Bankroll Formula – Part 4 – Risk of Ruin

Bankroll Formula – Part 4 – Risk of Ruin

Latest Casino News 04 Sep , 2019 0

The Risk of Ruin is the inverse of the chance of NOT going broke with a particular size of Bankroll due to short term variance - for example, if you want to ensure you do not go broke 99% of the time, the Risk of Ruin is 1% or 0.01.

You can use a rough estimate of the SD, equal to 10 x WR/hour.

We can look at the BR formula in a different way from the Comfort Level approach (again ^2 = squared):

Bankroll = -(SD^2 / 2 x Hourly Win Rate) x the Inverse of the Risk of Ruin


Assume your profit is $20/hour or 1BB/hour. What should your BR be for 5%, 1% and 0.1% chance of going bust? (we use BB = Big Bets in the formula)

5% = -(200 ^2 / 40) x Inverse of 0.05 = -40000/40 x Inverse of 0.05 = $2996

1% = -(200^2 / 40) x Inverse of 0.01 = -40000/40 x Inverse of 0.01 = $4605

Therefore if you are a winning player with a SD of 10xWR you can expect to play for ever with 99% confidence at this level with a BR of $4605

0.1% = (200^2 / 40) x Inverse of 0.001 = -40000/40 x Inverse of 0.001 = $6908 (or roughly 345 Big Bets)

Therefore you can be 99.9% confident of playing for ever with a BR of $6908 - and this is where the rough guide of 300BB for a BR comes from.

The full formula for Risk of Ruin = e ^(-2WR*BR / SD^2) or e to the power of -2WR*BR / SD^2

There are a number of assumptions for Risk of Ruin:

a) A Normal Distribution of results
b) A constant Win Rate
c) A constant Standard Deviation.

If the actual parameters over time vary too far from these assumptions a review of the actual Risk of Ruin % should be made.

If we take an example:

A winning poker player has a Win Rate of $30/hour, Standard Deviation of $600 and a Bankroll of $15000 (WR and SD can be expressed as bb/100, it doesn't affect the result):

Risk of ruin = e ^(-2*30*15000/600^2)
Risk of Ruin = e ^(- 900000/360000)
Risk of Ruin = e ^(- 2.5)
Risk of ruin = 8.208500%

The Risk of Ruin is approximately 8.2%


Source by Richard Sun


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