Lifetime bankroll and risk of ruin

[Dopple]

If I have good 5 -100 bj available now at a nearby location I would think I would be better off in the long run say after 100 hours of play if I popped up to say double of triple the kelly betting or Ustons TC +1 as I can always go back to work and build up my bank again. I know I will win in the long run and could in fact suffer several thousand in the short run but without trips to Vegas few and far between I am better off always IMHO putting as much money as I can down especially when it is really good say a +8 TC with maybe 2 decks left.

How can I be wrong here correct me if you wish, just food for thought.

 

[ah...craps]

Well in arnold snyder's book, he suggests not using your current bankroll to determine betting but instead your replenishable bankroll. However, betting 4% of your bankroll when you have a 2% advantage will greatly increase your ror...you should familiarize yourself with gambler's risk of ruin, variance, standard deviation, etc. Even fully kelly betting i've read is generally reserved for team play as large teams can generally afford the higher ror as they can form a new bank...most of which will not consist of their own money.

 

[Dopple]

But may I suggest that there is in fact perhaps immediate ruin and trouble for having to wait until you can replenish your bankroll but in the long run you should net better and be working with a bigger bank as your winnings will provide that for you. Perhaps there could be less time at the table however in the beginning so it would be better to ramp up.

If you had a $1,000,000 bank would you not go to the full 16x max spread at the most minute advantage for theoretically correct play.

 

[ah...craps]

Sounds to me like you basically want to put all your money on black and let that determine if you'll be playing bj in the future. I don't condone that...but to each his own.

Huh? With a 7 figure bankroll and table maximum of $100...you should be betting $100 when you have the advantage and $0 when you don't to attain maximum benefit. Or you could just open up your own casino...your call. A betting spread is used to control variance...

 

[callipygian]

I think you have a fundamental misunderstanding of what Kelly betting means. Kelly betting is a proportion of your bankroll, which means that ideal Kelly betting requires constant bet resizing. Every time you lose a hand, you should resize your bet. Of course, the casino isn't going to take a $7.63 bet, so in reality Kelly betting never exists - your bets are quantized to whatever increments the casino will allow you to bet.

Full Kelly betting without resizing will by itself lead to a huge ROR - it's pretty close to 50% by my calculations, but my sim isn't meant for estimating high ROR, so maybe someone else can jump in. Greater than full Kelly without resizing is going to lead to even higher ROR.

Once your lifetime ROR breaks 50%, you're better off just taking your entire bankroll to the craps table and hoping to double up with one bet.

 

[rukus]

I think you have a fundamental misunderstanding of what Kelly betting means. Kelly betting is a proportion of your bankroll, which means that ideal Kelly betting requires constant bet resizing. Every time you lose a hand, you should resize your bet. Of course, the casino isn't going to take a $7.63 bet, so in reality Kelly betting never exists - your bets are quantized to whatever increments the casino will allow you to bet.

Full Kelly betting without resizing will by itself lead to a huge ROR - it's pretty close to 50% by my calculations, but my sim isn't meant for estimating high ROR, so maybe someone else can jump in. Greater than full Kelly without resizing is going to lead to even higher ROR.

Once your lifetime ROR breaks 50%, you're better off just taking your entire bankroll to the craps table and hoping to double up with one bet.

full kelly betting without resizing leaves you with a 13.5% ROR. fully kelly betting with constant resizing leaves you with a 0% ROR.

 

[Automatic Monkey]

full kelly betting without resizing leaves you with a 13.5% ROR. fully kelly betting with constant resizing leaves you with a 0% ROR.

Any resizing will give you a 0% RoR if a small enough increment is allowed.

All Kelly's theorem does is find the ideal balance between profitability (in our case, win rate) and risk. If we took all the players on this site and sent us out to play our game, keeping accurate records and with no resizing, as a team we'd make a maximum amount of money over time at full Kelly, even though 13.5% of us would crash and burn. Changing our bets so that either more or fewer of us crashed and burned would reduce our sum profit. But that might be the better thing to do, depending on how much we feared being one of the 13.5% or how unwilling we are to wait for our money with the relatively small Kelly bets.

