Page 31 of The Final Vow

‘No wonder my dad always beat me at Monopoly.’

Bradshaw frowned. ‘That makes no sense. Monopoly isn’t a game of cha—’

‘Poe’s stupidity aside, can we move on, Tilly?’ Flynn said, recognising a tangent when she saw one.

‘Of course, DCI Flynn,’ Bradshaw said. ‘OK, so we’ve established that with two fair dice, there’s a one in thirty-six chance of throwing a twelve. In percentages that’s a touch over 2.78. What are the chances of throwing a seven?’

Poe took his time. Did some mental arithmetic. He imagined two dice. Worked through the possible combinations of throwing a seven. One and six. Two and five. Three and four. Four and three. Five and two. Six and one.

‘Six chances,’ he said eventually. ‘A six in thirty-six chance.’ ‘Well done, Poe!’ Bradshaw said excitedly. She started clapping and kept it up until Mathers and Flynn reluctantly joined in. ‘Three cheers for Washing—’

‘Not a chance,’ Flynn said.

‘CanIdo three—’

‘No.’

‘Aw.’

‘Tell us what this means, Tilly,’ Poe said.

‘Do you know what an icosahedron is, Poe?’

‘It’s a dinosaur, isn’t it?’

‘Don’t be ridiculous. An icosahedron is atwenty-sided die, rather than six-sided. Now, obviously the number range is going to be much bigger, but can you calculate the chances of throwing forty?’

‘A double twenty?’

Bradshaw nodded.

‘We’re not all human calculators, Tilly. Why don’t you tell us?’

‘The chances of throwing a forty with two icosahedrons is one in four hundred, Poe. That’s a quarter of one per cent. DCI Flynn, what are the chances of throwing aonewith two icosahedrons?’

‘The same as a forty,’ Flynn said immediately. ‘A quarter of one per cent.’

‘You’re an idiot. The lowest number you can throw with two dice is two. A double one.’

‘Well, why fu . . . bloody ask then?’ Flynn snapped, reddening.

‘Because you wouldn’t let me do three cheers for Poe,’ Bradshaw said. ‘Anyway, the reason I’m telling you this is because, just like with two six-sided dice, there is symmetrical distribution when it comes to twenty-sided dice probability. Instead of seven, with icosahedrons twenty-one is statistically the most likely number to be thrown. That means, if the dice are fair, there’s a five per cent chance of them showing twenty-one. It’s 4.75 for twenty and twenty-two, 4.5 for nineteen and twenty-three, and so on, all the way down to two and forty, which as I said is a quarter of one per cent. In other words, the numbers most likely to occur are bunched up in the middle. If you looked at a bar graph with two on the left of the horizontal axis, forty on the right and twenty-one in the middle, the distribution would be triangular.’

Poe nodded. ‘OK, we stumbled a bit along the way, but we got there eventually, Tilly,’ he said. ‘But I’m not sure how throwing dice helps him randomly select his victims.’

‘That’s because heisn’trandomly selecting victims, Poe,’ Bradshaw said. ‘He’s randomly selectinglocations.’

Chapter 24

‘Please switch on the monitor, Commander Mathers,’ Bradshaw said. ‘Poe is nearer, but he won’t know how to do it.’

Mathers suppressed a grin but did as she was asked. The screen flickered blue. The Thames Valley Police logo appeared. It bounced around the screen like it was trapped.

‘This is a secure system,’ Mathers said. ‘I’ll get you the password.’

Bradshaw snorted. She typed some commands into her laptop and the logo disappeared. In the darkened trailer the screen lit up her face like she was telling a ghost story. She typed in a few more commands and a map of the UK appeared on the wall-mounted monitor. She superimposed a series of squares over England and Wales. She leaned back and studied her work, blowing an errant wisp of hair away from her eyes.

To some people – not Poe, obviously; he was far too mature – the shape of Great Britain resembled a witch riding a pig. The witch’s head and hat were Scotland. Her body extended from the north of England to the Midlands, her legs reached the south coast. The pig’s arse, fittingly, was East Anglia; its head was Wales. Its front legs were Cornwall and Devon. In other words, Great Britain was an odd-shaped island. Pinched at the top, wide at the bottom.