The Spoilers

June, the daughter of Sir Robert Hellier, a wealthy movie mogul, dies of an overdose of heroin dissolved in a solution of methylamphetamine. So Sir Hellier decides to finance a no-cost-spared war against the drug mafia. He hires Dr Nicholas Warren, the doctor who was actually the doctor who kept prescribing heroin to June (a fact Hellier knew) for the job. Warren then gets rag-tag team in place: Major Andrew Tozier, a mercenary soldier; John Follet, a casino operator; Daniel Parker, a Navy Man; Ben Bryan, a psychologist working in the field of drug addiction and Michale Abbot, a reporter. This unlikely team then goes to the Middle East and ends up destroying a thousand kilos of heroin. Ho hum.

Along the way, John Follet, who has learnt quite a bit of the mathematics of probability in his line of work, gives a few practical lessons to his companions. In a tricky situation where the team is cornered and has a choice of trying to escape by road or by a sea route, Follet uses a randomization decision-making matrix to choose the escape path to take.

A few of the mathematical references:

‘Are you crazy?’ demanded Follet. ‘It just doesn’t work that way. In any game of equal chances a lucky rich man will beat hell out of a lucky poor man any time. Bernoulli figured that out back in 1713 — it’s called the St Petersburg paradox.’ He gestured towards a roulette table. That wheel carries a nut of fifty thousand pounds — but how much do you think the customers are worth? We’re in the position of playing a game of equal chances against the public — which can be regarded as infinitely rich. In the long run we get trimmed but good.’ ‘I didn’t know you were a mathematician,’ said Warren. ‘Any guy in this racket who doesn’t understand mathematics goes broke fast,’ said Follet. ‘And it’s about time your British legislators employed a few mathematicians.’ He scowled.

[…]

“It’s one hundred per cent honest,’ said Follet stoutly. ‘As long as you have the percentages going for you then you’re all right and cheating isn’t necessary, I’ll show you what I mean because right now I feel lucky. On this road we’ve been meeting about twenty cars an hour — I’ll give you even money that in the next hour two of those cars will have the same last two digits in the registration number. Just a game to pass the time.’ Warren thought it out. There were a hundred possible numbers — 00 to 99. If Follet restricted it to twenty cars then it seemed that the odds were on Warren’s side. He said carefully, ‘For the first twenty cars you’re on.’ ”

[…]

“The name for it is a sucker bet. You didn’t have much of a chance.’ ‘I don’t see it,’ said Warren. Follet laughed. That’s because you’re a mathematical ignoramus. You figured that because there were a hundred possibles and only twenty chances that the odds were four to one in your favour, and that I was a chump for offering evens. You were the chump because the odds were actually in my favour — no less than seven to one. It pays to understand mathematics.’ Warren thought it over. ‘I still don’t see it.’ ‘Look at it this way. If I’d bet that a specific number would come up twice in the first twenty then I would have been a chump. But I didn’t. I said any two numbers in the first twenty would match.’ Warren frowned. He still did not get the point, but he had always been weak in mathematics. Follet said, ‘A proposition can be defined as a bet which looks good to ‘the sucker but which is actually in favour of the smart guy who offers it. You dig into the holes and corners of mathematics — especially probability theory — and you’ll find dozens of propositions which the suckers fall for every time.’

[…]

‘So we can stick to the coast or we can head out to sea. She has the same choice. What do you want to do?’

‘I’d sooner stick to the coast,’ said Tozier. ‘If she caught us at sea where it wouldn’t matter how many guns she popped off I wouldn’t give much for our chances, especially if that yacht is loaded to the gunwales with her cut-throats.’

‘Haven’t you thought that she’ll think that you’ll think that and automatically come along the coast and catch us anyway? Ill bet she can see us right now.’

‘How the hell do I know what she’ll think?’ burst out Tozier. ‘Or what any other woman will think?’

‘There’s a way around that,’ said Follet. ‘Here, take the wheel.’ He stepped on one side and produced a pen and a notebook. ‘Now, if we go along the coast and she searches out to sea our survival is one hundred per cent — right?’

‘Until she catches on,’ said Warren.

‘We could get clear away,’ argued Follet. ‘And the same applies to the situation vice versa — we go to sea and she goes along the coast. Andy, what chance of survival would you give us if she caught us at sea?’

‘Not much,’ said Tozier. ‘Say, twenty-five per cent.’

Follet noted it down. ‘And if she caught us on the coast?’

‘That’s a bit better — she couldn’t be as noisy. I think we’d have a good chance of coming out - say, seventy-five per cent.’

Follet started to scribble rapidly and Warren, looking over his shoulder saw that he was apparently working out a mathematical formula. Follet finished his calculation, and said, ‘What we do is this. We put four pieces of paper in a hat — one marked. If we pick the marked paper we go to sea; if not, we stick to the coast.’

‘Are you crazy?’ demanded Tozier. ‘Would you leave something like this to chance?’

‘I’m crazy like a fox,’ said Follet. ‘How much have I won from you at the coin-matching game?’

‘Nearly a thousand quid — but what’s that got to do with it?’

Follet pulled a handful of loose change from his pocket and thrust it under Tozier’s nose. ‘This. There are eight coins here — three of them dated 1960. When I matched coins with you I pulled one of these at random from my pocket; if it was dated 1960 I called heads -if not, I called tails. That was enough to give me my percentage — my edge; and there wasn’t a damned thing you could do about it.’

He turned to Warren. ‘It’s from game theory — a mathematical way of figuring out the best chances in those tricky situations when it’s a case of if I do that you’ll know I’ll do it but I do the other thing because I know the way you’re thinking and so it goes on chasing its goddamn tail. It even gives the overall chances — in this case a little over eighty-one per cent.’