Two Plus Two Older Archives Risk of ruin question
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#1
12-20-2003, 05:39 PM
 Eihli Senior Member Join Date: Aug 2003 Posts: 363
Risk of ruin question

brucez's br formulas:

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

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

where B is bankroll, sigma is SD, u is hourly earn, and r is risk of ruin

Do sigma, B, and u need to be in big bets or money? Or does it matter?

Say I'm playing 2/4 making 2 bb an hour with 10 bb SD.
The equation B = -(sigma^2/2u)ln (r) or
B = -(10^2/2*2)ln(.05) = 74.89
but
B = -(40^2/2*8)ln(.05) = 299.57

So when sigma and u are in an amount of money, it gives you your BR in big bets?

But using one of brucez examples in which you make \$30 an hour with a SD of 650, i get this
B = -(650^2/2*30)ln(.05) = 21094.94
And in that case it gives me a dollar amount instead of a BB amount for B.

I'm confused.
#2
12-20-2003, 05:57 PM
 bigpooch Senior Member Join Date: Sep 2003 Location: Vancouver, Canada Posts: 759
Re: Risk of ruin question

Doesn't matter what units you use for the formulas. BTW,
these formulas are mere approximations but excellent ones
nonetheless! Also, the time interval commonly used is per
hour, but you could use anything else (personally, I prefer
ten minutes as this is quite easy to do online since the
more data that is accumulated, the more quickly it is to get
smaller confidence intervals and hence, a better estimator
for the win rate).
#3
12-20-2003, 06:36 PM
 Eihli Senior Member Join Date: Aug 2003 Posts: 363
Re: Risk of ruin question

B = -(40^2/2*8)ln(.05) = 299.57

So that's saying I need \$299.57 for a 5% ROR playing 2/4 making \$8 an hour with \$40 SD? Just 79 bb? Where did I mess up?
#4
12-20-2003, 07:39 PM
 Bozeman Senior Member Join Date: Sep 2002 Location: On the road again Posts: 1,213
Re: Risk of ruin question

2 BB/hr is good, 10 BB/sqrt(hr) is not a big variance, and 5% is a relatively large RoR, so this is why the number (79 BB) is much less than the canonical 300 BB.

Craig

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