Congratulations to the winners of the last Infinity competition, don’t forget to check out our latest competition.

In this issue we were fortunate to have a number of contributors. In particular we would like to thank Benjamin Shuhyta for his valuable help, and Matthew Versluys and Andrew Payne for their expert advice. Once again we are extremely grateful to the Office of Economic and Statistical Research (OESR) for their continued sponsorship. Have you checked out their website lately (http://www.oesr.qld.gov.au/views/home/infinity/inf_fs.htm). They have been involved in some very interesting research projects, some of which may be appropriate for use in schools.

Take for instance their article on continuous shuffling machines at Blackjack tables. In casinos, Blackjack dealers use three decks (156 cards) at one time.
At regular intervals these 156 cards need to be shuffled. To save the dealer time, and hopefully to produce a more random shuffle, the casino may use a shuffling machine. But how does the casino choose a good shuffling machine?

The OESR have been evaluating shuffling machines to ensure that once the cards are mixed there is nothing predictable about their order. Their test was based on recording the immediate neighbours (cards on either side) of each card in the deck. Then, after shuffling, recording the final proximity (the number of cards apart) of these neighbours. In this way they were able to study the subsequent separations of two neighbours, and decide if the process was random or not. In setting up the experiment they needed to decide, how many neighbouring cards should be observed, and what deviation between observed and expected (theoretical) results would be tolerated. A Chi-square goodness-of-fit test was adopted and a power analysis suggested that a sample size of 182 neighbours was required to have a 90% chance of detecting non-randomness. Thus a shuffling machines performance was accepted if the Chi-square test statistic was small.

Checking out the predictability of your favourite shuffling process would appear to offer plenty of scope for a school project. For instance, other tests of non-randomness could be devised, or simple frequency counts could be taken or basic probabilities could be explored.