ROR Derivation Question

[DavidC]

I'm looking at blackjack stuff right now, but I'm looking to really understand what I'm doing before I just start following the examples of people that know what they're doing... "Raise preflop," has never been good enough advice for me unless I knew why.

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Some variables:

Evh is "EV per hand" and is expressed in units.

Evh = B/Wr - Ha where B is the bonus, Ha is the house edge, and Wr is the wagering requirements of the bonus.

Evb is B - Wr*Ha: "The EV of the bonus." and is expressed in absolute terms. It's not relevant to this discussion.

Rw is "riskiness over reward" and is Var/Evh.

Rr is risk of ruin.

Br is bankroll in units.

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Rr = exp(-2*Br*Rw), therefore
Br = -Rw*ln(Rr)/2

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I'm looking to figure out why the Rr formula is the way it is. [img]/images/graemlins/smile.gif[/img]

Looking at an old Bruce post, I run into the following formula for a simple coinflip game:

more variables:

"p" is your chance of winning the flip and "q" is chance of losing.

Therefore p=1-q and q=1-p.

Now they calculate risk of ruin r as:

r = q + (1-q)*r^2.

I'm really confused by what r would be on the right side of this formula. Is it possible to give p,q, and r a value at this point on the right side of the formula in order to come up with a value for r on the left side?

I'm going to assume we can rewrite that formula (at this point) as r=q+p*r^2, letting {p,q} = 0.5

r = 0.5+r^2/2

How do we find out what r^2 is?

Edit: Here's the link to the Bruce post... this is basically where I'm stuck.

--Dave.

Edit: I've read through like three posts on this subject, as well as some stuff on the Central Limit Theorem with Statistical Fine Print and I'm pretty thoroughly confused. I like math, but this is a bit over my head right now.