I just read the FAQ post on sticky bonuses at bonuswhores.com (
link to article ), and I'm curious if anyone (Bruce? pzhon?) can show me the derivations of some of the forumulas....
Following the naming convention on the linked to article, let:
D=deposit
B=bonus
X=your target (you aim for $X or $0=bust)
BR=your whole gambling bankroll
First question is about your chance of success, which (for a fair game) is (B+D)/X. I can see that this formula is true when I plug in some different numbers (eg, if X = 2*(B+D), you just bet everything and clearly you have a .5 chance of winning). But what I cannot figure out how to prove is 1) the formula in the general case and 2) how to show the forumula does not depend on your bet sizes or betting strategy. I'd like to see how these two things are done.
Second question is about the following quote from the linked to article:
[ QUOTE ]
Since there is no house advantage, for any X, you can extract more EV out of the bonus. Let's say you've reached a value of X, and you set your goal to reach X+dX or bust trying. Simple calculation shows that for this bet:
EV=B/X * dX
SD=(X-B)/sqrt(X) * sqrt(dX)
[/ QUOTE ]
How were these two equations arrived at?
I believe the last question is a simple one, but I've never seen ROR (I think that's what coming into play here) described like this before. The author notes that:
[ QUOTE ]
Using arguments similar to the ones justifying 300BB bankroll requirement in poker, my personal criterion for bankroll is: (I am conservative when it comes to bankroll)
BR = 4*Var/EV
I think this is equivalent to requiring ~500BB bankroll for limit hold'em.
[/ QUOTE ]
First, does this mean that with a BR of (4*Var/EV), you will have the same chance of busting out while playing sticky bonuses indefinitely as would a winning player (based on some reasonable winrate like 1BB/100 or 2BB/100) at limit holdem? If not, what does it mean?
Second, where does this formula come from? Is this just a recasting of the ROR formula given, eg, by bruce in
this thread, or it something else entirely.
Thanks for any info/proofs,
gm