Premium Bond Winner ?

JGal

Over a 5 year period with the full amount of bonds I have 'won' amounts other than £25 only 4 times. All of these were for £100, and they have occured in pairs, 2 x £100 in March 2017 and 2 x £100 in Feb 2018. I find this coincidental. Assuming I did get 4 x £100 wins over a 60 month period, what are the odds of them being distributed liked this? Much less than those of winning a big prize I imagine.

AnotherJoe

I didn't win anything this month

londoninvestor

JGal wrote: »

Assuming I did get 4 x £100 wins over a 60 month period, what are the odds of them being distributed liked this? Much less than those of winning a big prize I imagine.

So assuming 4 wins in 60 months, I make the probability of 2 in one month and 2 in a different month to be about 0.082%, which is just under 1 in 1200.

(To be "exact" it's 59/60 * 1/60 * 1/60 * 3. That assumes though that the chance of a bond winning £100 was the same in all 60 months, which won't be quite true as they change the distribution of prizes over time.)

Reasonably unlikely, but not at the winning-a-million level of unlikeliness

Ifts

Same as the last three months for me, 2 x £25 on 50K

[Deleted User]

Another month, another 25 quid.

I've added 12-months rolling Income and Yield to by spreadsheet.


Image here (delete space, I am new and I can't post links)
https:// imgur.com/a/6nl92YG


Text version:

11/2018    50        12 months rolling income:    575    12 months rolling yield:        1.15%
12/2018    50        12 months rolling income:    625    12 months rolling yield:        1.25%
01/2019    50        12 months rolling income:    600    12 months rolling yield:        1.20%
02/2019    25        12 months rolling income:    525    12 months rolling yield:        1.05%

11/2017    £50,000 – full depo
12/2017    0
01/2018    75
02/2018    100
03/2018    125
04/2018    75
05/2018    0
06/2018    25
07/2018    50
08/2018    25
09/2018    0
10/2018    50
11/2018    50
12/2018    50
01/2019    50
02/2019    25

JGal

londoninvestor wrote: »

So assuming 4 wins in 60 months, I make the probability of 2 in one month and 2 in a different month to be about 0.082%, which is just under 1 in 1200.

(To be "exact" it's 59/60 * 1/60 * 1/60 * 3. That assumes though that the chance of a bond winning £100 was the same in all 60 months, which won't be quite true as they change the distribution of prizes over time.)

Reasonably unlikely, but not at the winning-a-million level of unlikeliness

My first thought was 4/60 x 4/60 + 4/60 x 4/60 = 1/112.5 but my A level maths days are many years ago.

londoninvestor

JGal wrote: »

My first thought was 4/60 x 4/60 + 4/60 x 4/60 = 1/112.5 but my A level maths days are many years ago.

I am also a bit rusty and had to do a little simulation in Excel to convince myself

1) Pick two distinct months of the 60 and call them A and B (but the order doesn't matter). There are 60 * 59/2 ways of doing this.

2) Now we're interested in cases where two of the prizes happen in month A and two in month B. For each choice of A and B, there are 6 ways this can happen (AABB, ABBA, ABAB, BBAA, BAAB, BABA). The probability of each way is 1/60 * 1/60 * 1/60 * 1/60.

So overall we get 60 * 59/2 * 6 * 1/60 * 1/60 * 1/60 * 1/60

= 3 * 59/60 * 1/60 * 1/60

~ 0.000819

WaywardDriver

londoninvestor wrote: »

I am also a bit rusty and had to do a little simulation in Excel to convince myself

1) Pick two distinct months of the 60 and call them A and B (but the order doesn't matter). There are 60 * 59/2 ways of doing this.

2) Now we're interested in cases where two of the prizes happen in month A and two in month B. For each choice of A and B, there are 6 ways this can happen (AABB, ABBA, ABAB, BBAA, BAAB, BABA). The probability of each way is 1/60 * 1/60 * 1/60 * 1/60.

So overall we get 60 * 59/2 * 6 * 1/60 * 1/60 * 1/60 * 1/60

= 3 * 59/60 * 1/60 * 1/60

~ 0.000819

Agree with your calculation although arrived at in different way:
Prob(1st win in any month) * Prob(2nd in same month) * Prob(3rd in different month) * Prob(4th in same as 3rd)
= 1 * 1/60 * 59/60 * 1/60
This corresponds to your AABB with other possibilities ABAB and ABBA, so multiply above by 3.

Tabatha_Kitten

Nothing since July last year on £21k. I must be really unlucky

tony4563

Second blank month on 50k

Bit disheartening to be honest, although you should really treat it as a bit of fun

Considering moving the lot to a fixed rate account paying 2.1%

Sure your moneys tied for a year but at least you are guaranteed something every month