Mathematics in everyday life

Inge Telnaes

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The theory of probability was essentially started with people trying
to describe games of chance mathematically. Ever since the histories
of the two have been intertwined. However, there is a recent tidbit
buried in a Wired story about a slot machine hacker (a nice read,
by the way), that I was not aware of.

It concerns the Norwegian mathematician Inge Telnaes. In 1984 he
obtained a patent for an “Electronic Gaming Device Utilizing A Random
Number Generator For Selecting The Reel Stop Positions.” Prior to
that, slot machines were mechanical devices. Suppose that you
have, say, a machine with three wheel, each with 12 symbols, with one
of these 12 a cherry. The likelihood of getting three cherries (let’s assume
this is the jackpot combination) is 1 in 1728. So you should be getting
about $1700 on a $1 bet if you hit the jackpot. That does not seem
so attractive by the today’s standards. The only way to increase the
payout is decreasing the chances of a jackpot. With a mechanical device
adding a wheel is a possibility. For instance adding a
fourth wheel in the previous example would get us to about a $20K jackpot.
But people intuitively know that chances of getting four cherries are
tiny. Another possibility is to make bigger wheels. However, to get to the
astronomical jackpots of today you would need machines with enormous
wheels.

So Telnaes proposed a very simple solution: Create the illusion that
the device is purely mechanical, but let a random number generator
determine the combination of symbols that appear on the wheel. I think
this is brilliant: I mean, pick a number between 1 and a million. Now tell
somebody that in return for a dollar, you will give them $980K if they
guess the number correctly. I doubt that many people would take
you up on this. Yet take a chip that does exactly this, put it in
a machine with blinking lights and spinning wheels with bars and cherries,
and you can make billions. You can now make the odds whatever you want,
promise astronomical jackpots, and still come out ahead.


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