6 sims of 9,999,999 hands is 59,999,994 total hands
average result: (.0037+.0037+.0039+.0047+.0085+.0077)/6=.0054
standard deviation is sqrt(26.8/59,999,994)=.00067
your deviation was .0054-.0072=-.0018
that's .0018/.00067= 2.7 standard deviations (still unlucky, ~.5%)
as for bad streaks, R(1) for AA is 0.99941, which means the
probability of losing B bets is 0.99941^B, for example, on 5 coin
quarters, $3,000 would be $3000/$1.25=2400 bets and the probability of
a losing streak of that magnitude is 0.99941^2400=.24=24% even though
the game is positive in the long term if played with perfect strategy
N0 for AA is 26.8/.0072^2 = 517,000 hands, meaning that at 517,000
hands of perfect play your odds of net winning are 84%, at 2,068,000
hands (4N0) of perfect play your odds of net winning improve to 98%,
at 4,653,000 hands (9N0) of perfect play your odds of net winning
improve to 99.9%
A little bit of cashback (or comp,bounceback,bonus,gas cards ...)
improves things dramatically, for example AA with .28% cashback has an
N0 of 26.8/.01^2 = 268,000 hands
OK, I have run 6 simulations of 9,999,999 hands of AA (without a
reboot) and things are looking better (maybe my computer is a slow
learner). the ending paybacks were in order, 100.37, 100.37,
100.39,
ยทยทยท
--- In vpFREE@yahoogroups.com, "jimnkelli" <jbecker11@c...> wrote:
100.47, 100.85, and 100.77. According to the msg about standard
deviations, I guess this is all within margin, I did notice that
during one run there was a sustained loss of 50,000 coins, although
the game was 128,000 coins ahead at the beginning of the bad streak,
It would be really poor randomness (unlucky) if that were at the
beginning of someones play of a positive game (ouch).
Happy Royals
Jim