Computer Simulations

I've been working on a program to compare different card counting systems. So far I've looked at OPP and Hi-Lo by simulating millions of hands and counting the number of wins, loses, and pushes for each true count. The program runs on basic strategy but disallows splitting. I've found a large amount of variance and weak correlation (although a positive trend).

I'm certain there are better ways to compare systems than using "percent win" vs. "count." I've found a little information concering SCORE, but haven't been able to find any of the underlying equations. Any comments would be appreciated.

First, running mere millions of hands will not cut it.

Take, for example, the hand of A4 vs 5. In a 6-deck shoe, this will occur 2 * 24/312 * 24/311 * 24/310, or 0.0009192 of the time. The reciprocal of that is ~1088. If you accept you need at least 100,000,000 incidences to nail down the result, you would have to run 108,800,000,000 total hands at EACH true count to gather enough data to have reliable data for hands which occur that often.

Second, mere win, loss and push precentages don't tell you much. The favorable rules create "premium" hands, such as BJs, doubles and splits, which make the average win larger than the average loss, and make the average for both larger than the initial bet. For example, in the 6D Atlantic City game, the average win is ~1.2045 and the average loss is ~1.0995 times the initial bet. This difference is what narrows the roughly 5% house advange in win vs loss down to about a 0.4% house edge when it comes to net $$, or EV.

So, you have two choices:

1) change your programming approach; or

2) go to sites like qfit.com and bjmath.com and look at the results of others' sims.

I think a better way to compare systems would be to play against the same arrangements of cards.

The basic formula for SCORE is 10^6 x (EV per round)^2/(Variance per round), assuming the bets are optimized for a given bet spread. You can learn the details of how this is accomplished by studying the source code of PowerSim and (primarily) ScoCalc. These are both free, open source programs available here:

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