In a message dated 10/15/2003 9:05:39 PM Central Daylight Time,
erchalb@cantv.net writes:
Now we have to
use Chebyshev's theorem to obtain that, with 75% confidence, her
return should be between $85,218 and $74,046 for the 9/6 JB machine;
and it should be between $80,985 and $71,009 for the 5/6 JB. When I
look at the big overlap the two intervals make, I must admit it does
not make any difference at all at which machine she played those
16,000 hands. Of course, someone else might conclude something
differently than I do from the figures.
I haven't paid much attention to Chevy Chase's Theorem since he left SNL, but
I, in my own simple way, see a problem with playing a bad paytable even if
you are only playing, as the woman in your example was, a half hour a year.
Even if the woman is not playing optimal (Good Lord, is that the right word? 
strategy. With all the talk of 10,000; 100,000; 1,000,000, hands... or
theoretical ER and an infinite number of hands some may forget that there are
concrete, every session consequences to choosing an inferior paytable. In your
example, the choice is between a 9/6 and 6/5 JB pay schedule. The fullhouse and
flush are common hands. They are likely to occur even in a short session. If
the woman plays a dollar machine with 5 coins, every time she gets a FH she
will be getting $15 less on the 6/5 machine and for the flush she will be
sacrificing $5. On a quarter machine it would be $3.75 and $1.25 and this is a BIG
deal IMO. In even a short session of a few hundred hands these hands are
very likely to occur. If the woman hits say one full house and two flushes (not
unlikely) she has sacrificed $25. For what? Is $3.75 or $15 or $25
unimportant to her? It isn't unimportant to me. Which is, of course, to say that it
is important;-)
Look at it as a consumer, which is I think what many of us are. There are
two stores next to each other. One sells an ice cold bottle of soda for $1.
The other sells the same kind of ice cold soda for $1.23. You are outside and
you are hot and thirsty. Where do you get your soda? It is only 23 cents
after all and maybe you only buy one soda a year, but the consequences of similar
bad decisions over time may cost us a significant amount of money. Most of
us, well versed in consumerism, will choose the $1 soda. Is gambling so
different? It isn't to me. And as an added benefit, this attitude can drive
competition. Who wouldn't like to see better paytables more prevalent?
Admittedly, my explanation is simple. My math skills are pretty minimal, and
I'll confess I have no idea what the Sheboygan Theorem is <BG>, but it works
for me. Feel free to disagree.
Chandler
"...there is always a well-known solution to every human problem--neat,
plausible, and wrong." H. L. Mencken
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