newbie,couple of premium bond questions

As future results are in no way affected by past outcomes, there is also no guarantee of a "positive correction" on this in the future.

My faith in premium bonds is fast receeding.

All you need to do is sell 5k worth and I guarantee thet you will win at least 100GBP the following month. Try it if you don't believe me.

Reply to
Miss L. Toe
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No, this is wrong. Once you are behind you expect to stay behind (and once you are infront you expect to stay infront).

Your _expectation_ for the long term _future_ is that you will get about a 3% ROI. This is irrespective of what return you might have actually got in the past.

If this wasn't the case the everybody who was infront should sell to finish that "run" and then rebuy to start a new "run".

If the returns are still down for a second year I would either sell and rebuy or query it. It's not that unlikely that you will only get 150 return on 20K but two years on the trot would be - the most likely explanation is that some of the numbers are missing from the draw.

(IIRC 150GBP on 30K is about 1 in 200)

Tim.

Reply to
google

wrote

No, it is right.

wrote

That's right too.

You do still "... expect to get closer and closer to the average the longer you wait...", but that doesn't mean that you expect to cross, or even reach, the average.

wrote

If you do that, you'll *guarantee* not being in one month's draw!

Reply to
Tim

It is absolutely wrong.

The statement 'Accordingly you should get some above average results "any year now"' is why people irrationally continue to gamble. Whether you've had a run of good or bad luck, all you can expect in the future is a run of average luck.

Depends on how you measure closer.

If you are 100GBP ahead now, you expect to be 100GBP ahead in 5 years time.

If you expect 300GBP/year return on average and in year 1 you made

400GBP then by year 6 you expect to have made 400+150000.

So

100/400 = 25% ahead 100/1900 = 5% ahead

But you remain exactly the same amount ahead on average.

If you take a set of people who were all ahead 100GBP at the end of year 1. On average, at the end of year 6 they will have made an additional 1800 each. Some will have done better, some worse. But on average they will have got average returns.

Ditto for a group of people who were all behind 100GBP at the end of year 1.

There is no basis in fact whatsoever for the idea that your returns will approach the mean once they have diverged.

Tim.

Reply to
google

Actually the last sentance of the statement is correct(if you ignore the word accordingly), whilst on average all you can expect in the future is the average - you ought to get some better than average years in the future and some worse than average. So you ought to "get some above average results" (and some below).

However the first statement "in a way future results *are* affected by past outcomes" is false.

Reply to
Miss L. Toe

Ronald Raygun wrote: ...

That's wrong. If a die (unbiased) is thrown a hundred times and fails to come up with a '6', the chance of a '6' on any future throw is just 1 in 6. History does not affect future probabilities; however, one might be led to question one's certainty that the system is unbiased, so in that die example, /in practice/ one would probably give odds of rather less (not more!!) than 1 in 6 of a '6' appearing on the next throw.

For my part, with 8000 PB units and failing to win anything for 6 months, that's something like a 1 in 10 chance iirc. Not quite up to expectations - I did run some simulations, which suggest the /most likely/ /annual/ return for that number is around 2.5% if I recall; although the curve is pretty broad. But having missed 6 months does not improve the outlook for the next six in any way at all.

Reply to
Mike Scott

"Miss L. Toe" wrote

Agreed.

"Miss L. Toe" wrote

No need to ignore it...

"Miss L. Toe" wrote

No, it is perfectly true. Imagine the average return is 3.5%pa, but you have averaged 2.5%pa so far. In that case, you expect your total average return in the future to

*increase* steadily up towards 3.5%pa (you don't expect it to cross, or even to quite reach it, but you expect to get closer & closer to 3.5% into the future).

Now, imagine that you have averaged 4.0%pa so far. In that case, you expect your total average return in the future to *decrease* steadily down towards 3.5%pa...

Notice that you expect it to *increase* in future if you've had *bad* luck in the past, and *decrease* in future if you've had *good* luck in the past? So - future results *are* affected by past outcomes!

Reply to
Tim

Indeed. Here's another way of thinking about it:

Suppose the winning probabilities and your holding are such that you should average twelve £50 prizes per year. (For the purpose of this exercise, let's assume £50 are the only kinds of prizes there are).

This leads you to expect, in any given year, to win 12 prizes, and indeed you expect to win one each month.

This doesn't mean you will in fact win exactly one each month *even if* in a particular year you do in fact turn out to win 12 prizes.

Those 12 prizes will be randomly distributed across the 12 months, and although you *expect* to win 6 in each half of the year, you might win

3 in the first half and 9 in the second.

Why should your expectation of winning 12 prizes in the year starting

3 months ago change, simply because you happen to have won no prizes in the first 3 months?

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.

Reply to
Ronald Raygun

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.

Mark

Reply to
Mark Goodge

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." 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.
Reply to
Mike Scott

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

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.
Reply to
Ronald Raygun

Ronald Raygun wrote: ...

