Bankroll

[tjr5259]

If someone plays blackjack part time and has a full time job and plans to keep playing blackjack no matter what the outcome of each session, could this player be considered to have an infinite bankroll? For example, say a player sets his mind to playing blackjack for his entire life and takes a certain percentage of his paychecks every week to put on a blackjack table and no matter win or lose, next week he will be back with the same percentage of his salary to play more blackjack. He can go "bankrupt" for a week if he loses that allotted money for the week, but will be back at it next with with a replenished bankroll. Could this be considered as an infinite bankroll over the long run?

[marriedputter]

If someone plays blackjack part time and has a full time job and plans to keep playing blackjack no matter what the outcome of each session, could this player be considered to have an infinite bankroll? For example, say a player sets his mind to playing blackjack for his entire life and takes a certain percentage of his paychecks every week to put on a blackjack table and no matter win or lose, next week he will be back with the same percentage of his salary to play more blackjack. He can go "bankrupt" for a week if he loses that allotted money for the week, but will be back at it next with with a replenished bankroll. Could this be considered as an infinite bankroll over the long run?

Yes. This is called a replenishable bankroll.

Let's say that you decide to play as if you had a $10,000 bankroll. Let's say that you won't actually have that total bankroll for a year but you have paychecks that will provide $833 a month. You can play with that $833 each month and pretend that your total bankroll is $10,000. This means however that there is a good chance that you will lose that $833 because you consider your total bankroll to be $10,000 (not $833).

Playing at 1/4 Kelly, you could make $25 dollar bets with a 1% advantage (around a TC of +3 assuming Hi-Lo), $50 with a 2% advantage (TC+5), $75 with a 3% advantage, and $100 with a 4% advantage. If you sit down to a table and immediately get a high count, you could lose that $833 in 5 minutes! You then would have to have the discipline to wait until the next paycheck next month, which is not easy to most to do. On the flip side, if you win, you will have more than $833 and take a bigger hit, but ultimately may lose it all due to variance.

Many use a replenishable bankroll, but not many have the discipline to stop playing right then and there if they lose it all.

[bjarg]

An infinite bankroll?
Dont you think that if you actually had an infinite bankroll you wouldnt be wasting your time playing blackjack?
If anything what you do have is a replenishable bankroll.
If I remember correctly you should be able to find stuff to read in the bjinfo old archives.

[muffdiver]

No. He could lose his job tomorrow.

[tjr5259]

Yes. This is called a replenishable bankroll.

Let's say that you decide to play as if you had a $10,000 bankroll. Let's say that you won't actually have that total bankroll for a year but you have paychecks that will provide $833 a month. You can play with that $833 each month and pretend that your total bankroll is $10,000. This means however that there is a good chance that you will lose that $833 because you consider your total bankroll to be $10,000 (not $833).

Playing at 1/4 Kelly, you could make $25 dollar bets with a 1% advantage (around a TC of +3 assuming Hi-Lo), $50 with a 2% advantage (TC+5), $75 with a 3% advantage, and $100 with a 4% advantage. If you sit down to a table and immediately get a high count, you could lose that $833 in 5 minutes! You then would have to have the discipline to wait until the next paycheck next month, which is not easy to most to do. On the flip side, if you win, you will have more than $833 and take a bigger hit, but ultimately may lose it all due to variance.

Many use a replenishable bankroll, but not many have the discipline to stop playing right then and there if they lose it all.

So for simulation purposes this person could use 10,000 dollars for their bankroll?

[mcallister3200]

So for simulation purposes this person could use 10,000 dollars for their bankroll?

Kind of sort of. That's the idea, but doing so leaves them in a position where they could possibly tap out in the middle of a shoe, which slightly changes the math. Norm has some charts in his book on effect of that on expectation, but I'm too lazy to look up the page and cite it.

[tjr5259]

If I remember correctly you should be able to find stuff to read in the bjinfo old archives.

Found it thanks.

[NotEnoughHeat]

I'm not convinced that one should consider such a bankroll as infinite (though replenishable seems fine). This type of bankroll has limitations and lacks features that an infinite bankroll does not. Any kelly fraction whatsoever would tell you to bet an infinite amount (any fraction of an infinite amount is infinite as well) any and every bet where you have an advantage. Also, a replenishable income has time constraints. Only so much of you bankroll is available in a particular time period. You could play as if you had a $12,000 bankroll if you had 10k now and earmarked 2k from your next paycheck as part of your bankroll, but would you really play as if you had a 500k bankroll just because in over 10 years (assuming semi-monthly paychecks) from now you'll have that much money added to your bankroll? With an infinite bankroll, this wouldn't be a concern. You would martingale all you want, with an advantage, without having to wait exponentially longer and longer to be able to afford your next bet after a catastrophic series of losses.

Also, I wouldn't consider it infinite for other reasons. You don't live forever (and thus could not work and earn an income forever). I suppose you could consider your descendants' income part of the bankroll, but that requires a whole additional set of assumptions.

[marriedputter]

Only so much of you bankroll is available in a particular time period. You could play as if you had a $12,000 bankroll if you had 10k now and earmarked 2k from your next paycheck as part of your bankroll, but would you really play as if you had a 500k bankroll just because in over 10 years (assuming semi-monthly paychecks) from now you'll have that much money added to your bankroll?
Also, I wouldn't consider it infinite for other reasons. You don't live forever (and thus could not work and earn an income forever). I suppose you could consider your descendants' income part of the bankroll, but that requires a whole additional set of assumptions.

Surely he doesn't think this way. Committing 10 years worth of future profits to the blackjack table isn't wise. You could of course lose your job but wouldn't that be obvious to anybody? The trick is to look at your profession and ask yourself how likely it is that you will have that profession over a certain period of time. If you feel that you will have it for 1 year, then that could be the way to go. For others, they may only look out to 6 months. But who in the world would assume that their job is secure 10 years from now?
Infinite is not to be taken literally. Surely he just meant infinite in the sense that as long as the income continues to come in, he has an "infinite" bankroll, meaning that a future lack of a job is the only thing that will disrupt this "infinity."
Hopefully he would have enough sense to have a reserve fund set aside for emergencies like unexpected unemployment. That should come first before ever devoting a dime to blackjack.