Page 23 of The Final Vow (Washington Poe #7)

‘You look like the kind of scamp who played dice games in the schoolyard, Poe,’ Bradshaw said.

Poe rolled his eyes. ‘I’m only nine years older than you, Tilly,’ he said. ‘I played Cops and Robbers, Cowboys and Ind . . . and Native Americans.’

‘Nice save, Poe,’ Flynn said.

‘Thank you.’

Bradshaw waved them away. Impatient. ‘If you throw one die, Poe, what are the chances it will land on a six?’

‘One in six.’

‘That’s right. If the die is fair, each possibility is equally likely. The chance of throwing a six is the same as the chance of throwing a one. Now, if you have two dice, what are the chances of throwing a twelve?’

‘One in twelve, obviously.’

‘Don’t be feebleminded, Poe.’

Mathers hid a smile. Flynn openly laughed.

‘It’s not one in twelve?’ Poe said.

‘It’s one in thirty-six, Poe.’

‘It is?’

‘There are thirty-six possible outcomes when throwing two dice and only one of them is a double six.’

‘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.

‘Can I do 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 a twenty -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 a one with 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 he isn’t randomly selecting victims, Poe,’ Bradshaw said. ‘He’s randomly selecting locations .’