By Philip Gull

 

Rory Sutherland, Compound Probability and The Lottery

 

Rory Sutherland is a very smart man, although I think his maths is slightly off sometimes.

The following might be completely incorrect, and if that’s the case, I apologise.

His psychology is still fantastic.

 

He told us that less people would play Russian Roulette a thousand times to win 1 billion pounds than play it once to win 1 million pounds.

 

I think this is a false equivalence.

 

The odds of surviving Russian Roulette once are five sixths (5/6). The odds of surviving Russian Roulette a thousand times are five sixths to the power of a thousand, which equals 6.5 x 10 to the power of minus 80.

 

Or almost a billion billion billion billion billion billion billion billion billion to one.

 

Lets reframe the question:

 

(5/6) = 0.833

 

(5/6)^52 = 0.000763

 

If you play Russian Roulette 52 times to win a billion pounds, your expected value is almost exactly what it is if you play it once to win a million.

 

But, I think most of us would still rather play it once for the million.

 

In fact, I’m willing to wager even though a billion pounds is a thousand times your million winnings, I doubt many of us would go above three plays.

 

I saw an advert on the tube for a new National Lottery game, called Set For Life. If you win, you win £10,000 a month for 30 years.

 

I thought this was incredible. I’ve never been interested in playing the lottery, because the millions you win feel as distant as the odds of winning.

 

But instead of telling me the prize this week was £3.6million, the National Lottery, the prize was reframed in the language and form of every young person, who worries about the cost of their phone bill, their utilities, their rent, their monthly take-home.

 

The monthly lump.

 

And for the first time, I entered the Lottery. I didn’t win. I didn’t match a single number, in fact.

 

But for the first time, I thought I might win.