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.