Add new comment

Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.
Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!
How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?
Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.
PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.
One weak point seems to me to be formula for the expected amount.
I'd have thought it would be less appropriate for a one off choice between hanging on to an envelope and swapping it for just one other containing either half or double, and more for one in which there were a long series of such envelopes each either doubling or halving the previous, making it more and more likely as you go on that if you were to stop you'd be 25% ahead of that first envelope. If you started by swapping £10 for the chance of getting £5 or £20, and then getting and swapping back £5 for £10 or £2.50; or instead getting and swapping back £20 for £10 or £40, the formula suggests to me the longer you go on doing this the more likely you are to have 5x£10/4 = £12.50 when you arbitrarily stop.
Swapping under these conditions becomes more reasonable as you go on, given you never know what's in the envelope you have now and thus able to retire earlier with bigger winnings. But at least you never come out an overall loser from when you started, at worst just ahead by a ridiculously small fraction of a penny.