NS&I calc

I_Am_Herenow

Hi, I read with interest the introduction to your premium bonds calculator (e.g. that it was made by a post-doc) - has the creator of the calculator written a paper or similar on how they arrived at the formulae now in use (or, indeed, what those formulae are)?

Cheers

xrjtg

I think that all the prize information is published by NS&I so that there's just a bit of simple maths needed to put together the calculator. Was there anything in particular you'd like to know?

EDIT: simple in a technical sense that allows the calculations to take 6 hours!

xrjtg

An example: suppose you have one hundred balls in an urn, 1 of which is blue, 10 of which are green and the rest of which are red. We now choose 5 balls at random by drawing one from the urn, putting it back, then repeating until we've seen 5 balls. What is the probability that we get at least one green ball? The probability that any 1 ball selected at random is not green is 9/10, so the probability that none of the 5 balls are green is (9/10)^5 = 0.59049. The rest of the probability goes to the case that we get at least one green ball, so there is a 1-0.59049 = 0.40951 probability that at least 1 of our 5 balls was green.

Now suppose that we win £5 for each green ball and £50 for each blue ball that we draw. If we want to know the probability that we will win at least £10, this is the same as the probability that we will get either 1 blue ball or 2 green balls among our 5, which can be calculated using basic probability theory.

Premium bonds are more complicated because (I think) the draws are made without replacement (one bond can't win twice), and there are so many more "balls" to consider. Naively, all the answers from the calculator could be calculated using methods like that outlined above, but this could take a very long time, so it's possible that the author has made some optimisations. The fact that they are a postdoctoral cosmologist is less relevant than the fact that they are likely to have experience of using computers to perform statistical calculations.