A Salford maths professor says this is the best possible arrangement of numbers around a dartboard.

No sport requires a knowledge of numbers quite like darts.

The rules are these. Each player starts with 501 points and every number hit must be subtracted from the total. The game is won by the first player to reach zero, with the added requirement that the last dart thrown must hit a double or the bull.

(A dart in the outer ring is a double, in that it doubles the value scored, and in the inner ring is a treble, which triples the score. The bull is worth 50.)

The fact that you can only finish on a double  favours players who are good at sums. When I interviewed darts legend Bobby George a couple of years ago he said: “If I hadn’t learnt to count I wouldn’t have won what I have won.

“For example, just say you have 126 left. People who can’t count go for treble 20. But if you miss and you get 20 you cannot finish from 106 with two darts.

“I would go for treble 19. If you you miss and get 19 you have 107 left, and you can finish with two darts – treble 19 and bull.”

George said that when he was starting out he would take his dartboard to bed with him to work out which numbers gave more chances to finish if he missed the treble of the number he as aiming for. He said that at first his opponents described his number selections as “unorthodox” but they soon saw the wisdom of his approach, even if some of them (mentioning no names) weren’t clever enough to work it out themselves.

“You can win more games if you can count.”

I was thinking about this last night as I was watching the World Darts Championship from Lakeside. I can’t really explain it, but I find watching darts incredibly nostalgic and addictive.

And i was reminded of an excellent talk I saw at the Mathsjam last year by Professor Dave Percy of Salford University about an issue that has interested mathematicians for years: What is the best possible positioning of numbers round a dartboard?

The current dartboard positions were devised by Brian Gamlin in 1896, pictured right. The 20 is at the top and the others are arranged in such a way as to put low numbers next to high numbers so that you are penalized if you go for – and miss – the highest numbers.

Dave decided he would have three constraints for his perfect board:

1) low numbers near high numbers to penalize over-ambitious players as above.

2) let the numbers alternate between odd and even.

3) let the board have rotational quasi-symmetry – in other words, let the different parts of the board look as similar as possible, so the same kinds of number are more or less evenly spread out.

When he crunched the numbers (and the theory here is not for beginners) he came out with the board at the top of this post, which is the optimal solution for the constraints. Ta-dah!

It’s interesting to note that 8 of the 20 numbers are in the same place as in Gamlin’s board.

A full analysis of Dave’s optimal dartboard will be appearing in a forthcoming issue of Mathematics Today.