No, no, no!!!!!!!

Probability is about /knowledge/. Let's go back to the die. Throw it, oh, 1200 times. /On average/ you expect 200 sixes. Throw it another

1200 times -- /an average/ you expect another 200 sixes, for a total of 400 out of 2400 throws.

Now, suppose the die is cast for the first 1200 times, and you look at the result and find that there are /no/ sixes present. The question now is what is the expected number for the full 2400 throws. This is a /different question/ from the last paragraph. There it was "expected number after 2400 throws"; now it is "expected number for 2400 throws /given the first 1200 have no sixes/". And the answers are different because your knowledge is different. In the second case, you expect a total of 200 sixes, ie 1 in 12 overall.

Think of a gamble. Someone has thrown a die, say, a hundred times -- and there's been no six. By your way of thinking, a six would be virtually certain on the next throw. Does that seem reasonable? What odds would you accept?

Look at it another way. You have to walk to the shops. The weather forecaster says there's a 10% chance of rain, so you decide to risk not taking the brolly. But if instead you look out of the window and see the storm raging outside, your knowledge makes his 10% figure meaningless for your situation: you take the brolly :-)

In the premium bond case, if you have some lean months, well, that's /certain/ after the fact, and future prize distributions aren't affected one jot.

Reply to
Mike Scott

snipped-for-privacy@woodall.me.uk wrote: snip

No - no numbers are missing from the draw, it doesn't work that way. There aren't any numbers in the draw in the first place. Numbers are generated first and only then checked to see if a bond exists that matches them. The only effect of selling and rebuing is that you are out of the running for 1 or more months depending on your timing.

Reply to
dtren

The point, as someone else has alluded to in another subthread where a die is thrown 1000 times and there are no sixes, (about 1 in 10^80) is that there comes a point where your suspicions are that the game isn't fair rather than a run of bad luck.

My grandmother won nothing on 10k of premium bonds for about 15 months from purchase. (this is not that unlikely, about 1 in 500). My uncle, when he found out this had happened, queried it with a letter something along the lines of "never won anything since buying these bonds. How likely is that to happen?" and she won 300GBP in the three months after the letter came back saying something like "no it's perfectly fair and she's just been unlucky".

I am suspicious that there are circumstances where errors are made and purchases of bonds aren't being entered into the draw correctly. If

25k of a 30k holding is correctly entered and 5k missing then it will need a lot of years of unusually low returns before you would have any sort of confidence that there was a problem somewhere.

Someone else in this thread has suggested that if you have a large holding that isn't doing well then redeem 5k and you will guarantee a win.

A financial advisor I was talking to recently said that most of his clients with a 30k holding see better returns in the first two years of holding bonds than in subsequent years and many of them sell and rebuy after two years. (This is contrary to my grandmothers experience)

The plural of anecdote is not evidence. But I would be extremely surprised if there weren't occasional errors where peoples bonds weren't entered into the draws or someone redeems their bonds and rather than just their 5k being removed, both their 5k and another 5k gets removed.

There is almost no way to test for this. If I've done my sums correctly, the probability of no win in 12 months for a 30k holding is about one in three million. Finding just one person who has been this unlucky in the last 12 months would, however, be a good pointer to there being something worth investigating. (could just be unclaimed prizes so my first assumption if someone claimed they had won nothing at all would be to get them to check for wins they didn't know about)

Tim.

Reply to
Tim Woodall

Yep, this is my experience too

You get told which one of your bonds won.

I can see that each of my 4 original sets of 5k has won something.

I also won 550 pounds from my 1400 of 'reinvestments'. Rather a good return.

Reply to
tim.....

In message , Tim Woodall writes

Yes, she had been just that. 'Random' means 'Random' which also means 'Unexpected Concentrations' etc., You can not expect a uniform distribution of wins. If a uniform distribution happened, then that would be evidence of a lack of randomness.

Hmm, but numbers arent entered into the draw all.

Hmm, but what about the external audit?

That poster is a fool.

the FA is also a fool, and also a liar. The £30k limit has not been in place long enough for him to make such an assertion. He may be confusing his evidence with the fact that more recently bought bonds win then those bought many years ago. This is purely because there are more recently bought bonds in issue than those issued ages ago.

Good.

Well there is also the factor of human error, but as I understand it the internal and external audit procedure should pick up such elementary errors, but I can only use the word 'should'.

The way to check for this is to ask them to check specific numbers. As the individual bond numbers of bonds in issue arent entered into the 'draw' as such, it will be possible for the draw results to be re-examined for those numbers which were drawn but which werent identified as being in existence at the time and not spotted as winners. There is an audit trail which I think is possibly more sophisticated than you envisage.

Reply to
John Boyle

Thanks....

Reply to
Miss L. Toe

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