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• lowbrim
• By lowbrim 11th Sep 17, 8:03 PM
• 457Posts
• 291Thanks
lowbrim
Can anyone explain to me why when I win more than one premium bond prize in a month that invariably (around 30% of the time) the winning premium bonds are out of the same batch. I would have thought that if each bond had equal chance of winning that the chances of getting two bond winning in the same month out of the same batch would be almost impossible but it happens on very regular basis. Am I missing something ??
Page 1
• EachPenny
• 11th Sep 17, 8:17 PM
• 5,770 Posts
• 15,306 Thanks
EachPenny
It depends how big your batches are. If you invest thousands at a time then that series of numbers are more likely to have multiple wins than, say, a series of numbers from the reinvestment of a £25 win.

At one stage I invested £20,000 in one go. Unsurprisingly that series of numbers produces a large proportion of my wins, and in consequence features most commonly where I win more than one prize a month.

I think I've only ever once won two prizes from within a £25 series - I don't mean two prizes in one month, that's two prizes in the whole time I held the £25 bond.
"In the future, everyone will be rich for 15 minutes"
• lowbrim
• By lowbrim 11th Sep 17, 9:26 PM
• 457 Posts
• 291 Thanks
lowbrim
Yes, but even with a £20k batch on the assumption every premium bond has equal chance of winning I would have thought that the chances of 2 numbers coming up in that 20,000 in one month against the billions issued would have very high odds and this happens on a regular basis. Or is it not true that each number is entered individually?. The only explanation I can come up with is that the draw is in a number of stages and in the last stage batches that have got through the initial stages are them drawn individually. Is there a statistician in the forum who can explain how it is done and if it is done the way I suspect is the claim that every bond has equal chance of winning still strictly true?
• jimjames
• By jimjames 11th Sep 17, 9:54 PM
• 12,658 Posts
• 11,328 Thanks
jimjames
Yes, but even with a £20k batch on the assumption every premium bond has equal chance of winning I would have thought that the chances of 2 numbers coming up in that 20,000 in one month
Originally posted by lowbrim
If the rate is 1% then you'd expect that £20k to generate on average a prize of £200 each year. As most prizes are £25 then you'd expect to win on average 8 out of 12 months from that series. That doesn't sound very high odds, in fact quite the opposite.
Remember the saying: if it looks too good to be true it almost certainly is.
• Alter ego
• 11th Sep 17, 9:56 PM
• 2,407 Posts
• 2,384 Thanks
Alter ego
It's a problem I wouldn't mind having, my wins are neither multiple or regular.
Ignore me if you like, it's not the real me anyway.
• dividendhero
• 11th Sep 17, 10:03 PM
• 210 Posts
• 188 Thanks
dividendhero
Can anyone explain to me why when I win more than one premium bond prize in a month that invariably (around 30% of the time) the winning premium bonds are out of the same batch. I would have thought that if each bond had equal chance of winning that the chances of getting two bond winning in the same month out of the same batch would be almost impossible but it happens on very regular basis. Am I missing something ??
Originally posted by lowbrim
Maybe you're an agent for MI5

They used to pay spies in premium bond "wins" - no tax, no awkward questions..trebles all round
• redpete
• By redpete 11th Sep 17, 10:17 PM
• 4,261 Posts
• 3,786 Thanks
redpete
Invariably means always, every time. 30% is not invariably. Random events can look like coincidences, we are built to recognise patterns and sometimes see them, or assume them, when nothing more than random variation is happening.
loose does not rhyme with choose but lose does and is the word you meant to write.
• EachPenny
• 11th Sep 17, 11:19 PM
• 5,770 Posts
• 15,306 Thanks
EachPenny
Yes, but even with a £20k batch on the assumption every premium bond has equal chance of winning I would have thought that the chances of 2 numbers coming up in that 20,000 in one month against the billions issued would have very high odds and this happens on a regular basis. Or is it not true that each number is entered individually?. The only explanation I can come up with is that the draw is in a number of stages and in the last stage batches that have got through the initial stages are them drawn individually. Is there a statistician in the forum who can explain how it is done and if it is done the way I suspect is the claim that every bond has equal chance of winning still strictly true?
Originally posted by lowbrim
The details of how the draws are conducted are available online. But in broad terms, a long list of random numbers is generated. The first number on the list is checked to see if it corresponds to an eligible bond number. If it does, that bond is the first winner. If the number isn't an eligible bond the process moves on to the next random number in the list. That process repeats until there are no more prizes to be allocated.

It follows that the draw process has no idea of the ownership of a particular bond number, and is therefore 'blind' to whether a particular number is part of a batch of any particular size. In theory it is possible that two consecutive numbers will be drawn at some point within a monthly draw. But those consecutive numbers could belong to two different holdings, or to just one - it is random.

A way of visualising your question is to imagine each 'batch' of numbers you hold to be a paper target sized in proportion to the value of each batch. My £20k would be quite a big target, each of the £25 ones would be much smaller - about 1/800th the size. So if the £20k target was a piece of A4 paper, each £25 one would be approximately 9mm by 9mm. If you placed all of my 'targets' at the far end of a rifle range and fired a loosely fixed machine gun in the general direction of the targets you would probably find the following:
a) a lot of the bullets would be nowhere near my targets.
b) the 'A4' target is the one most likely to have a bullet hole in it.
c) most of the 9x9mm targets will be untouched.
d) if two bullets have hit a single target it is most likely to be the 'A4' one.
e) it is possible that a single 9x9mm target will have been hit by two bullets, but only if both bullets followed almost precisely the same path.

