01 June 2008

Betting on his life

Man set to win on 'lifetime' bet, from the BBC.

In April 2007, a British man, Jon Matthews, was diagnosed with lung cancer and given nine months to live. He placed a bet with a bookmaker, William Hill, of 100 pounds at 50 to 1 odds. He's still alive, and he's collecting his 5000 pounds today.

Now, I have to think that the bookmaker offered odds which were much too long. Assuming that "nine months to live" actually means anything, I'd guess it's the median survival time. So this man had a probability of something like 1/2 of living the nine months. The bookmaker should have been offering 1 to 1 odds. (Actually, not even that, because they've got to make a profit!)

And even if it's the mean survival time that's meant, I doubt the distribution is sufficiently skewed to make a real difference. I suspect that "you've got X months to live" is just something that doctors say to patients informally, though, and it may not be sufficiently well-defined to quibble about this.

Of course, as the article points out, bets like this don't get made often. If they did, the bookies would pretty quickly figure out that they shouldn't be offering such large payoffs.


Anonymous said...

This probably has something to do with chemo therapy. I think intuitively the bookie would most likely realize that 50/1 odds would be too high unless the person making the bet looked really sick at the time. This is often the case with patients who are on chemo therapy and people think its the cancer making them look ill when its really the medicine.

There's an example about this is in Fooled by Randomness that, these distributions tend to be skewed and if you survive say 3 years then your chances of surviving significantly longer than that are good...

Also it seems this guy has survived 13 months already, rather than 9, so it seems like the bookies hedged their bet some.

Finally, is there any chance this guy is just a regular customer and the bookie, who's taken much more from this guy over his life time, was just being nice to someone he thinks is dying.

Anonymous said...

According to metro (a free London paper) the bet was on the man surviving for 25 months, so perhaps 50-1 were pretty reasonable odds (for the bookmaker) after all.

Ben Allen said...

The nice thing about making a bet like this is, well, what have you got to lose?

Emily said...

You don't have to go to a bookie to make bets on life. You can just go to any insurance provider and buy a life insurance policy. You would just be making the inverse bet. That is your betting that you will die before you avearge life expectancy.

I wonder if there is a way to short a life insurance transaction ? Maybe even create a derivative on the original life insurance contract ?

For example let's take a celebrity or politican. For example, John McCain, presumably he has a certain expected life according to census life tables. We could then create a contract with a pay-off if he lived longer than expected. We could then let market participants take long or short postitions in the contract. Based on demand and supply the derivative contract would be price. I wonder how different a life span a market contract such as the one I am describing would imply then the average life expectancy according to census data.