Lifetime bankroll and risk of ruin

[bj bob]

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?

All right, just for giggles, let's say it's a $140 K megaroll and all 7 members are playing at .5 Kelly, i.e $100 max bet, therefore the chance of any one member tapping out would occur about one out of every 55 sessions, now since there are 7 members the chances , someone on the team would go broke about once in every 8 "team" sessions. That fact being given, how much is the rest of the team earning in the meantime?

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. don't think that's worth our time .

That's all good, but I want to determine not only what the "break even" point would be but, beyond that, how much +EV would the team as a whole would realize?

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....

Again I must agree with the real world implications, but that's exactly how most theories grow into practicalities, with a solid fundamental premise and then work out the practical logistics.

 

[Kasi]

... how much is the rest of the team earning in the meantime?...

The exact same amount per round as one person would make with a $10K roll playing full kelly.

If I understand this right, you had each team member double his roll to $20K so each team member is now playing to 0.5 Kelly as if he had only that $20K roll.

Apparently the min $unit has not changed. Each member has only doubled his $roll thereby doubling the min $units in his roll. He still will make the same $/rd just with more units to fall back on, and hopefully recover from, in bad times.

But, since each member is really playing with access to a $140K roll, in effect the team is still making the same amount per hand when played by any team member but with 14 times as many $min units as the original full kelly guy with a $10K roll. In effect the team is playing as a whole with a 0% lifetime ROR.

If you want the team, since it's apparently a team, and want a 0.5 kelly risk for the team as a whole, have each team member play to a min $unit 7 times greater and same unit spread as what it is now. That's usually the benefit of a team - each guy gets to play with higher $mins than he would with his own roll yet at the same risk he was willing to subject his own roll to. And hands played per hour goes up so it takes less time to double roll etc. N0 would be uneffected.

My kind of theoretical team lol.

 

[bj bob]

The exact same amount per round as one person would make with a $10K roll playing full kelly.....

Apparently the min $unit has not changed....
In effect the team is playing as a whole with a 0% lifetime ROR....

...... And hands played per hour goes up so it takes less time to double roll etc. N0 would be unaffected.....

My kind of theoretical team lol.

Bingo, bingo and bingo! All positive improvements. Same income, same min. units, elimination of RoR and a quicker route to N0ville. Thanks Kasi

 

[Kasi]

Bingo, bingo and bingo! All positive improvements. Same income, same min. units, elimination of RoR and a quicker route to N0ville. Thanks Kasi

Margaritaville, I mean N0ville, in terms of rounds played, will not change. It will likely happen sooner in terms of time since the the team is playing at, say, 700 hds/hr.

N0ville is fixed in terms of number of rounds needing to be played.

Just so we are clear what you may have meant by "quicker route" lol.

Doubling roll will take much longer, obviously. Since $roll is larger and $amount won per round is fixed.

 

[bj bob]

Margaritaville, I mean N0ville, in terms of rounds played, will not change. It will likely happen sooner in terms of time since the the team is playing at, say, 700 hds/hr.

N0ville is fixed in terms of number of rounds needing to be played.

Just so we are clear what you may have meant by "quicker route" lol.
.

That's exactly what I meant, in terms of time @ 700 hands/ hr. Same distance, faster rate.

 

[Automatic Monkey]

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....

What I was picturing was a system where everyone makes a regular fixed payment into a pool, just like an insurance premium, and this is used to restore anyone's bankroll if they lose it. Each player gets to keep whatever he wins, thus he has an incentive to play well and often. But he never has to resize his bets due to losses because he always has his insurance policy to back him up if he loses it all. The only number that would need to be calculated is how big the premium has to be. Whatever money is left in the insurance pool is distributed equally among all members when breaking bank.

Hey, that's exactly like any kind of shared bank situation, just a different way of doing the accounting. But you never get away from the trust issue.

Side thought: Would you rather be screwed by a teammate, or have your teammates sincerely believe you had screwed them?

 

[Kasi]

That's exactly what I meant, in terms of time @ 700 hands/ hr. Same distance, faster rate.

Well, I figured you knew that lol. - that was a just-in-case for others lol.

But ask yourself, you've taken 7 guys each of whom was willing to play at 0.5 kelly and a 1.83% risk with a $20K roll so the only thing these 7 guys gain by becoming equal investors is the lower risk.

Equal time to double roll. Less time to N0ville, granted, so now their original effective risk of 0 becomes a risk of yet even closer to zero. Would they care?

Why would I or the other 6 guys want to join a team with a 0 risk when I/we were willing to play at 1.83% in the first place with our own $20K? It will take just as much time to double my roll anyway.

The only real benefit is to be able to bet to a higher $roll with the same risk.
OK - maybe increase $unit by 4 or 5 instead of 7 and lower risk to 1 in 1000 or something - why not maybe? I'm all for compromise lol.

At least get the extra return on your investment per time-unit.

Otherwise, if you like that 0 risk to begin with, maybe save your money until you have it

 

[bj bob]

Well, I figured you knew that lol. - that was a just-in-case for others lol.

Why would I or the other 6 guys want to join a team with a 0 risk when I/we were willing to play at 1.83% in the first place with our own $20K? It will take just as much time to double my roll anyway.

The only real benefit is to be able to bet to a higher $roll with the same risk.
OK - maybe increase $unit by 4 or 5 instead of 7 and lower risk to 1 in 1000 or something - why not maybe? I'm all for compromise lol.

And that's exactly why I threw that "ideal" situation out for discussion in the first place. Start with some absolute ideal and then customize it to the real world.
It seems to me that the size of the team, the % of Kelly, RoR and the spreads could all be reviewed and modified to as to find the "perfect" balance for actual team play.

 

[blackjack avenger]

7 = 1

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?

Given this scenario it seems the 7 would have the same outcome as 1 in the long run.

If by playing Kelly you mean continuous resizing in the theoretical world the answer should be yes.

 

[stophon]

If you have two players each playing on a 10k bankroll betting full kelly then they are playing with a 13.5% ROR. If the players combine their BR's then they are now playing with a 1.83% ROR. If you put 7 players together (I think thats what your saying bj bob) then you have a 13.53^7 ROR, or you will go broke about once every 1.2 million times.

When you bet more than kelly, I assume your EV increases at a slower rate than your ROR does? Just as when you bet under kelly your EV decreases at a faster rate than your RoR.

 

[blackjack avenger]

Full Kelly is Not 13.53% ror

When you say the word Kelly you are talking about optimal betting with continuous resizing.

If you say playing with a 13.53% ror that is something different