| Premium bond prizes available | |||
| Prize | Value | Number | Probability |
|---|---|---|---|
| A | 1000000 | 2 | 3.37e-07 |
| B | 100000 | 71 | 1.20e-05 |
| C | 50000 | 142 | 2.39e-05 |
| D | 25000 | 255 | 4.30e-05 |
| E | 10000 | 712 | 1.20e-04 |
| F | 5000 | 1421 | 2.39e-04 |
| G | 1000 | 15021 | 2.53e-03 |
| H | 500 | 45063 | 7.59e-03 |
| I | 100 | 1535556 | 2.59e-01 |
| J | 50 | 1535556 | 2.59e-01 |
| K | 25 | 2803175 | 4.72e-01 |
| Totals | 1191675 | 5936974 | 1.00e+00 |
These are the number and value of available prizes each month. The probablility column is calculated from the number of each prize and total number. Other data is taken from the NS&I website
From April 2026 the chances of winning each month are 1/23000 for each £1 bond. The prizes available and the associated probabilities of winning are shown in the left table.
Calculating the longterm winnings from premimum bonds is achieved in 2 steps.
A vector containing 22999 ‘zeros’ and a randomly placed single ‘one’ is generated. This is sampled m times, where m is the £ value of bonds held. The resulting vector of length m is summed to give the number of prizes won, n, for that month.
The number of prizes generated from step 1, n, is used in a new sampling function where prizes shown in the lefthand table are sampled n times taking into account their associated probabilities.
The output over a year is presented in the table in the middle panel showing the number and values of prizes won, along with a summary for the year.
The right panel is for simulating winnings over a chosen number of years. The histogram displays an approximately normal distribution of winnings on a log scale. The log scale helps visualise the wide range of possible winnings and a log scale is reasonable when considering the progression of prizes available (see also here). However, when exploring lower holdings it looks like the pattern of returns more likely follows a poisson distribution.
The simulated prizes over a year are shown here, including individual prizes each month and a summary for the year. The yield column is the % return on investment scaled to a full year.
The plot shows the distribution of wins each year for the specified number of years. The pink line indicates the % return which should be around 3.3% per year according to the NS&I website. Payments are tax-free, which may be important for higher rate tax payers.