Test for unfair Blackjack

Quote: dfde50

presumably since the wizards statistics are based on one hand vs one dealer hand, flat betting or what not, etc, the multihand aspect makes it really hard to scientifically apply whatever happened to the wizard's statistics.

You remind me that the SD for multi-hand blackjack is different than single hand .... for three hands it's higher (1.52) but spread over three hands ... the math gets a little more complicated, but not by much ... lets assume that instead of μ=182 (our expected loss) but rather it's equal to 1/3 or 60.67 (this is an over simplification, but it definitely gets us in the ballpark) so the standard deviation for our expected value would actually be lower SD = (182/3) * sqr(3) * 1.52 ... or about 160 betting units ... this puts my losses halfway into the 4th standard deviation (μ + 3.506σ) ... for a normal distribution curve, this puts my results outside of 99.95% of all data ... or about 2000-1. ... the results are considerably less believable now. I've been unlucky before .... but this would be an extreme case.

No - the best run was +500.50.

SDs	No.
less than -3	1
-3 to -2	19
-2 to -1	138
-1 to 0	352
0 to +1	332
+1 to +2	131
+2 to +3	26
more than +3	1

Any chance you're set up for multi-hand? ... I was actually playing 3 at a time.

Playing 3 at a time would increase the variance a bit - since three hands would be affected by the dealer's result (e.g. if the dealer had a 6 and bust or A and got BJ that would affect 3 hands rather than just 1). Given the trial with one hand, suggested your experience was more likely to be due to bad luck, running three hands wouldn't change the decision. I suspect you have to be well outside 4 SDs before there's a realistic suspicion of something fishy.

As you probably guessed, my design assumes there is only one initial hand (although it caters for infinite splits) so would be non-trivial to change. Also remember I'm running UK rules and only 1000 runs, so it's already an approximation to your scenario.