# How Claude Shannon used information theory to cheat at Vegas roulette

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He’s not using “information theory” to track the position of the ball. He’s just using “physics.”

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It’s a win-win from the casino’s perspective. Casino gets the cash, and the “customer” gets to same some time!

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Babbage, mate.

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NRS 465.015
Definitions.
As used in this chapter:

1. “Cheat” means to alter the elements of chance, method of selection or criteria which determine:
a) The result of a game;
b) The amount or frequency of payment in a game;
c) The value of a wagering instrument; or
d) The value of a wagering credit.

Using that computer was definitely altering the elements of chance. Which was the whole point of the exercise.
So, yes, cheating.

I will, however, concede that Thorp and Shannon were not cheaters - this was done as a proof of concept, not out of greed.
Sometimes you have an idea and just have to see whether it works…

Only if “steampunk engine” qualifies. And even then, Pascal and Leibnitz might take issue.

These humans will figure it out one day – they’ve made a lot of strides over the past hundred years or so, doncha think?

But yes, I am totally with you – when you begin to understand that the basis of everything is informational in nature, it can have quite a radical affect on your perspective on pretty much everything.

Learning about John Wheeler’s “It from Bit” hypothesis was another interesting point for me.

Gleick’s The Information is an absolute must-read!

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Let us not forget Ada Lovelace!

From Wikipedia:

“Augusta Ada King-Noel, Countess of Lovelace (née Byron; 10 December 1815 – 27 November 1852) was an English mathematician and writer, chiefly known for her work on Charles Babbage’s proposed mechanical general-purpose computer, the Analytical Engine. She was the first to recognise that the machine had applications beyond pure calculation, and created the first algorithm intended to be carried out by such a machine. As a result, she is often regarded as the first to recognise the full potential of a “computing machine” and the first computer programmer.”

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Actually it was not. They did not affect the wheel. The chance of the ball arriving in a particular slot was unaffected. What they did was the equivalent of a poker player being better at “reading” the other players, but with electronic assistance. It is up to the casino to make roulette a game of pure chance, not the players.

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I’m about halfway through the book, and it’s a so-so bio of a great man. The writing is a bit weak, with inconsistent levels of detail all over the place. I was hoping that Shannon would merit something better. Ed Thorp’s recent autobiography also touches on Shannon when describing their joint time at MIT, and is an interesting read until the last quarter of the book.

Cory mentions Gleick’s “The Information,” which covers much of the same material. Gleick can be a good writer, but when he goes off point he’s very tiresome (his recent “Time Travel” is a good example). My issue with “The Information” is that Gleick gets a fundamental point wrong on only the second page, ascribing the naming of the word “bit” to Shannon when it was in fact coined by fellow Bell Labs scientist John Tukey. Made me wonder how many other details he got wrong.

My favorite book about the dawn of the computer age is “Turing’s Cathedral,” by George Dyson. Dyson mentions Shannon at points, but the focus is John Von Neumann and his collaborators at the Institute for Advanced Study in Princeton. Shannon had a fellowship at the IAS the year before he joined Bell Labs, and interacted with Von Neumann as well as other IAS residents including Weyl, Godel, and Einstein.

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The chance of the ball arriving in a particular slot was unaffected. But if a player introduces a method that lets them know where the ball will end up in advance, and lets only them know this and not the other players, it is cheating as defined by NRS 465.015.
This does at least alter the value of a wagering instrument.
It also alters the elements of chance. Not of the chances regarding which number comes up, but of the chances of the players to pick the right number. It is up to the casino to make roulette a game of pure chance - but for all players alike.

By your argument using poker as an example1), it would be okay not to just “read” the other players by looking for tells in their body language, but actually read their cards (or the cards in the deck) with “electronic assistance” or by using marked cards. This is basically using information that is in the public domain versus using inside information.

1) Which is arguably apples and quinces. Roulette is, as you say, a game of pure chance. There is no system. Unless the wheel is tampered with, results are random.2)
Poker is a combination of chance (the luck of the draw) and skill.

2) I had the opportunity to take a behind the scenes tour of a newly opened casino in the late 1980ies. They kept track of all the numbers on all the tables and used computers and statistical methods to make sure the numbers really were random. If any hint of a pattern would start to emerge, 1) that particular table went into unscheduled maintenance right away 2) extra checks on the floor for any signs of collusion between personnel and patrons were made.
What really surprised me was that during all opening hours of the casino there were at least three civil servants from the IRS on the premises to keep an eye on things.

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The “element of chance” in roulette is where the ball lands. Thorp and Shannon did not alter this in any way.

They predicted where the ball would land. This is something most gamblers try to do, and which the casino encourages them to do, with displays of which numbers are “hot” or “cold” or the like. The only difference is that they were successful while others were deluded. This does not make them cheaters.

In your followup you fixate on the notion that they had information which others at the table did not. This is not cheating, as established by Nevada case law. If the dealer at blackjack deals cards in such a way that a skilled observer at one position on the table can see his hole card, but others at the table cannot, the courts have ruled that using that information is not cheating.

As for your example of marking cards at poker, the crime there is in marking the cards, not in observing marks that may already exist. Thorp and Shannon did not tamper with the roulette equipment in any way.

…and anyway, even if you find all those arguments unconvincing, ask yourself this:

If using a roulette computer were cheating, then why did Nevada bother to amend their laws in 1985 to add the device statute? And why were the many people openly advertising blackjack computers for sale before 1985, under their own names, never prosecuted for possessing and selling equipment intended for cheating casinos? Obviously, it’s because everyone involved knew that the laws regarding cheating didn’t apply, and they needed something new.

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Well, as Malcolm Turnbull has let us know, the laws of Australia supersede the mere laws of mathematics, and lawyers can define things how they like. And you can’t argue with lawyers unless you have a lot of money and don’t mind losing it.

However, there are two interesting points about roulette.
The first is that it is supposed to be a game of pure chance. There is of course a big difference between the results being random and something being a game of chance. In the case of roulette it is the possibility of forecasting the result of a turn while it is still possible to place bets, depending on where in the cycle the croupier says “Rien ne va plus”.
If that point is before the outcome becomes predictable, the house has nothing to worry about. Presumably the house takes good care that this is the case. In the old Swiss system where bets could be placed right to the last moment, it would be different, but such casinos were owned by local communes or a society and members had to come recommended.

The second point is that this is because, even with a degree of interference with the wheel that is on or past the edge of detectable, the house still wins.
In Europe the house has an advantage of 1/37 due to the zero; in the grasping US casinos where there is a double zero the advantage is 2/38, or over 5%. This even applies, of course, to pair/impair and rouge/noir because the zeros are not treated as even or of one colour.
Provided the game is not rigged in the favour of the better by more than 5%, there is no point in having a system because the house always wins in the long term.
My suspicion is that detecting and expelling anyone trying to game the system is security theatre intended to persuade the gamblers that there is a system that will enable them to beat the house, and the house is worried that someone will find it. Because that keeps some people gambling.
The rational approach to roulette is exemplified by a couple I heard of who simply allocate a certain amount per month to visiting a casino and stop when they have either run out of money or doubled it. If the latter, next week they go to the opera. Treat it as a fairly expensive entertainment, fine, try to game the system, risk losing a lot of money.

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