Order of Operations / Math Formula for Replenishable BR

[Nikky_Flash]

X = BR ( 1 + sqrt(1 + 4 I N 0/(k BR)) ) / 2

This is a formula from (http://www.bj21.com/bj_reference/pag...lformula.shtml) for when you have a bankroll you are playing with , but you have a regular-job that allows you to put savings into the BankRoll .
X is a number that you can use for a imaginary BankRoll , because of the constant adding to BankRoll , this is what, in theory , we can use to size Max bets with . I need to solve for X , I did this fast , and am tired , I would very much like better math people than me to look at my work below, for errors and please comment , thank you
Variables legend :
BR this is the part of my Bank Roll I'm willing to put up as risk, for this formula I just used $ 2,000
I is the non-gambling income per round (or the
non-gambling income per month divided by the number of
rounds you play per month), in reality I make a different amount each month , for this formula I just used $2,000 and for hands per hour I used a very small number because of ploppies being slow sometimes and wonging alot to slow things down , so I just used 50 hands per hour or something like that , I wong in and out alot , trying to cut down.
and sqrt() is the "square root" function.
N 0 is the doubling time in rounds, --- I use a style very similar to COB , just with 5-50 spread, 6 deck games ,
k is your Kelly factor ( I used 0.75 ),
X is now going to be , the effective bankroll that you are allowed to use to size
your bets,

( I set it up for 10 hours of playing time per month, that's about average for me , most others will use a much higher number there)
We do the work in the parenthesis first ...

X = 2000$ ( 1+ sqrt of ( 1 + 4* 4 * 10,000 / .75 * 2, 000) / 2

X = " " 1500 / 2

X = " " ( 1+ 160000 / 1500 ) / 2

X = " " ( 1+ 106.67) / 2
X = 2000$ ( 1 + sqrt of 107.67 ) / 2
X = 2000$ ( 1 + 10.3764) / 2

X = 2000$ ( 11.3764) / 2
X = 22752.8 / 2
X = $ 11376.40

[bigplayer]

I would imagine you could probably change the formula to change the + sign to a - sign to account for when you have a given BR but instead of adding "I" extra income per month to it you are taking "I" salary. I'm not a math guy so I have no idea if this formula is correct or not, but it is a great question to ask and answer. I think Mathprof has some work of this type in the bj21.com archives.

[Bodarc]

Nikky

Are you estimating 10 hours play per month?

btw for others who may not know the source of this formula: http://bj21.com/bj_reference/pages/renewablebankrollformula.shtml

[Skull]

I am not one of those "math people" unfortunately, but yes, the math is correct. I get $11376.255 actually, but that's just a rounding effect.

That is assuming, as Bodarc pointed out, that you are using 10 hours/month.

[Nikky_Flash]

Nikky

Are you estimating 10 hours play per month?

btw for others who may not know the source of this formula: http://bj21.com/bj_reference/pages/renewablebankrollformula.shtml

Yes , thanks Bordarc ,

I get out to real Casinos on average one to three times a month averaged out to about 10 hours ...
Thanks for pointing that out + adding the link , I forgot -( I went back and fixed it )

[Nikky_Flash]

I am not one of those "math people" unfortunately, but yes, the math is correct. I get $11376.255 actually, but that's just a rounding effect.

That is assuming, as Bodarc pointed out, that you are using 10 hours/month.

Ok thanks Skull

[Three]

N 0 is the doubling time in rounds, --- I use a style very similar to COB , just with 5-50 spread, 6 deck games ,

Assuming 100 rounds per hour may be a bit optimistic for playing a small BR. Most places you would be red chipping which would have you getting more like 60 to 80 rounds per hour. Crowded tables with side bets and slow to make decision ploppies can really slow a game down considerably.

I is the non-gambling income per round (or the
non-gambling income per month divided by the number of
rounds you play per month), in reality I make a different amount each month , for this formula I just used $2,000 and for hands per hour I used a very small number because of ploppies being slow sometimes and wonging alot to slow things down , so I just used 50 hands per hour or something like that , I wong in and out alot , trying to cut down.
and sqrt() is the "square root" function.

