In which I eat statistics for breakfast

Clearly, the best complement to a nice bowl of Crunchy Nut Corn Flakes is a lively debate about probability. Allow me to explain...

The weekend just passed included my father's 60th birthday. Consequently, the family all went away together for the weekend. A good time was had by most.

Over the weekend, Richard had been "playing" Clock Solitaire. I say "playing" because it's actually a purely mechanical "game" with no skill at all - the cards are randomly shuffled, and if the random sequence is just right you "win". Otherwise, you "lose". There are no choices, and hence no ability to alter the outcome.

In case you aren't familiar with this fun and exciting way to pick up playing cards in random order, here are the rules:

Shuffle the cards well. Then, deal them into thirteen piles, with one at each of the positions associated with the faces of a clock (1 to 12), and the thirteenth at the centre. Then, pick up the top card in the central pile. Place this, face up, by the pile corresponding to the value on the card (with Jack = 11, Queen = 12 and King = Centre). Then turn over the top card on that pile, and repeat.

You lose if you find you can't pick up any more cards. Since each pile has four cards (except the centre), and there are four cards of each value, you lose if the fourth King comes out before the other cards are done.

On Sunday over breakfast, we discussed the following crucial question: what are the odds of winning?

The answer is 1 in 13. Proving it is really quite difficult, and beyond the scope of this blog. The short version is that you have a sequence of 52 cards, and win if and only if the last card in sequence is a King. There are 4 Kings, so the odds are 4 in 52, or 1 in 13. The difficult part of the proof comes with the "and only if" part of the statement above - one of the scenarios we postulated suggested having the '5' and '7' piles pointing to each others, and proving that that cannot happen while the King is also last in sequence is tricky.

The debate was held between myself, Richard, and our father. So, for those who are keeping score, that's two Maths/Computing graduates and a university lecturer in Maths. We got as far as our "problem scenario" before being distracted by another burning issue of the day (I think it was fruit & veg). I Googled for the rest.

Probably the most interesting thing about the debate was not the debate itself, but rather the reactions of those who were observing. We had two observers, one a primary school teacher and the other a student nurse (one of whom has objected to being identified here in the past, so they shall remain nameless). Neither has a particularly mathematical background. That's not an insult, nor a value judgement, merely a statement of fact.

Anyway, the reactions ranged from puzzlement, to a sentiment of "why can't we just play the game, like normal people?", to some mild hostility to so complex a subject before the first meal of the day.

I must say, I find such reactions interesting, although not surprising - I've encountered them before. The fact is, maths, computing and probability are all hard, complex subjects, and many of the conclusions one comes to are counter-intuitive. The simple fact is that without a certain amount of grounding in the subject it is simply not possible to understand some of the problems involved, never mind the solutions to those problems (the Clock Solitaire problem isn't one of the ones that the layman can't understand, of course). And, when confronted with a topic that they don't understand, people are going to react in a less than enthusiastic manner.

To briefly tackle the "why can't you just play the game" question, I should point out that there is no real game to Clock Solitaire. Once the cards are dealt, that's it. And, since the dealing of cards is random, the "game" amounts to just wasting time. Which sounds absolutely thrilling.

However, the question of what are the odds of success? Well, that represents an unknown, a mystery. What's more, unlike "Lost", it is a mystery with a definitive answer, and established means of working our that answer. And isn't that worth discussing? Personally, I found it fascinating.