Question about ROR/Bankroll thread from the archives

[Rasputin]

I ran across this thread on bankroll and risk of ruin in the archives.

The discussion centered about a bankroll formula described by BruceZ as follows:

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The formulas in that book will significantly underestimate bankroll requirements and risk of ruin. This is because they do not take into account the chance of going broke before reaching the point at which at which a given standard deviation loss is maximum. Use these formulas instead:

B = -(sigma^2/2u)ln(r)

r = exp(-2uB/sigma^2)

where u is your hourly rate
sigma is your hourly standard deviation
r is your desired risk of ruin
B is your bankroll

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If I look at this, it seems to indicate that the bankroll requirement to avoid ruin is independent of the level you're playing at.

This strikes something that cannot possibly be correct.

What am I missing?

[pzhon]

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B = -(sigma^2/2u)ln(r)

r = exp(-2uB/sigma^2)

where u is your hourly rate
sigma is your hourly standard deviation
r is your desired risk of ruin
B is your bankroll

[/ QUOTE ]

If I look at this, it seems to indicate that the bankroll requirement to avoid ruin is independent of the level you're playing at.

This strikes something that cannot possibly be correct.

What am I missing?

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The main thing is that your win rate u is not a constant. It depends on the level you are playing. Slightly less importantly, your standard deviation sigma also depends on the level. For many people, the desired risk of ruin depends on their level, too: Losing your entire balance may be no big deal if you play for spare change at $1-$2, but it may be devastating if you are feeding a family at $15-$30.

Exactly how your win rate depends on the level would be interesting to determine. I've been assuming that there is a bit less than a 1 BB/100 drop for each step up, starting with $2-$4, but I don't have enough data to verify that.

[Sniper]

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If I look at this, it seems to indicate that the bankroll requirement to avoid ruin is independent of the level you're playing at.

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2 points:

1. The calculation doesn't tell you the bankroll required to AVOID ruin, just the bankroll required to set your risk of ruin at the level that you input into the formula.

2. The calcuation is not independent of the level of play, even though play level is not explicitly part of the calculation. The formula presumes that the inputs of win rate and standard deviation are experience based results on 1 level. Thus your level of play is a part of those numbers. The bankroll required to get your desired risk of ruin is for continued play only at that level.

[Rasputin]

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2 points:

1. The calculation doesn't tell you the bankroll required to AVOID ruin, just the bankroll required to set your risk of ruin at the level that you input into the formula.

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Good point, true enough.

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2. The calcuation is not independent of the level of play, even though play level is not explicitly part of the calculation. The formula presumes that the inputs of win rate and standard deviation are experience based results on 1 level. Thus your level of play is a part of those numbers. The bankroll required to get your desired risk of ruin is for continued play only at that level.

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So what you're saying is that someone has a $30/hr winrate at 10/20 and a $30/hr winrate at 15/30 that their standard deviations will be different enough to account for the difference in level?

[WhiteWolf]

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So what you're saying is that someone has a $30/hr winrate at 10/20 and a $30/hr winrate at 15/30 that their standard deviations will be different enough to account for the difference in level?

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The SD, expressed in $ per hour, would be greatly different at the different levels, even if you only take into account the fact that the BB is 50% higher at 15/30.

[Sniper]

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So what you're saying is that someone has a $30/hr winrate at 10/20 and a $30/hr winrate at 15/30 that their standard deviations will be different enough to account for the difference in level?

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Yes!

Some other things to consider:

The formula relies on Win Rate & SD based on a snapshot of past performance. Since there is no guarantee that your performance relative to your average competition will stay constant in the future, you should monitor your performance and calculate your necessary bankroll to maintain your desired risk of ruin on an ongoing basis.

Also, you can significantly reduce your risk of ruin by adding a drop down (in level) point. Which may allow you to play comfortably at a higher level (with a higher risk of ruin at that level) with a smaller bankroll.