Bankroll Formula?

[Patrick del Poker Grande]

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BR = -(SD^2 * Ln R)/(2 * WR)

What is Ln in this formula, and where can it be found on my scientific calculator?

Thanks.

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Ln is Natural Log - it's the LN button on your calculator.

[Patrick del Poker Grande]

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BR = -(SD^2 * Ln R)/(2 * WR)

BR - Bank Roll
SD - Standard Deviation
R - Your accepted Risk of Ruin
WR - Win Rate

eg. WR = 2 BB/hour, SD = 16 BB/hour R = 0.001 (0.1%)
BR = -(16^2 * Ln 0.001)/(2 * 2)
= 442 BB

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I have a hard time believing that the units in this formula should be BB/hr instead of BB/100. Is this a typo, or does someone disagree with me?

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If you use BB/100 for the win rate, then the standard deviation also needs to be expressed in terms of BB/100. Since both numbers will be based on the same number conversion of hands/hour (actually hours/100 hands), the results should be the same either way. Use BB/hr or BB/100, just be consistant and don't mix and match.

Shauna

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Yes. I realize this and if you'd read the rest of the thread, you'd see that I knew this. If you simply put in BB/100 in for BB/hr with some conversion factor for hr/100, then the BR answer doesn't come out the same. The problem is that the units on SD aren't BB/hr or BB/100, but something like sqrt(BB^2/hr) or sqrt(BB^2/100). Since it's been a while since stats class and calculating SD, I had forgotten for a minute what the units were on SD. My problem with the formula/example ended up being the units on SD (and therefore the conversion from hours to 100 for SD), not the formula itself.

[IsaacW]

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BR = -(SD^2 * Ln R)/(2 * WR)

BR - Bank Roll
SD - Standard Deviation
R - Your accepted Risk of Ruin
WR - Win Rate

eg. WR = 2 BB/hour, SD = 16 BB/hour R = 0.001 (0.1%)
BR = -(16^2 * Ln 0.001)/(2 * 2)
= 442 BB

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What is the time frame for the "risk of ruin" number? Is it one "time unit" of your other numbers, i.e. if you're basing the calculation on BB/100 is the risk of ruin that much every 100 hands?

[Nottom]

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What is the time frame for the "risk of ruin" number? Is it one "time unit" of your other numbers, i.e. if you're basing the calculation on BB/100 is the risk of ruin that much every 100 hands?

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IIRC, It should be over your lifetime.

[Patrick del Poker Grande]

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What is the time frame for the "risk of ruin" number? Is it one "time unit" of your other numbers, i.e. if you're basing the calculation on BB/100 is the risk of ruin that much every 100 hands?

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IIRC, It should be over your lifetime.

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How can that be when all the units on everything else are in hours or 100 hands?

[Yads]

It doesn't matter if you use per hour or per 100 hand statistics. If you all of your stats are per 100 hands then use those stats. I got the formula from this article, it also describes how you calculate your SD. But yeah it doesn't have to be in BB/hr, it can be in BB/100 hands if you'd like

http://www.thepokerforum.com/angel1.htm

[swolfe]

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Actually multitabling will cause a need for a bigger bankroll. Your standard deviation will go up slightly, and your win rate down slightly, due to mistakes and shallow reads. It's nothing near double though.

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why do people always say this? even if your SINGLE TABLE win rate goes down and your SINGLE TABLE SD goes up, then, assuming you don't turn into a losing player, your win rate for the session (the time spent playing 8 tables) will be 8 times your single table win rate and the session SD will be sqrt(SD_1^2*8), which you'll find is significantly less than if you single tabled a game that had a winrate equal to your 8 table rate.

to use the numbers from the example given:
WR = 2 BB/hour, SD = 16 BB/hour

your 8 table win rate will be 16BB/hr and your 8 table SD = sqrt(16^2 * 8) = 45.2 BB/hr

the SD isn't 8x your win rate any more, it's less than 3x.

so now, calculate the 8 table bankroll using these numbers:
BR = -(SD^2 * Ln R)/(2 * WR)
= -(2048 * -4.605)/(2*16) = 294BB

A LOWER BANKROLL REQUIRED

[Patrick del Poker Grande]

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It doesn't matter if you use per hour or per 100 hand statistics. If you all of your stats are per 100 hands then use those stats. I got the formula from this article, it also describes how you calculate your SD. But yeah it doesn't have to be in BB/hr, it can be in BB/100 hands if you'd like

http://www.thepokerforum.com/angel1.htm

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That's great. We've already established that. We're on to the last piece of the puzzle now:

What are the units on Risk of Ruin? Is it X% every hour or 100 hands, or is it X% lifetime? I don't see how it could be over your lifetime here, since all the other terms in the formula are expressed in terms of hours or 100 hands. Some sort of sense suggests that it should be over lifetime, though, as you'd have to run it out to about 6+ decimal places if you were to do it for your lifetime in a per 100 hands basis.

[swolfe]

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That's great. We've already established that. We're on to the last piece of the puzzle now:

What are the units on Risk of Ruin? Is it X% every hour or 100 hands, or is it X% lifetime? I don't see how it could be over your lifetime here, since all the other terms in the formula are expressed in terms of hours or 100 hands. Some sort of sense suggests that it should be over lifetime, though, as you'd have to run it out to about 6+ decimal places if you were to do it for your lifetime in a per 100 hands basis.

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risk of ruin is unitless. it's the probablity that your bankroll will ever be depleted given the win rate and SD.

in the bankroll calculation it's just a number picked that you feel comfortable with. if you're okay with a 10% risk of ruin, then you can probably play on a 100BB bankroll.

you can calculate your risk of ruin by plugging in your actual bankroll, win rate, SD, and solving for RoR.

obviously things change...your bankroll is going to increase and if you stay at the same stakes with the same win rate and SD, then your risk of ruin will continuously get smaller.

[swolfe]

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so now, calculate the 8 table bankroll using these numbers:
BR = -(SD^2 * Ln R)/(2 * WR)
= -(2048 * -4.605)/(2*16) = 294BB

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okay, oops, i calculated using a 1% RoR instead of a .1%.

BR = -(2048 * -6.908)/(2*16) = 442BB

this is the same bankroll as the single table bankroll.