Different Viewpoint on Premium Bonds

benbay001

Doesn't it mean that you would need to keep your £50k invested for 65000 years, before it becomes more probable that you would have won, than not?


To put that into perspective, mammoths died out 10000 years ago.

Malthusian

jrs101 wrote: »

Compared to the lottery it isnt.

That's like saying that an ant is massive compared to an amoeba, so I'm going to put a saddle on it and ride it to the moon.

And its safe too. And it typically pays out 1.4 or whatever it is.

On average, not typically.

Typically you get significantly less than 1.4%, because for Premium Bonds to pay out massively more than the average to a tiny number of people, the vast majority have to get less.

eskbanker

jrs101 wrote: »

Compared to the lottery it isnt.

The odds of winning the lottery jackpot are circa 1 in 45m, so buying 25,000 tickets with your £50K would mean much better odds of about 1 in 1,800, for a prize that's likely to be greater than £1m.

jrs101 wrote: »

And its safe too.

That's obviously the key difference, together with the fact that buying lottery tickets is a one-off rather than entering repeated draws. However, this all seems to be a different question - you were musing on the chances of winning £1m from PBs, not comparing projected returns with the lottery....

jrs101 wrote: »

And it typically pays out 1.4 or whatever it is.

No, the return (in terms of the arithmetic mean) is 1.4%, i.e. the prizes are 1.4% of the pot, but for typical returns it's much more meaningful to use the median, which is more like 1.2-1.26%, given the distorting effect of the prize split that's so heavily slanted to the small £25 ones.

Malthusian

benbay001 wrote: »

Doesn't it mean that you would need to keep your £50k invested for 65000 years, before it becomes more probable that you would have won, than not?

Not quite, as that's not how cumulative probability works. You only need to play for about 45,000 years before it becomes more improbable to win than lose. But your mammoth comparison is still valid.

And bear in mind that there's a coin flip's chance that you still won't have won a million pounds after 45,000 years.

And don't forget to deduct the opportunity cost of all the compound returns you could have made if you'd invested prudently over a 45,000 year timescale.

Premium Bond interest, like all lotteries, is a tax on being bad at maths. Even though you keep your stake, it's still playing the lottery with your interest, and I've heard it said that putting your money in a best-buy account and playing roulette with the interest is better value (but can't verify that).

That said, they are still worth considering for multi-millionaire higher rate taxpayers who have a gigantic pile of cash for which long-term investment isn't suitable.

Reaper

Malthusian wrote: »

Not quite, as that's not how cumulative probability works. You only need to play for about 45,000 years before it becomes more improbable to win than lose. But your mammoth comparison is still valid.

I know you understand this Mathusian but for others... the sad thing about probability is after 45,000 of playing without success your chances of winning are... no better than before.

To put in another way if you flip a coin 10 times and it comes up heads every time what are chances of it coming up heads next time (assuming it was chance and not a dodgy coin)? The answer is 50-50. Past events have no effect on the future probability.

However it is valid to consider FUTURE cumulative probability.

jrs101

How did you calculate the 45000 years?


I'm still reasonably thrilled with a 1 in 65000 chance.

oldfella

my approach is to buy a few, you then have an extremely small chance of winning a large amount. Buy a lot and you have slightly less than extremely small chance of a big win.

not good odds, save or invest the large amount on more predictable returns.

capital0ne

and don't forget all winnings are tax free

londoninvestor

Malthusian wrote: »

That said, they are still worth considering for multi-millionaire higher rate taxpayers who have a gigantic pile of cash for which long-term investment isn't suitable.

Agree, although the cash pile doesn't have to be gigantic - a top-rate-tax-paying millionaire with an equity allocation of 90% would still have a £100k allocation to low-risk assets, and PBs wouldn't be a bad choice for half of that.

Thrugelmir

Reaper wrote: »

I know you understand this Mathusian but for others... the sad thing about probability is after 45,000 of playing without success your chances of winning are... no better than before.

What if you were allowed to reinvest your winnings?

After all compunding is the secret to investing. Capital growth alone with income withdrawn is comparatively dismal.