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Inge Telnaes

August 20, 2011

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

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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  1. Hi Kreso,

    Its an interesting post. I also read the article you linked to and it seems they might be implementing some learning algorithm to adjust the volatility of the game to best extract money from each individual. Its like there’s some interesting math/computer science behind that, but at the same time, it seems totally evil.

    Did I ever tell you about my brilliant idea for a non-profit casino? You can double your money, or lose it all and right it off as a charitable donation. There would be different slot machines to lose your money to Alzheimers research, or parkinsons research, or basic math and science research.


    • josic permalink

      I like the casino idea – but isn’t that somewhat like the lottery? However,
      the ability to choose an “Alzheimer disease” machine would be nice.
      Would there be a “compulsive behavior” machine? I am sure that would
      be popular.

  2. The slot machine inventor, Charles Fey, used the illusion of 20 characters on each of 3 reels. (20X20x20=8000 possible combinations). However he only had 10 position stops for each reel (10X10X10=1000). After that inventor had his idea purloined by Herbert Mills, most machines were produced using matching 20 characters & stops. Except for a few (such as Keeney) manufacturers, predominately Bally, expanded to 22 stops (and characters). (22X22X22=10,648). In the late 1950s Jennings built some 25 stop (and characters) machines (25X25X25=15,525 combinations possible.

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