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Saturday, 22 November 2014

Some investment advice

The best investment advice I can offer today with an expected payoff overnight of somewhere between 20% and 48% (depending on your valuation, I'll come to that in a minute) is .....  the National Lottery.

Now the National Lottery is widely regarded as a tax on stupid people, who are usually not that strong at add ups and take aways, so allow me to do the maths for you.

In tonight's draw there is a double rollover jackpot prize estimated to be £10 million, 20 £1 million prizes and 50 Lotto raffle winners of £20,000, whatever that means, in addition to the normal non-jackpot prizes.

Now we know that the last draw featured a £5,905,060 which wasn't won, so the current draw adds £4,094,940 to the jackpot fund.  Now the jackpot is 66.4% of the prize fund after deduction of the prize for 3 balls, which makes that prize pool equal to £6,167,078.  Now we know that the total prize money, excluding the raffle prizes, is 42.47% of total sales and that there is a 1 in 56.6559273965 chance of winning a £25 prize for guessing 3 correct balls, i.e. a payoff of 22.06% leaving a jackpot poo of 20.01% of total sales, so that the total expected sales for this draw will be £6,167,078/20.01% = £30,220,413.

So the UK population is going to spend  £30,220,413. What can they expect back? Well first of all there are the 20 £1 million prizes and the 50 £20,000 prizes giving a payoff of £21 million.

Then there is the the jackpot, which is nominally worth $10 million, but which is not certain to be won.  With 49!/43!/6! possible choices of balls there is a 1 in 13,983,816 chance that any individual player will pick the correct 6 balls, but with 30,220,413 in sales, or 15,110,206 players there is a (13,983,815 /13,983,816) ^15,110,206 or 33.94089% chance that nobody will win, so the expected jackpot is £6,605,911.

Then we can add the prized for getting 3 balls correct £6,667,531 (=15,110,206/56.6559273965*£25), and the other non-jackpot prizes (1-66.4%)* £30,220,413*20.41% or £2,072,138.

That makes a grand total of £36,345,580 against an "investment" of £30,220,413.

Not bad, but it gets better depending on your perception of the value of the good causes, which receive 28% of the total sales.  You may consider that these are just a blight on society, of benefit to a limited minority including the quangocrats who handle the funds, inwhich case they are worthless.  Alternatively you might consider that they represent good value for money and are a public asset to which you are happy to donate.
Take the latter view and you have an average expected payoff equal to 48% of your stake money.  Take the former and you still have a payoff of 20%.

Of course your chances of actually coming out ahead are fairly small (a little better than 1 in 56), but your expected winnings are such that, for once, the argument to buy a lottery ticket is overwhelming to any hyper-rational person.

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