The key is what d someone with average luck win?
On the topic of winning prizes, Martin went on to examine the likelihood of success: Imagine everyone with the same number of bonds lined up in order of winnings - the one in the middle defines average luck (in maths, the median average). It s complex to work out exactly, so years ago I had our Premium Bond Probability Calc built. It uses multinomial probability to show your odds (I had to get a post-doctoral cosmology statistician to design it). It shows, currently with AVERAGE LUCK OVER A YEAR:
£100 of bonds wins NOWT - in fact, 29 in 30 with £100 win nothing.