Thus the actual mixing even with a true random generator input is very limited in it’s range. Thus the question of how big the state array is? Often it’s tiny and just spans a few cards due to the mechanical limits of the mixer and it is very linear in it’s operation. At best it’s a simple “block swap” at worst just a linear feed hopper. Whilst the output can appear complex it’s not at all random and in the case of mechanics fully reversable.īut whilst these card shufflers can appear to have a very large state array due to the input store, in practice it’s not.

Worse due to just how small the mechanical bounds are they are generally not that hard to reverse the sequences.įor those with a little more than curiosity consider the machines as being in several partsįor reliability the “mix function” has to be mechanically simple, and is in effect at best can be compared to a simple “cellular automata” / “state machine”. The problem is that all machine based CSA’s are bound and thus without an actual TRNG input are by definition not just determanistic but predictably so. Tags: gambling, loopholes, random numbersĪs I’ve mentioned in the past I have an interest in “Card Shuffling Algorithms”(CSA) for security applications including as “entropy spreaders” on “True Random Number Generators”(TRNGs). Although the mechanical shuffling action appeared random, the mathematicians noticed that the resulting deck still had rising and falling sequences, which meant that they could make predictions about the card order. With his collaborator Susan Holmes, a statistician at Stanford, Diaconis travelled to the company’s Las Vegas showroom to examine a prototype of their new machine.

Stanford mathematician Persi Diaconis found other flaws: The casino lost millions of dollars before the gang were finally caught. The images, transmitted to an accomplice outside in the casino parking lot, were played back in slow motion to figure out the sequence of cards in the deck, which was then communicated back to the gamblers inside. The gang used a hidden video camera to record the workings of the card shuffler through a glass window. …the executives had recently discovered that one of their machines had been hacked by a gang of hustlers. We never did it-I remember that we didn’t even try very hard-but this article shows that we probably would have found non-random properties: Many years ago, Matt Blaze and I talked about getting our hands on a casino-grade automatic shuffler and looking for vulnerabilities.

On the Randomness of Automatic Card Shufflers

Automatic card shuffler not working