 

[rukus]

Any resizing will give you a 0% RoR if a small enough increment is allowed.

All Kelly's theorem does is find the ideal balance between profitability (in our case, win rate) and risk. If we took all the players on this site and sent us out to play our game, keeping accurate records and with no resizing, as a team we'd make a maximum amount of money over time at full Kelly, even though 13.5% of us would crash and burn. Changing our bets so that either more or fewer of us crashed and burned would reduce our sum profit. But that might be the better thing to do, depending on how much we feared being one of the 13.5% or how unwilling we are to wait for our money with the relatively small Kelly bets.

dont disagree with anything you said here, i was just correcting the post above mine about 50% ror for full kelly with no resizing.

 

[Automatic Monkey]

dont disagree with anything you said here, i was just correcting the post above mine about 50% ror for full kelly with no resizing.

Oh sure, I know you know this stuff. I just like saying it sometimes.

I suppose Kelly's theorem would have applications in the insurance industry too. Let's say a bunch of us got together and contributed to an insurance pool, to replenish the bankroll of any contributor who busted out. That would be a reasonable form of team play, wouldn't it?

 

[callipygian]

full kelly betting without resizing leaves you with a 13.5% ROR.

I believe that number is for full Kelly betting with Wonging, as proper Kelly betting forces you to Wong in/out at TC +1 because EV<0. I'm assuming he isn't Wonging (as most people don't) in which case the ROR ends up being higher.

Although I did recognize a methodological flaw in my calculations - I double-counted the betting ramp, so I ended up with a higher variance than I should have. My recalculation still shows 39% but my main point is that full Kelly without Wonging produces a pretty high ROR by itself, going double Kelly will probably be comparable to the craps game.

 

[Kasi]

All Kelly's theorem does is find the ideal balance between profitability (in our case, win rate) and risk. If we took all the players on this site and sent us out to play our game, keeping accurate records and with no resizing, as a team we'd make a maximum amount of money over time at full Kelly, ...

I don't know.

I thought Kelly maximizes the (logarythmic) growth rate of our roll, taking into consideration risk and reward like you say.

I don't think it maximizes EV as you also maybe seem to say.

Like maybe maximizing growth and maximizing EV are 2 separate goals

Like I said, I don't really know lol.

Any thoughts welcome.

 

[rukus]

Oh sure, I know you know this stuff. I just like saying it sometimes.

I suppose Kelly's theorem would have applications in the insurance industry too. Let's say a bunch of us got together and contributed to an insurance pool, to replenish the bankroll of any contributor who busted out. That would be a reasonable form of team play, wouldn't it?

indeed would be a reasonable form of play if you split the risk amongst enough players (which depends on your betting level and individual bankrolls). i wonder how the math would work out vs just pooling everyones bankroll into one big one but no one changing their bet sizes to match the new mega roll. though you still run into the trust issues. "woops guys, i busted by bank again, so im calling out my insurance policy (again :devil".

 

[callipygian]

I thought Kelly maximizes the (logarythmic) growth rate of our roll, taking into consideration risk and reward like you say.

I don't think it maximizes EV as you also maybe seem to say.

Like maybe maximizing growth and maximizing EV are 2 separate goals

That's exactly it - Kelly maximizes long-term win rate, adjusted for downswings and upswings over time. EV is something that is invariant with how many hands you play, it's defined by the decisions you make with no regard to whether you actually win or lose.

 

[bj bob]

Oh sure, I know you know this stuff. I just like saying it sometimes.

I suppose Kelly's theorem would have applications in the insurance industry too. Let's say a bunch of us got together and contributed to an insurance pool, to replenish the bankroll of any contributor who busted out. That would be a reasonable form of team play, wouldn't it?