As the machine gun was not fixed firmly, and would move ever so slightly between shots due to recoil, the chances of two bullets following almost precisely the same path is very very remote.

They obviously don't use a machine gun to pick premium bond prizes (but it might make the draw more fun ) but it hopefully illustrates that even a random process can have results which, on first sight, look like they are 'fixed' or planned.

The bullets aren't magically drawn to the big target, it is just more likely (all else being equal) that the bigger target gets hit once, and if it is hit once that it gets hit for a second time.
"In the future, everyone will be rich for 15 minutes"
• AnotherJoe
• 11th Sep 17, 11:33 PM
• 9,856 Posts
• 11,020 Thanks
AnotherJoe
Can anyone explain to me why when I win more than one premium bond prize in a month that invariably (around 30% of the time) the winning premium bonds are out of the same batch. I would have thought that if each bond had equal chance of winning that the chances of getting two bond winning in the same month out of the same batch would be almost impossible but it happens on very regular basis. Am I missing something ??
Originally posted by lowbrim
yep, the human brain looks for patterns, not the absence of them. By pure chance some winning bonds will be in clusters and people are likely to notice those. Other people (most) who dont have clusters of winning numbers wont notice the absence of clusters.

Since its random, it would be remarkable amongst all of the millions of bond holders if some didnt have patterns, eg some people will be saying "hey all my numbers that win are odd (or even) or they are in order that i bought them, etc. There are any number of patterns you can look for. If you took a million people and had them spin a coin ten times and see what happened you'd have huge numbers saying its not random since they got all heads ... or all tails .... or alternate heads and tails ... or the first five heads and the second five tails, and so on. People find patterns. These are inevitable out a of a large group. Chance does not mean "evenly distributed"

And once you've spotted a "pattern" you'll keep looking for it and seeing it and discard those times it doesn't occur. Such as when "invariably" turns out to be less than 1 in 3, LOL.
• eskbanker
• 11th Sep 17, 11:46 PM
• 7,543 Posts
• 8,182 Thanks
eskbanker
Another way of looking at it is to model the probability of two prize-winning numbers being drawn from different batches - as pointed out further up, it obviously depends on batch sizes but this puts me in mind of the birthday problem, where in a random group of 23 people, it is statistically more likely than not that at least two will share a birthday (and if the group is 70 people it's 99.9% likely that two will share a birthday), despite this seeming counter-intuitive at first glance.
• lowbrim
• By lowbrim 12th Sep 17, 9:40 AM
• 457 Posts
• 291 Thanks
lowbrim
Just to clarify I do not have a 20k batch my biggest batch is 5000. of which I have a few and I still find it unusual that whenever I get more than one win they are invariably out of the same batch. As I said in the original post there may be a logical explanation but because it happens so frequently I do not believe the process is NOW along the lines outlined on the website and outlined by EachPenny. Happening 1 in 3 times on batches of 5000 bonds to me is a regular occurrence. I do have the maximum number of bonds so in my mind the chances of two (I have had 3) coming up out of the same batch of say 5000 in a holding of 50000 in a single month and having NO other winning bonds in that month to me sounds almost impossible given the amount of bonds issued.
• Malthusian
• 12th Sep 17, 9:56 AM
• 4,337 Posts
• 6,841 Thanks
Malthusian
Just to clarify I do not have a 20k batch my biggest batch is 5000. of which I have a few and I still find it unusual that whenever I get more than one win they are invariably out of the same batch.
Originally posted by lowbrim
Could you make your mind up over whether it is "invariably" (i.e. every single time, without variation) or "less than one third of the time"?

We can't really have a sensible discussion about statistics if the opening statement is "This coin is loaded, it comes up tails every single time, apart from the 50% of times it doesn't."
• coyrls
• By coyrls 12th Sep 17, 10:18 AM
• 999 Posts
• 1,052 Thanks
coyrls
Put it this way: having a winning bond picked from a batch doesn't reduce the chance of another winning bond being picked from the same batch.
• IanSt
• By IanSt 12th Sep 17, 11:58 AM
• 260 Posts
• 194 Thanks
IanSt
Just to clarify I do not have a 20k batch my biggest batch is 5000. of which I have a few and I still find it unusual that whenever I get more than one win they are invariably out of the same batch.
Originally posted by lowbrim
How many of these big batches do you have?

If you had just the one, then yes it would be unusual for such an occurrence to continue, but not mathematically impossible and random numbers can look to be very unusual. However if you've got 10, then it's a lot less unusual.

With ten batches that can happen a lot more than you may think. For instance it only needs 23 random people to be in a room for there to be a 50% chance that two of them have the same birthday.
Last edited by IanSt; 12-09-2017 at 12:07 PM.
• Zanderman
• 12th Sep 17, 2:07 PM
• 1,712 Posts
• 4,312 Thanks
Zanderman
Can anyone explain to me why when I win more than one premium bond prize in a month that invariably (around 30% of the time) the winning premium bonds are out of the same batch. I would have thought that if each bond had equal chance of winning that the chances of getting two bond winning in the same month out of the same batch would be almost impossible but it happens on very regular basis. Am I missing something ??
Originally posted by lowbrim

You have 20 bonds.

10 are individuals, not in a sequence.

The other 10 are a sequence of 10.

Each of those 20 has an equal chance of winning, as winning is random.

But, on average, 50% of the wins will be from one of those in the sequence.

So you will think the 'sequence' ones win more often than the individuals, as 50% of wins are from the sequence.

But it's an illusion. Every bond has an equal chance. You just associate the sequenced ones as somehow linked. They aren't.

If your sequence is a long sequence the illusion is greater.