Premium Bond Calculator Discussion

talexuser

It only depends on how much you spend in that in each the chances increase the more you spend, but it does not affect the differences between the 2, each £ has the same chance of winning in both.

The odds on winning the lottery are around 3000 times better for winning many millions rather then one million. The big difference is with the lottery your £ has gone forever, whereas with bonds you still have it.

double-slit

How to calculate the chances using the Premium Bonds Calculator.
For example I have £22,500 and the probability of winning £1million
is 1 in 96,879.
How is this worked out.

MSCurious

double-slit wrote: »

How to calculate the chances using the Premium Bonds Calculator.
For example I have £22,500 and the probability of winning £1million
is 1 in 96,879.
How is this worked out.

Presumably, you want to look at the chance of winning £1mn or more within one year?

Compute first the probability of not making a £1mn win in a monthly drawing.
In the January 2015 drawing, two bonds won £1mn while in total 52,557,358,318 bonds won less than £1mn or nothing.

There were 52,557,358,320! / ( (52,557,358,320 - 22,500)! * 22,500!) possibilities to assign wins or no-wins (without replacement) to
your 22,500 bonds. "!" means factorial, for instance 4! = 1*2*3*4 = 24.
There were 52,557,358,318! / ( (52,557,358,318 - 22,500)! * 22,500!) possibilities to assign wins of less than £1mn or no-wins (without replacement) to
your 22,500 bonds.
Hence in January 2015, the probability that your 22,500 bonds did not get any of the two £1mn prizes was
52,557,358,318! / ( (52,557,358,318 - 22,500)! * 22,500!) * ( (52,557,358,320 - 22,500)! * 22,500!) / 52,557,358,320! =
52,557,335,820 * 52,557,335,819 / (52,557,358,320 * 52,557,358,319) = 0.9999991438

Assuming that the distribution of prizes and the total number of bonds remains the same in the next 12 months, then the chance to
make at least one £1mn win (with 22,500 bonds) is
1 - 0.9999991438^12 = 0.000010274 = 1/97,329

This is slightly less than the chance of 1/96,879 you mention. Presumably, this number is based on bonds data from December 2014 or earlier months?

double-slit

Thanks thanks, I am not good at the maths and appreciate your help.

worldtraveller

worldtraveller wrote: »

I've had a £1 premium bond since 1957 (AB5*****) and it's not won anything!

Still hasn't!

MSCurious

worldtraveller wrote: »

Still hasn't!

With £1 investment, your chance of winning at least £25 in the next ten years is about 0.46%.


By buying another 150 bonds, you would improve your chance of winning in the next ten years to slightly more than 50%.


With 998 premium bonds, your chance of winning in the coming ten years even would reach 99%.

Royalman007

"Dig Into Details" no longer seems to work. Clicking has no effect. Tried with IE, Chrome and Firefox.
As an aside, Martin's advice is great. But the MSE Website is truly the Website from Hell. It gives me more grief than all the other websites I use put together. Does Martin ever us it himself? Even his weekly email has to be viewed separately as all the links never work. I get gazillions of emails and only his has this problem!

Temrael

Hi MSE, will the Premium Bond tool need to be updated to account for the change in the odds from April? And will the "sweetspot" of £13k change, or will it remain at £13k but you'd just expect a smaller average return?

I'm just thinking that people buying bonds now will be first drawn in April, so it might be worth updating the tool sooner rather than later.

Edit: Ahh, I see from the new footnote in the Premium Bonds article that you guys need to wait for confirmation of the prize distribution.

eskbanker

Temrael wrote: »

Hi MSE, will the Premium Bond tool need to be updated to account for the change in the odds from April?

[...]

I'm just thinking that people buying bonds now will be first drawn in April, so it might be worth updating the tool sooner rather than later.

The changes apply from May, not April....

Temrael

Ahh yep, I misread it. It says the current rates apply "until the April 2017 draw" at NS&I which I took to mean April was when it changed.