Very interesting perspective. Let's take this scenario and say that we have a team of seven AP's playing a strong DD game with a BR of $10K each (EMFH). with the understanding that the "team pool" is available to any member who taps out and his 10K will be replenished so he can continue playing. This replenishment comes solely out of the winnings of the others' BR. With this scenario, would this team be able to continue to play perpetually @ 1.0 Kelly?

 

[rukus]

Very interesting perspective. Let's take this scenario and say that we have a team of seven AP's playing a strong DD game with a BR of $10K each (EMFH). with the understanding that the "team pool" is available to any member who taps out and his 10K will be replenished so he can continue playing. This replenishment comes solely out of the winnings of the others' BR. With this scenario, would this team be able to continue to play perpetually @ 1.0 Kelly?

you would need to look at the drawdown and BR growth probabilities for playing @ 1.0 kelly and then look at the joint probabilities that multiple players draw down at the same time while others increase their BR. without much deeper thought, i am still leaning towards thinking you can just consider this as 1 person playing with a new megaroll for analysis of tapout/BR growth probabilities purposes, but maybe i am wrong?

 

[bj bob]

you would need to look at the drawdown and BR growth probabilities for playing @ 1.0 kelly and then look at the joint probabilities that multiple players draw down at the same time while others increase their BR. without much deeper thought, i am still leaning towards thinking you can just consider this as 1 person playing with a new megaroll for analysis of tapout/BR growth probabilities purposes, but maybe i am wrong?

That's the reason I chose a 7 man team since that's approximately the 13.5% RoR which Kelly addresses, i.e 1/7. So just doing the cursory math, one could assume that 2 players tapping out at the same time would be 13.5 x 13.5= 1.83% of the time, same as .5 Kelly.

 

[rukus]

That's the reason I chose a 7 man team since that's approximately the 13.5% RoR which Kelly addresses, i.e 1/7. So just doing the cursory math, one could assume that 2 players tapping out at the same time would be 13.5 x 13.5= 1.83% of the time, same as .5 Kelly.

true, i caught your deliberate use of 7 players. we arent just interested in a player tapping out, but in probabilities like when a player or two taps out while others have drawn down far enough that they can no longer wholly replenish the tapped out players. that would determine the viability for using a system like this as a sort of insurance policy.

 

[bj bob]

true, i caught your deliberate use of 7 players. we arent just interested in a player tapping out, but in probabilities like when a player or two taps out while others have drawn down far enough that they can no longer wholly replenish the tapped out players. that would determine the viability for using a system like this as a sort of insurance policy.

And that was my fundamental question. At what % of Kelly (fixed or resized) can a 7 man team realistically expect to play continuously by being "self-insured"?

 

[zengrifter]

If I have good 5 -100 bj available now at a nearby location I would think I would be better off in the long run say after 100 hours of play if I popped up to say double of triple the kelly betting or Ustons TC +1 as I can always go back to work and build up my bank again. I know I will win in the long run and could in fact suffer several thousand in the short run but without trips to Vegas few and far between I am better off always IMHO putting as much money as I can down especially when it is really good say a +8 TC with maybe 2 decks left.

How can I be wrong here correct me if you wish, just food for thought.

Use 1/4Kelly on BR as calc'd to future BR with replenishment discipline and you'll be fine. zg

 

[rukus]

And that was my fundamental question. At what % of Kelly (fixed or resized) can a 7 man team realistically expect to play continuously by being "self-insured"?

understood. so let's assume each of the 7 has 10k. i think we can answer it (or at least simplify the math) by looking at it as if its one player using a megaroll (7 x individual bankrolls) but betting 1/7 kelly.

we just need to define the level of everyone's combined bankroll (70k to start, or this one megaroll) at which we can no longer re-supply a teammate who has tapped out. is it 35k? is it 60k?

we would also need to define "playing continuously" - we can all keep playing continuously but with a BR that is projected to neither grow nor shrink in the long run. dont think that's worth our time .

i definitely understand the idea. and while it truthfully seems more like an academic study given the trust issue inherent with every team, im always interested in new ideas. i think the idea needs to be fleshed out a bit more before any math can be run on it....