To: WSFAlist at keithlynch.net
Date: Sat, 8 Mar 2003 03:18:15 -0500
Subject: [WSFA] math problem
From: ronkean at juno.com
Reply-To: WSFA members <WSFAlist at keithlynch.net>

Here is a math problem some may find interesting.  Or perhaps it is more
of a logic problem than a math problem.

Slot machines have been proposed for Maryland, and one of the objections
to allowing slot machines is that players would lose money, which might
result in finacial distress for some players, and their families.  Slot
machines typically have a 'payout ratio' of about 85%, which means that
on the average, 15% of each bet is lost, over the long run.  On any given
day, some players win on net, and some lose, but in the aggregate 15% of
the total money bet is lost (with an 85% payout ratio).

It occurred to me to propose a possible solution to the problem of slot
players losing inordinate amounts of money - the solution would be to
make the slot machines have a 100% payout ratio.  To pay for the cost of
operating the casino, and to provide a profit for the operators and
revenue for the state, a set fee each day would be charged to players who
enter the casino.  Someone pointed out to me, though, that many slot
machine players are in the habit of playing until they lose nearly all of
their money, that is, they tend not to quit when they are ahead.  For
those players, it seems that more than half of them would lose nearly all
of the money they had available to play with on a given day, or would be
in a losing position at the time the casino closes that day.  Some of
them would win for the day, in spite of themselves, if the casino
happened to close at a time when they were ahead.

So it seems, then, that there exists a 'losing strategy' for playing
slots, the strategy being to play until all, or nearly all, of the
available money is lost.  That strategy does not guarantee a loss ony
given day, but it seems as though a player who follows that plan would
lose money over the long run.  Assuming that the slot machines have a
100% payout ratio, it seems that if there is a losing strategy, there
must conversely be a winning strategy, a strategy which, while it would
not guarantee a net win on any given day, would yet be expected to yield
net winnings over the long run.

So, the question is, given a 100% payout ratio and the existence of a
substantial perentage of players who on any given day persistently play
until they have lost nearly all of their funds and then stop for the rest
of the day, is there a winning strategy, and if so, what is it?

Ron Kean

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