In a message dated 10/28/2003 5:45:54 AM Pacific Standard Time,
harry.porter@verizon.net writes:
A couple of additional comments before I walk out the door this
morning, Brian. It occured to me to also look at this with the
ROR/bankroll calculator that can be found at gamblingtools.net
http://www.gamblingtools.net/vp/vpanalyzer.html
This tool provides for the separate input of game paytable and
cashback rate.
For comparison I used two paytables/cb, akin to your example, each
having 101% ER and 28.3 var.
- 10/7 DB, .0083 cb (i.e. .83%)
- vp w/RF=4040 (808 bets), no other pays, .975 cb (97.5%)
I had the analyzer solve for the bankroll that represented a 5% Risk
of Ruin for these paytables.
In each case the bankroll requirement was 3816 bets, suggesting again
that (assuming all other variables are equal) values for Total Return
w/cb and Variance are sufficient to determine game risk, and that two
games for which these values are identical will present equal risk.
I'm sure my brain will churn later today to come up with a straight
forward, common sense explanation why that's the case, but it's a bit
beyond me right now. (Of course, as you suggested, it wouldn't hurt
for someone who's a little more on top of this than either of us to
chime in :).
Actually, you've convinced me, Harry. If the ROR calculator takes into
account the CB percentage, and it comes up with the same BR requirement for both
games, that is, at least barring higher authority, good enough for me! Thanks for
setting me straight on this topic, as I had always assumed that, everything
else being equal, a higher CB percentage was slightly better!
Brian
[Non-text portions of this message have been removed]