With all the posts on both Duamond in a Day( DDAY) and the central
limit theory, I thought I would throw in my two cents also, including
some data that might be interesting to some of the members.
The CLT (maybe as a correlary ) states that sample averages from a
non-normal ( skewed ) distribution form a closer to normal
distribution.
This can be helpful for those interested in getting DDAY by making
the sample size equal to the DDAY requirement. For Laughlin the
requirement is 1800 points in a day and VP points are 1 for every 10$
played. Thus the $ requirement is 1800x10= 18,000$ in a day.
The best play at Laughlin is 50 play nickel 9/6 JOB. This requires
72,000 hands ( or 1440 deals ). At 400 deals per hour this can be
done in about 4 hours with potty breaks.
I will show 50 sessions of results below results from Winpoker for
1440 deals at 10 play for quarters. This would be worse in terms of
volatility than would be the 50 play nickels.
The following are listed in the order played. They are the amount in
$ that would have been won or lost for each 1440 deals ( or 14400
hands)played:
-396.00 +1024.00 -1324.00 -924.00 +826.00 -562.00
+769.00 -1193.75 -1346.25 -127.50 -1135.25 +1095.00
-453.75 +1383.75 -673.75 +355.00 -817.50 +1173.75
-101.25 +373.75 -875.00 -1182.50 -998.75 -871.25
-676.25 -715.00 -1175.50 -455.00 -152.50 -1242.50
+543.75 +525.00 +1711.25 -183.75 +757.50 +155.00
-643.75 -717.50 -150.00 -626.25 +457.50 -848.75
+540.00 +451.25 -375.00 +682.50 -832.50 -217.50
-1111.25 -556.25
The average is - 217.96 ( or 98.79 payback) a little low
The number or RF were 18 ( or one every 40,000 hands)
The median loss was -425$ ( the most important statistic for DDAY)
The standard deviation for the averages was 796$
There were 17 ( or about one third of sessions)
Since the return was considerably below the EV ( 98.9 vs 99.5) and
there would be a lower SD with 50 play nickels, the median loss for
DDAY should be below $400.
One other note. If you wanted you could play 10 play nickels at
Laughlin ( would require at least 16 hours on one machine) and the
results above could be consolidated into 10 sessions to exactly
simulate DDAY , however more results would be needed to be
meaningful. But 10 play nickels would lower volatility even more by
getting 7200 deals per session.
Hope this is interesting to some of you.
Bob from PA