From: Ronald Raygun 
Subject: Re: newbie,couple of premium bond questions
Newsgroups: uk.finance
Date: Mon, 11 Dec 2006 13:12:09 GMT

Mike Scott wrote:

> Mark Goodge wrote:
>> On Sun, 10 Dec 2006 17:47:42 GMT, Ronald Raygun typed:
>>> 
>>> The whole point of random distributions is that clustering happens, and
>>> the more no-win months you have in any sample of months, you expect the
>>> likelihood of getting more than one win in at least one of the other
>>> months in your sample, to increase.
>> 
>> You'd expect it, but of course you'd be entirely wrong to do so.
>> Previous results have absolutely no effect on future results, if the
>> draw really is random.
> 
> Absolutely.  The pragmatic would even reverse the expectation: "This die
> hasn't rolled a 6 in 1000 throws - it is therefore reasonable to assume
> it's biassed, and I will /lower/ my expectations of a 6 next throw."

Perhaps so, but in the case of PBs, we *know* (don't we?) that the we can
completely dismiss any hint of bias.

> Very different from "...hasn't rolled a 6 in 1000 throws, so I expect a
> 6 almost certainly next time to make up the average." The latter idea is
> clearly arrant rubbish.

The "almost certainly" part of that is indeed rubbish, but the rest is not
quite rubbish, because averages *do* tend to "make themselves up" in the
long run.  If the payout rate is such as to make you expect 1 win per month
or 12 per year, you cannot be confident of getting 1 win in any given month,
or even of getting 12 in any given year, but you can be *more* confident of
getting 12 in a year than 1 a month, and even more confident of getting 120
wins in 10 years.

Because clustering happens, then no matter how long you've gone without
a win, when you do eventually get a win, there's a good chance that it's
part of a cluster and that its neighbourhood will give you an above average
win rate.  Essentially you can think of shorter-term averages as fluctuating
more strongly than longer-term ones, and wins are more likely to be found
in sub-periods where the short-term average lies above the long-term value
than below it.  Hence your confidence of getting 12 wins during 2007 should
not be unduly shattered (yet) simply because you've had no wins at all in
the first three months.  You're not allowed to get nervous until a further
3 months have elapsed.