Saturday, July 30, 2005

it could be you

Mr Philips by John Lanchester is a novel about a day in the life of a middle-aged accountant. Not a common premise for a book, admittedly, but it's a wonderful read nonetheless.

This section I particularly loved:

It came up one morning a few months ago, when they were all sitting around before the monthly progress meeting of the Accounts Department.

'Hang on a minute,' said Abbot, the youngest of them. 'The odds against winning the Lottery are fourteen million to one, right?'

'The odds against winning the jackpot,' said Monroe in his Aberdonian voice. 'Six divided by forty nine times five divided by forty eight times four divided by forty seven times three divided by forty six times two divided by forty five times one divided by forty four, which is 0.00000007151 or one in 13,983,816, usually referred to as one in fourteen million. So if the prize is greater than fourteen million quid it becomes a rational bet as supposed to just a stupidity tax.'

'Assuming all the money goes to only one winner, which you can’t assume,' said somebody else.

'Fourteen million to one that you’ll get all six numbers right,' said Monroe. 'There is however another risk here which affects the likelihood of winning. Does anybody want to tell me what it is?'

Mr Phillips, who knew the answer because he had heard Monroe on the subject before, kept silent so as not to spoil his fun.

'No takers. All right. The additional factor that needs to be taken into consideration is the chance of being dead by the time the Lottery results arrive — since, obviously, the chance of dying in any given week is much, much higher than that of winning the Lottery.'

There was a pause, the sound of six accountants sizing up a mathematical problem in their heads.

'What’s the death rate? How many people die every week?' said Austen.

'According to the relevant Government agencies,' said Monroe, 'the population of England at the time of the last estimate was 49,300,000. The previous year, deaths totalled 526,650. The death rate per week was therefore 10,128, rounded up to the nearest cadaver. Using these data we find that for an Englishman the chance of dying in any given week is therefore 0.0002054, or one in 4,880.'

'So your chance of winning the Lottery,' said Abbot at his calculator, 'is, er, 2,873 times worse than your chance of being dead by the time of the National Lottery draw.'

'But we’re assuming you buy the ticket at the start of the week,' Monroe went on. 'In other words, if you buy your ticket at the start of the week and hold it until the draw, your chance of being dead by the time of the result is much better than your chance of winning. But most people don’t buy the ticket on Sunday, they buy it in the middle of the week before the draw, and so their odds are better. If you buy your ticket at four o’clock on Friday afternoon your chance of not being dead before the result must be significantly improved.'

They were already doing the sums.

'Assuming the deaths are spread evenly over the calendar – '

— which Mr Phillips didn’t feel you could assume. Surely more people died in winter and at weekends, of drinking and fighting and the stress of being cooped up with their families and so on? But he didn’t say anything -

'That means that the chance of dying, for a random member of the population, is 0.0107 per year, or 0.0000293 per day, or 0.00000122 per hour, or 0.0000000203 per minute. In other words each of us has a 1 in 49,200,000 chance of dying in any given minute. So in order for the probability of winning the jackpot to be greater than the chance of being dead by the time of the draw one would have to bet no earlier than,' Monroe tapped some figures into his Psion Organiser, 'three and a half minutes before the draw.'

'Christ,' said someone.

'But that’s averaging the risk out,' Monroe continued. 'Obviously a nineteen-year-old girl who doesn’t drink, doesn’t smoke, has no familial history of anything and whose great-grandmother is still alive at the age of 102 is more likely not to be dead than a sixty-year-old chain-smoking alcoholic with a Private Pilot’s license. We’d need to get hold of some proper actuarial tables,' he concluded, giving the word 'proper' a discreet but very Scottish emphasis. At that point Mr Mill the useless departmental head came into the room, the conversation petered out and the meeting began instead.

Monroe, however, did not forget. About two weeks later a notice appeared on the board in the company canteen saying ATTENTION LOTTERY GAMBLERS, and below giving a break-down, along the lines discussed, of the averaged-out risk of being dead compared to the chance of winning the Lottery. The table gave a time after which the chances of winning the Lottery were better than those of being dead by the end of the week.

Under 16

1 hour 10 minutes
1 hour 8 minutes
51 minutes
28 minutes
11 minutes
4 minutes
1 minute
24 seconds


Anonymous said...

So, it would be a 'rational bet' for me to buy a ticket, on weeks where the jackpot exceeds £14 million, no more than 51 minutes before the draw.
Not bad, but this doesn't take into account the fact (we assume) that when the jackpot is higher more people will buy tickets. We really need some information on average ticket sales relative to size of jackpot.

merrick said...

It does mention the chance of other people sharing the jackpot; 'Assuming all the money goes to only one winner, which you can’t assume,' said somebody else.

But you are right, if there are more people buying tickets then you have a higher chance of sharing the jackpot.

My favourite lottery statistic comes form the week of the launch. One journalist asked Ladbrokes for odds on an assortment of mad bets. The one that sticks in my mind is 1,000:1 on 'The Archbishop of Canterbury announcing the presence of the Antichrist among us within two years'.

So, 14,000 different £1 lottery tickets or a quid on the Archbishop of Canterbury saying the Antichrist is here by August 2007 is an even bet, then.

Anonymous said...

Statistically, nobody over the age of 34 should win, seeing as there's a ticket buying cut-off point about 30 min before the draw? Or am I being pedantic?

merrick said...

It's not that nobody over the age of 34 should win, it's that the odds on them being dead before the draw are greater than the odds of them winning.

Not pedantry, merely a slight misunderstanding of statistics.