The super-rigging of poker machines

Are poker machines rigged? Of course! Even the most optimistic gambler knows that the odds are stacked against them. But it is worse than that: poker machines are super-rigged.

Gambling is gambling. For those who engage, its unpredictability is part of the charm and the excitement. But, for any gambling game mathematics can still guide your expectations.

If a game is fair then winning or losing comes down to luck, and in the long run you expect to get back close to what you gambled. Of course, no one expects pokies to be fair. In fact, of each $100 gambled you can only expect to get back about $90. It is in this sense that the pokies are rigged. This rigging is also more costly than it may appear, because it is likely that the same money will be gambled over and over, with a fraction lost each time.

But how can poker machines be super-rigged? The trick is in the psychology, to make it appear that the chances of winning are greater than they really are. Such scams have a proud tradition in carnival games. The comparable super-rigging of some poker machines has been documented by Melbourne barrister Tim Falkiner.

To illustrate super-rigging, consider the following simple game. Throw a pair of dice. If the sum is 10 or higher then you win the Big Jackpot, with smaller prizes for other totals. This game can easily be rigged to give less than 100% money returned, simply by adjusting the sizes of the prizes.

Now consider the same game, but super-rigged with dodgy dice. Imagine we swap the 4 and the 6 on one die for the 3 and the 5 on the other: so, the sides of the dice are now 1-2-3-3-5-5 and 1-2-4-4-6-6.

The dodgy dice together have the same numbers as normal dice. This implies that the average sum of a roll of the dice has not changed, giving the psychological impression that prize-winning totals are just as likely.

But actually, the chance of winning the Big Jackpot has decreased dramatically. With normal dice there are 6 of the 36 possible rolls that will sum to 10 or higher; the rolls indicated in the left diagram below.

With the dodgy dice, there are now only 4 such rolls, as indicated on the right. So, the chances of winning the Big Jackpot have gone down from 6/36 to 4/36 - a 33% reduction. And, cunningly, the chance of "just missing" by rolling a 9 has doubled, from 4/36 to 8/36.

It is exactly this type of super-rigging that is programmed into the pokies. Think of the five poker machine wheels as 30-sided dice. Some wheels are starved of Jackpot symbols, which is then disguised by loading a few more Jackpot symbols on other reels. The consequence is that winning the Big Jackpot is much less likely than it appears. And, the chances of "just missing" - encouraging another go - is much more likely.

The use of super-rigged poker machines is incredibly sneaky. Is it also illegal? Tim Falkiner has argued that if such machines are "deceptive" then they could well be banned under the Trade Practices Act. However, the Australian Competition and Consumer Commission is apparently unconvinced that such machines are deceptive. We feel compelled to ask: what would be?

Burkard Polster teaches mathematics at Monash and is the university's resident mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator.

Marty Ross is a mathematical nomad, currently lecturing at the University of Melbourne. His hobby is smashing calculators with a hammer.

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