Does the distribution of prizes follow a mathematical model?
In particular, is there a statistical model we can use to predict the likelihood of a given outcome? Each day’s show is, we can assume, an independent random event, and the final awards vary from one new penny to a six-figure sum. The mean over the shows so far was £16,200 or so, but half the contestants left with £13,000 or less. This is evidence to suggest an Exponential distribution is appropriate, at least as a starting point. A pure Exponential distribution is “memoryless” – the chance of someone winning less than £5000 is the same as the chance of someone winning £20,000 but not £25,000. This doesn’t hold for Deal, where 20% of contestants leave with less than £5000, but 45% of those reaching £20,000 don’t make it to £25,000. In practice, this idea doesn’t quite hold water. A fifth of all contestants left with less than £5000; of those who won £20,000, almost half won less than £25,000. This isn’t enough evidence to dismiss the Exponential claim entirely. We mentioned in February
