Premium Bonds introduce 2nd £1m Prize!

MJSW

lipidicman wrote:

The odds of winning a million are lower than the lottery aren't they? and you can win a lot more than a million on the lottery

It's difficult to do a direct comparision, because they are different types of gamble. With the lottery you gamble your entire stake, with Premium Bonds you effectively gamble with the interest you could have earned by putting the money in the bank. To attempt a like for like comparision, you would need to try and look at it as per your second paragraph, ie buying the lottery tickets using the interest.

With £100, you could earn say £5 interest per year (ignoring tax), which would get buy you 5 lottery tickets per year. The probability of a single ticket winning the jackpot are just under one in 14 million. So with 5 tickets over a year, the odds of a jackpot would be around one in 2.8 million. With £100 in Premium Bonds, you would get 100 entries each month for 12 months. There appear to be about 27 billion Premium Bonds in issue at the moment, making the chance of a £100 holder winning one of the 2 x £1 million prizes about one in 135 million per month, or one in 11.25 million over a year.

So if I've done my sums right, the chances of winning the jackpot by depositing £100 and using the interest are about 4 times better on the lottery than on Premium Bonds. Then there is also the size of the prize to consider. The Premium Bond jackpot is fixed at the £1m, with the lottery it depends how many people you have to share the jackpot with and also on the size of the prize fund that week. According to http://plus.maths.org/issue29/features/haigh/ ,the largest jackpot ever won with all 6 correct numbrs was £22.6m and the smallest was £122,500. The mean jackpot is apparently around £2m.

The reason for this seems to be that the lottery allocates a much higher proportion of the prize fund to the jackpot than Premium Bonds. With Premium Bonds, the amount allocated to the £1m prizes is less than 3% of the total prize fund. With the lottery it is around 52% of the total prize fund.

How about this - put the money in a high interest account (eg ISA/no-tax-paying-spouse, whatever) and use the interest to buy a lottery ticket (£52 for the year). Somebody needs to do some calculations and probability analysis, but this could be better?

This will be a no-brainer in favour of Premium Bonds. With Premium Bonds, all of the 3.25% 'interest' is returned as prizes. With the lottery, only 45% of the ticket sales are returned as prizes. So on average for each £1 ticket you buy, you only get back 45p.

Assume you put the money in an account earning 5%. If you 'invest' that interest in lottery tickets, on average you would get back only 2.25%, and that's assuming no tax on the interest. A basic rate taxpayer would receive only 4% net, and so would expect to get back 1.8% on average if they 'invested' it in lottery tickets. And a higher rate taxpayer would receive 3% net and so would only expect to get back only 1.35% on average.

deemy2004

the lottery odds would always be 1 in 14 million.
As it would be 5 X 14 million to one chance.

So the odds favour the premium bonds. With the premium bonds you get 100 X 12 chances.

With lottery you get just X5 chances per year.

Also your ignoring that 50 pence of every ticket goes in taxes and lottery fund so your at an even bigger disadvantage.

MJSW

deemy2004 wrote:

So the odds favour the premium bonds. With the premium bonds you get 100 X 12 chances.

I've taken all that into account! Whilst you get more chances with the Premium Bonds, the odds of hitting the jackpot on Premium Bonds are siginificantly worse than 14 million to one (approximately 13 billion to one each month per bond!). So even with 1200 chances each year, you are approximately 4 times more likely to win the jackpot on the lottery with just 5 tickets per year than you would be to win £1m with 100 entries per month on Premium Bonds.

However, if you are interested in the total expected return rather than just the odds of winning the jackpot, then Premium Bonds are far better.

Also your ignoring that 50 pence of every ticket goes in taxes and lottery fund so your at an even bigger disadvantage.

??? Have you actually read my post? The odds of getting 6 numbers are around 14 million to one, irrespective of how much goes in taxes and to the lottery fund. For the first part of my post (ie the odds of winning the jackpot), the amount going to the lottery fund and taxes is completely irrelevent.

If you are looking at the overall expected return then I have taken this into account: "With the lottery, only 45% of the ticket sales are returned as prizes. So on average for each £1 ticket you buy, you only get back 45p."

Please could you clarify exactly what you think I have ignored?

deemy2004

That with premium bonds your stake is £5 with the lottery it would be £2.50 hence you have more chance of winning with premium bonds... given that they have taken away more than half your stake in taxes etc...

MJSW

Exactly. And I have taken that into account! Which bit of

"This will be a no-brainer in favour of Premium Bonds. With Premium Bonds, all of the 3.25% 'interest' is returned as prizes. With the lottery, only 45% of the ticket sales are returned as prizes. So on average for each £1 ticket you buy, you only get back 45p."

did you not understand?

deemy2004

So we agree........................................ I think.......