Systems Archive 3

Re: 4 deck comparison...

Posted by Brh on 23 April 1999, at 12:36 a.m., in response to Re: 4 deck comparison..., posted by Troy on 22 April 1999, at 11:44 p.m.

Troy,

The theory behind Optimal Spreads is quite involved, but if you want to find out the meaning of the terms presented, go to

http://www.bjmath.com

click on 'Betting Strategies' -> 'Bet Sizing' -> 'The Theory of Optimal Betting Spreads' .

The first point is the unit ev itself is not a measure of system performance, it is simply one parameter. The value 'k' is the unit Equivalent Kelly Bankroll, which is equal to sd^2/ev. 'k' is used to determine the 'Unit_Bet' for a real dollar betting scheme, the unit dollar bet is the real dollar bankroll \$B(=\$10000) divided by k.

Why is 'ev' not a measure? It is because it does not take 'sd' into account, so that while an SS sim may have a higher 'ev', it will have a higher 'k', meaning that in unit terms, it has a larger risk of ruin. The correct unit measure is N0 which is the 'long run index', and is equal to sd^2/ev^2. DI is closely related, as DI=ev/sd. To put it a different way, an SS based system gets its gain from betting 'grunt', whereas a system with a lower BC but a higher PE, gets its gains by playing more accurately and getting a relatively lower sd.

In strict mathematical terms, N0 is the number of rounds to play, such that the total ev is equal to one sd. That is, if you have one sd worth of bad luck (86%), this is how long you have to play to break even. Clearly, the lower the value of N0 the better. Equivalently, the higher the DI, the better.

I use capital letters to denote real dollar amounts. For a real bankroll of \$10000, the values of EV and SD are the dollar win rate and SD per 100 hands, where the unit bet is given by \$10000/k.

It turns out that the EV is equal to \$10000/N0 (x100 hands), and this measure has recently been popularised by Don Schlesenger and John Auston, who called it the 'SCORE'. Basically SCORE is the win rate per 100 hands, for a fixed bettor with a 13.6% risk of ruin.

So the measures DI, N0 or SCORE are equivalent, and are the only true measures of system performance.

System   ev     sd    k     DI      N0   |  Unit Bet   EV       SD     %pl       TCW
b2_b1  0.16942 14.00  1157 12.10   6829  |   \$8.64   \$146.43   \$1210 100.00%      -
b2_hl  0.16897 14.04  1167 12.03   6906  |   \$8.57   \$144.81   \$1203 100.00%      -
b2_ss  0.16972 14.14  1178 12.00   6941  |   \$8.49   \$144.08   \$1200 100.00%      -
om_b1  0.16750 13.95  1162 12.01   6937  |   \$8.61   \$144.16   \$1200 100.00%      -
om_hl  0.16695 13.99  1173 11.93   7026  |   \$8.52   \$142.32   \$1192 100.00%      -
om_ss  0.16747 14.07  1183 11.90   7062  |   \$8.46   \$141.61   \$1189 100.00%      -

This is not a surprise, I have noted many times that the Brh-I/Halves/True-SS question is not one of the traditional PE versus BC debate. Brh-I retains its power for all spreads, since a insurance-bet correlation is a factor for all spreads.

Cheers,
Brett.

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