Extracting Money from Bankroll

[assume_R]

I remember a very lively thread lately discussing if you take money out of your bankroll every time you double it, and the consensus seemed to be you need those "positive swings of variation" to overcome the inevitable negative swings of variation. So my question is what if you don't just take money out of your bankroll every time you double, but a fixed amount per month? This seems reasonable, because you would ideally want to be able to spend some of your winnings every month (or year) on something.

So if you have a $30k BR and extract $100 every month, your "effective" bankroll will probably still be around $30k. Based on http://www.bj21.com/bj_reference/pages/renewablebankrollformula.shtml it actually would be $26k assuming you play 40 hours per month, full Kelly.

Now the formula in the link above seems reasonable, except when you extract too much money from you bankroll the value becomes non-real (square root of a negative number).

In the example above, if you try to "extract" $200 every month, it goes to $20k, but if you try to "extract" $300 every month the equation doesn't work.

So is there a reasonable amount people are willing to "spend" from their bankrolls? Otherwise I suppose you can ask what's the point of making this money, unless you're using this for retirement and are going to completely stop playing at some point!

 

[blackjack avenger]

You Answered Your ?

As you pointed out you can pull out small amounts of money compared to your overall bank with little effect.

and/or

If your ror is low enough you can pull out any funds over the original bank. If you only have a 1 in a 1,000 chance of going broke then if you pull out money and essentially start over you still have a low chance of losing all.

If you play long enough your bank should get to large to get your bets down anyway. So taking out funds won't be a problem:joker::whip:

 

[assume_R]

As you pointed out you can pull out small amounts of money compared to your overall bank with little effect.

I suppose my question is how much is considered a "small amount" versus overall bankroll.

 

[SleightOfHand]

I remember a very lively thread lately discussing if you take money out of your bankroll every time you double it, and the consensus seemed to be you need those "positive swings of variation" to overcome the inevitable negative swings of variation. So my question is what if you don't just take money out of your bankroll every time you double, but a fixed amount per month? This seems reasonable, because you would ideally want to be able to spend some of your winnings every month (or year) on something.

So if you have a $30k BR and extract $100 every month, your "effective" bankroll will probably still be around $30k. Based on http://www.bj21.com/bj_reference/pages/renewablebankrollformula.shtml it actually would be $26k assuming you play 40 hours per month, full Kelly.

Now the formula in the link above seems reasonable, except when you extract too much money from you bankroll the value becomes non-real (square root of a negative number).

In the example above, if you try to "extract" $200 every month, it goes to $20k, but if you try to "extract" $300 every month the equation doesn't work.

So is there a reasonable amount people are willing to "spend" from their bankrolls? Otherwise I suppose you can ask what's the point of making this money, unless you're using this for retirement and are going to completely stop playing at some point!

http://bj21.com/bj_reference/pages/overheadeffectonriskofruin.shtml

I considered methods of taking out money from your bankroll and came to a conclusion that I am satisfied with using. When playing a game with WR X and variance Y with bankroll Z, you will have a RoR of A. If the WR was X(1-F) with the same variance and BR, you will have a RoR of B, which is proportional to A. B = A^(1-F), where F is the fraction of the WR that you use as your "salary". This means that you can essentially give yourself an hourly salary and have an expected risk of ruin, which you can create at your comfort level.

So for example, if I am playing a game where I want to give myself a salary which is equal to half my win rate and maintain a risk of 5%, that means the game I have to play prior to the salary needs a risk of no more than A^1/2= .05 => A = 0.25%.

PS: Due to factors out of my control, this post may or not make good sense.

 

[assume_R]

Sleight, so as I understand it this is what you're saying:

Let's say you have a win rate of $40 / hour with a RoR of 8%. You want to extract $10 an hour for buying things, leaving you $30 / hour to reinvest in the bankroll.

Your new RoR is 0.08^($30/$40) = 0.15 = 15%. Extracting $10/hour essentially doubles your RoR.

I guess you don't modify the Variance at all, only the Win Rate?

Interesting... is this equation based on the link in your post or something you came up with?

 

[blackjack avenger]

The Real Danger

The Mathprof formula is probably what you are looking for.

However:joker::whip:

With a small bankroll you face a ror but the real danger you face is the risk of drawdown. This is when the bank gets so small that you cannot play due to table minimums.

If you bet Kelly resizing you have an approximate 50% chance of losing half your bank and a 10% chance of losing 90% of your bank.

If you bet fixed kelly you have an approximate 36% chance of losing half your bank.

Taking money out of your bank also greatly increases your risk of drawdown.

 

[SleightOfHand]

Sleight, so as I understand it this is what you're saying:

Let's say you have a win rate of $40 / hour with a RoR of 8%. You want to extract $10 an hour for buying things, leaving you $30 / hour to reinvest in the bankroll.

Your new RoR is 0.08^($30/$40) = 0.15 = 15%. Extracting $10/hour essentially doubles your RoR.

I guess you don't modify the Variance at all, only the Win Rate?

Interesting... is this equation based on the link in your post or something you came up with?

I believe it was a combination of the link I posted plus a post by Sonny from a while ago about a trick that can be done with RoR (I dont recall what about or where). But essentially, by extracting earnings by the technique I described, you are going to have the same variance with a lower win rate. This is because even during winning or losing sessions, your expected results shift closer towards the negative, without any change to how random (variance) the results may come out.