I also doubt your total income is a variable in the equation. What effects your theoretical BR is how much you can put into your BR each month. Since you said you don't know how much this is from month to month the formula may not be too useful unless you know how much in advance for the next month.

After rereading your post perhaps you have much of what I said compensated for already.

BR this is the part of my Bank Roll I'm willing to put up as risk, for this formula I just used $ 2,000

I am not sure why you are using only a portion of your BR for these calculations. You are trying to use a formula to work with a higher BR than you have but you don't use all of your BR as part of the formula. When it comes to BJ being able to play at $25 tables makes a big difference in the quality of games you have to choose from. Anyone that has run the gambit and successfully gone from red chipper to green chipper will tell you that was the hurdle that was the most helpful to cross. Your EV goes up drastically for many reasons as your N0 goes down. That would be a hurdle worth stretching into replenishable BR figures in order to get over.

[Bodarc]

Nikky

With your spread and hands per hour, your chance of losing $ 1,800 in 10 hours of play (using a month as one session) is about 2.5%. Surely you will not lose every month and with the ability to replenish at $ 2,000/month, you will never go broke.

With this in mind, I think your spread is much too low. With $ 5 as your minimum bet, you can very easily increase it to 2x$50, a 20 spread. I don't know about heat in your part of the country but I use a max of 2 x $ 75 which is a 30 spread with no problem. You can do a lot of things red chipping that you can't do at higher minimums. If you set a reasonable stop loss and with the ability to replenish $ 2,000 per month to your bankroll, you have no problem.

Sorry to ramble but these are just my thoughts. I'm sure you will get others.

[Nikky_Flash]

Nikky

With your spread and hands per hour, your chance of losing $ 1,800 in 10 hours of play (using a month as one session) is about 2.5%. Surely you will not lose every month and with the ability to replenish at $ 2,000/month, you will never go broke.

.

Hi Bodarc , I cant put 2,000 into my BR each month , the formula makes you use your regular work income , mine varies , so I plugged in 2000... from that it makes you divide that by your playing conditions...

[Bodarc]

"Suppose you have $9000 currently available for gambling and you can add $3000 a month to that amount."

That is the quote from the instructions for the formula. What you make per month has nothing to do with the money set aside for your bankroll. The only thing that affects it is how much you can add to your bankroll per month.

[Nikky_Flash]

"Suppose you have $9000 currently available for gambling and you can add $3000 a month to that amount."

That is the quote from the instructions for the formula. What you make per month has nothing to do with the money set aside for your bankroll. The only thing that affects it is how much you can add to your bankroll per month.

I see where I the variable "I" was suppose to go , I repeated the number "4" accidentally , and never even entered in what I would add each month to my playing BR; and the 2,000 $ I put in the correct spot after all -they have you putting your playing BR in two spots ; well then why do I have such a high final BR to play with ? , if according to the formula , I only entered in adding 4$ a month?

[Nikky_Flash]

what I would like to see is if I risk 2,000 for a static BR , and maybe see what the formula is if say I add 50 bucks a month to my playing finances , and if it don't change much , then maybe 100 bucks ...

then maybe the same for 3,000 for a static BR , and the rest the same ...

[Three]

X = 2000$ ( 1+ sqrt of ( 1 + 4* 4 * 10,000 / .75 * 2, 000) / 2

With a $200, static BR and a kelly fraction of 0.75:

Now I is expressed in dollars per round. N0 is in rounds. 50 rounds per hour for 10 hours is 500 rounds. So I is $4/round for a $2,000 a month addition to your BR.

X = BR ( 1 + sqrt(1 + 4 I N 0/(k BR)) ) / 2

X = $2,000*(1+ sqrt( 1 + 4*$4/round*10,000rounds/(.75*$2,000)))/2 = $1.000*(1 + sqrt(1 + $160,000/$1,500) =
$1,000*(1 + Sqrt( 323/3) = ~$11,380

well then why do I have such a high final BR to play with ? , if according to the formula , I only entered in adding 4$ a month?

I is in $/round not dollars per month. As I showed above you accidentally used the correct value for I which is $4/round when playing 50 rounds per hour, 10 hours/month adding $2,000/month.