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## Risk of Ruin/kelly

Question,

Is risk of ruin based on your minimum bet or top bet?

10k bankroll divided by 1000 units = 10 min bet size

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I've seen it defined both ways in different books and made me question myself.

I do bankroll divided by 1000

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Bankroll divided by x is a very general rule of thumb. If you want to know the actual risk of ruin:

risk of ruin = ((1 - w/sd)/(1 + w/sd))^(bank/sd)
w = win rate
sd = standard deviation
bank = bankroll
(units must all be the same, dollars or units; w and sd must both be per hand or hourly)

BJA3, chapter 8, verse 112.

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To answer the original question, which appears to assume counting and using a bet spread, the formula given by BackCounter is correct, but the w (win rate) and the sd (standard deviation) needed are the global w and sd determined by frequency, EV and sd at each count, each weighted by the amount bet at each count.

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Originally Posted by BackCounter
Bankroll divided by x is a very general rule of thumb. If you want to know the actual risk of ruin:

risk of ruin = ((1 - w/sd)/(1 + w/sd))^(bank/sd)
w = win rate
sd = standard deviation
bank = bankroll
(units must all be the same, dollars or units; w and sd must both be per hand or hourly)

BJA3, chapter 8, verse 112.

Another way to calculate ROR :-

ROR = e^(-2/a), a = Var/Bank/w

Var = sd^2

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Originally Posted by Gronbog
To answer the original question, which appears to assume counting and using a bet spread, the formula given by BackCounter is correct, but the w (win rate) and the sd (standard deviation) needed are the global w and sd determined by frequency, EV and sd at each count, each weighted by the amount bet at each count.

How about the "bank" ? Suppose the Bankroll = \$10000, and bet spread from \$10 to \$150, how to calculate the "bank" ?

57% of round with bet size = \$10
15% of round with bet size = \$20
13% of round with bet size = \$40
8% of round with bet size = \$80
4% of round with bet size = \$100
2% of round with bet size = \$120
1% of round with bet size = \$150

Average bet size = 0.57(10) + 0.15(20) + 0.13(40) + 0.08(80) + 0.04(100) + 0.02(120) + 0.01(150) = \$28.2

bank = \$10000/\$28.2 = 354.6 ?

OR

bank = \$10000/\$10 = 1000 ?

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I'm a little confused what the OP is looking for. The title of the thread is Risk of Ruin/kelly. First you would need to calculate a Kelly bet spread.

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Originally Posted by BJC
Question,

Is risk of ruin based on your minimum bet or top bet?

10k bankroll divided by 1000 units = 10 min bet size
Risk of ruin is actually not based on either your minimum or maximum bet. It's based on an optimal bet (OU) that, in certain cases,
may coincide with your minimum bet. Often, the minimum bet is related to the table minimum, but that may not always be the case.
However, it could be that the OU is \$8 or \$13, which doesn’t necessarily align with the table's minimum bet.

Sincerely,
Cac

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But isn’t ror based on what you are actually betting? The optimum Kelly unit may be \$13, but if you are spreading 10-160 then that will determine your win rate and sd, and your bank in units will be the money you have divided by 10.

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Yes. Just wanted to make sure what the OP was talking about. The title included the word Kelly.

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Originally Posted by BackCounter
But isn’t ror based on what you are actually betting? The optimum Kelly unit may be \$13, but if you are spreading 10-160 then that will determine your win rate and sd, and your bank in units will be the money you have divided by 10.
So long as you're consistent with the manner in which you make the calculations, it doesn't much matter what you call the unit size and therefore the bank size, in units. The formula calls for a per-hand SD and EV, in units. Whatever you use to express those two values, you will then use the same unit size to describe the size of the bank.

Read carefully BJA3, pp. 112-13 and look at the charts beginning on p. 116.

Don

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Duh . . . . So to use dollar amounts, pretend your unit is \$1. Kind of like the share price for a cash account.

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Originally Posted by BackCounter
But isn’t ror based on what you are actually betting? The optimum Kelly unit may be \$13, but if you are spreading 10-160 then that will determine your win rate and sd, and your bank in units will be the money you have divided by 10.
If for a 1-16 spread the optimal Kelly unit is \$13 (full Kelly), it means your RoR is 13.53% with a \$10,000 bankroll. If you keep that same bankroll but bet \$10 instead of \$13, your RoR will no longer be 13.53%; it will be lower. To maintain the same RoR, you would need to reduce your bankroll. In the case of betting \$13, your WR will be equal to the SCORE. However, if you bet \$10, your WR will be lower. The SCORE does not change.

Sincerely,
Cac

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