you would stop playing if at some point your current bankroll hits $50k. An important aspect in all of this is are you intending to draw down from the playing bank for any type of living expenses? As this can also cause a multitude of unforeseen problems.

**BoSox** · 12-28-2018, 10:29 AM

qhdon, I hope you realize your risk would be astronomical. For example your bankroll hits $70k and you adjust the full kelly bet based on that same $70k when in reality you are only playing with a $20k remaining bank.

**G Man** · 12-28-2018, 10:46 AM

If you want to stop at the 50K level, you should simply start with a 50K bankroll. What you propose to do is playing a 50K bankroll like a 100K bankroll at full Kelly. The result is that you're playing a 50K bankroll at 2 x Kelly. Recipe for disaster.

**Jabberwocky** · 12-28-2018, 02:26 PM

Your resizing scheme is too severe. Most pros resize after a 20% directional change while avoiding the kamikaze full Kelly approach. G Man is right, the variance will destroy you.

**Three** · 12-29-2018, 11:09 AM

Originally Posted by qhdon

Assuming that I am considered bankrupt when my current bankroll reaches half of the original bankroll, what would be the risk of ruin of doing this?

If that is your bankruptcy definition, shouldn't you consider you BR $50K?

Originally Posted by qhdon

How would the risk of ruin be affected If I did the same thing with 2/3 kelly or half kelly? What about if I assumed bankruptcy at 40% or 30% of original bankroll?

Tried to state my question as simple as possible but it's hard

I think you are making the problem more difficult than it needs to be. When I was trying to grow my BR without removal of some of the growth, I tried to keep my RoR in a "comfort range". When RoR got out of that range I adjusted my bets to put it back in the middle of the range. Now I grow my BR to be able to spend a portion of the growth.

Originally Posted by qhdon

How do other professional gamblers and card counters determine how much to bet?

Most have a very large BR, so bets are constrained by what you will be allowed to get away with betting. Because of this my RoR is less than .01%. I could bet crazy into small advantages to keep RoR higher and max bet a much much lower advantage but so far I am not comfortable with that. Now that my BR is so large I should probably give that more thought.

**DSchles** · 12-29-2018, 06:59 PM

Originally Posted by Three

Now that my BR is so large I should probably give that more thought.

You actually figured out all by yourself that playing with a ROR of one in 10,000 is probably a tad too conservative?

Don

**Three** · 12-29-2018, 11:22 PM

Originally Posted by DSchles

You actually figured out all by yourself that playing with a ROR of one in 10,000 is probably a tad too conservative?

I just feel uncomfortable betting a lot on a thin advantage. I make plenty of EV, they tolerate my play, and with the high likelihood of BR growth I usually don't need to play much to make my money goals which adds to longevity. It is a nice balance that fits me well. I have been reluctant to mess with it. The computer play part is easily tinkered with. Being allowed to do it in a casino is what I have been worried about.

**qhdon** · 12-30-2018, 04:01 AM

Thank you for all your answers.

Great words from highly intelligent folks.

I agree that adjusting after 10% change would happen too frequently and unrealistic.

I am a part time counter at my local casino.

My current goal is to build up my bankroll up to a point where I would feel comfortable to go pro and play full time. (At least 50k is what I'm thinking, 100k would be nice) I wish to get there as fast as possible.

I know that full kelly betting with no adjustments results in a 13.5% RoR, and theoretically, if a player was able to make exact full kelly bets with adjustments after every hand, the RoR would be 0. I am looking for a strategy I can use with my 12k current bankroll, that will get it above 50k asap. Until I become pro, I am willing to have a RoR as high as 15%. I don't intend to quit after losing half my bankroll; it's win all or lose all.

This is what I'm currently doing. I assume a 15k bankroll and bet full kelly. I assume the 15k bankroll because I intend to put a grand into my bankroll every two weeks. I believe that the probability that I lose all the money within 6 weeks is very low, considering I don't have too much time to play anyways.

The RoR for me is higher than 13.5%, because of the many hands I am forced to play at a disadvantage. (only DD where I live) I want a better betting system, one that adjusts the bets as I win or lose. I thought, rather than going full kelly with an assumed 15k BR, I should go full kelly with my current bankroll and make adjustments as I play. One problem was that if I do end up with half my BR, 6k, I can no longer play with my system because I would be playing with no advantage at all at that point. That is why I asked to assume bankrupt at half BR.

Any advice will be of immense help.

Honor to have Don and Three argue here as well.

Thanks!!