A story about how a winning streak can fool and lead to a mispricing of risk.

Rare as apples 

When I was a young lad I remember holding an apple and wondering, in one of my more philosophical moments, how remote the chances were that I should be holding this particular apple.  It was a French apple and I began imagining all the apples in all the orchards in France.  This single apple was picked, packed and journeyed across the Channel.  It was then passed to one of many distributors and sold to one of a thousand shops selling a million apples.  What are the chances, I pondered, of seeing that apple on a tree in the orchard and then it landing in my hand days later.  I didn’t really know the chances of course, I just knew they were remote.  I also understood that since I had an apple in my hand, one apple from one orchard was always going to make that identical journey just as I had imagined it. 

Can I make you an offer?

If I were to mark a cross on an apple in an orchard in France would you accept the following bet? If you buy an apple at random, picked on the same day as my marked apple, from your local store (without inspecting it first!) and it is not the marked apple I give you £1000.  But if it is the apple in question you live the rest of your life in poverty.  I suggest you would not need to consider for too long before accepting my bet.  You don’t need to calculate the odds as you are happy the chance that you will lose is so remote.  The odds are in your favour and in expected value terms, you’ve made a rational decision (as economists would say!).

You would no doubt think yourself unlucky to lose the bet.

Would you all accept my offer?

Now, let’s say I made that offer to everyone reading this.  Let’s suspend belief and say 1 million people read this blog and you all accept.  And why wouldn’t you, after all you make the decision and accept the risk independently of one another.   The chances are now very likely that one amongst you will lose the bet.  This doesn’t make the odds to you any different since you still stand the same chance of receiving the marked apple.  But it does concentrate the mind and perhaps you consider the risk less remote?

Lucky in life, until death

Take a million people and pair them into 500,000 pairs.  Each pair tosses a coin and calls heads or tails.  The winner goes through to play the game in round 2 of 250,000 pairs and so on.  There are 20 rounds (give or take) and one person will win.  Are they the best? Have they exhibited skill? No, they were the lucky apple.

But death comes to us all in the end

Now consider a million Betfair customers around the world betting against each other.  Each bet is a pair, one backing and one laying.  The above example suggests there will be one lucky apple that will win 20 bets in a row. Put yourself now in their shoes.  Provided they at least know one sport from another they will more likely than not think they have a gift.  After 3 or 4 wins in a row they may not.  “Beginners luck”, they may say.  After 10 bets they are feeling a bit more confident in their ’skill’.  After 15 bets they are getting cocky.  Worst still, after 20 bets they consider themselves invincible, take out a second mortgage and lump all on the 21st bet.  After all they’ve just won 20 bets in a row, surely they cannot be so unlucky to lose the 21st?  After all, what are the chances of that?