I've a sibling who anecdotally reports similar for an investment of several tens of thousands (enough that prizes should broadly average out) -- number of prizes dropped after initial purchase several years ago. Been meaning to look at exact probabilities with him.
In the meantime, Ghoul, I took a quick look at your chances of going six weeks without a prize. From my write-up on page 1 of this thread, your 100k investment should win 23.5 x €50 prizes per year. Assume the chances are spread evenly throughout the year (which may not be exactly true, but it will suit a rough calculation).
How do we calculate the odds of zero wins for a period? Think of a coin toss with a fifty-fifty (i.e. 1/2) chance of winning. If we consider your chances of winning at least once in a sequence of several tosses, it gets messy because you could win on the first toss, or the second, or both, or basically any combination of the tosses. But if we instead consider the odds of
not winning, that's a lot easier. To
not win, you have to
not win on the first toss
and not on the second
and not on the third etc. Combining odds this way (event one
and event two
and ...) is simply multiplicative, and since the odds of losing each toss are the same as the odds of winning, it's:
The prize bonds situation is very similar, but we'll do it in decimals instead of fractions. As mentioned, you'll win 23.5 prizes on average each year. That's 23.5/52 = 0.452 per week. That's your chance of winning each week and, since you must either win or not win, your chance of
not winning each week is (1 - 0.452) = 0.548. So your chances of not winning for
n weeks is simply 0.548 multiplied by itself
n times, or
.
So for the six week run you've just had, it's
approx. That means your odds were a bit better than one in forty of not winning. Not enough to support a conspiracy theory ...
yet ... it's the sort of thing you'd expect to see once a year perhaps. Also bear in mind your average number of €50 prizes still currently works out at 18 in a year, which is on the low side but well within the probability distribution (see the graph on page 1). But I'd be keeping an eye on it -- another two or three weeks without a win (odds of one or two hundred to one) and there would start being a serious whiff of rat. CRC and Rehab would be in the ha'penny place compared to a Prize Bonds scandal.
EDIT: I see that the prize fund went down by about 10% for 2014, so you are now only expecting about 21 prizes per year, which puts you even more in the ball park -- your odds of six weeks in the doldrums are now only slightly worse than one in twenty.
EDIT2: The number of bonds held has been growing by double digit percentages for some years, which would go some way toward explaining why newer bonds win preferentially. Also there is a reasonably high turnover in bonds, with anecdotal evidence that many are bought throughout the year and encashed at year end, so the odds of winning early in the year may be slightly diminished compared to the back half of the year.
