Double your bonus

Since Smartodds is connected to the world of gambling, the company has decided to handle the allocation of bonuses differently this year.

(Disclaimer: they haven’t really!)

Your manager will give you two closed envelopes, each containing a sum of money. You don’t know how much money is in either envelope, but you are told that the amount of money in one of the envelopes is exactly double the amount in the other. You have to choose one of the envelopes and open it – the money it contains will be your bonus.

But in typical Smartodds spirit, you have a chance to double your money. Having opened the envelope and seen what’s inside, you can either accept that bonus or swap it for the contents of the other (unopened) envelope, which you would then have to accept, without the option of switching back to the previous envelope. In this way you will receive either double the bonus you would have got by keeping the original envelope, or you’ll receive one half of it.

It’s a gamble – do you want to take it?

For example, suppose you choose an envelope and find that it contains £1000. You therefore know that the other envelope contains either £500 or £2000 . You can either keep the £1000 or swap it for the contents of the other envelope – but if you swap, you then have to keep what you find in the other envelope (£500 or £2000). Would you

a) definitely swap;

b) definitely not swap; or

c) either swap or not swap as it makes no difference?

After you’ve thought about it, please send me your (anonymous) answers by completing this survey. 

There are actually three questions in the survey: the first asks for your answer to the swapping question; the second is about your level of statistical training; and the third is about your position at Smartodds. The reason for the final two questions is that I’m interested in whether there’s a relationship between the possible answers to the first question and those of the other two. In a subsequent post I’ll discuss the swapping question itself and your answers to it. If, as well as completing the survey, you’d like to explain your choice, I’d be very happy to hear from you: mail me at

One other thing: you can probably find discussion on this problem by Googling. Please don’t, at least until you’ve answered the survey. In part because I’d like to see how your Google-free answers to the first question depend on the answers to the other two questions; and in part because not all of the discussion you might find on the topic is correct or helpful.


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