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Premium Bonds may give you some small prizes, or some large ones, or even the top prize but, **equally**, you may get nothing and you don't get anything until they've been invested for a full month. Probability and chance are separate things. Statistical Probability says you may expect to get X% in return but chance says you could get something or nothing at all.

Originally posted by **Terry Towelling**
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Sorry to be pedantic, but it almost certainly is not equally likely...With any given holding over any given time frame the probability of getting a none, a small or a large prize is certainly not equal. On a large holding (say £50k), it's highly likely that any given month you will win a small amount, very unlikely you will win nothing, and extremely unlikely you will win any big prizes.

Likewise, with a small holding, it's highly likely you will see no winnings, a small chance of a small prize, and again an extremely small chance of a big prize.

Also I'm not entirely sure what you are trying to say at the end...? Probability and chance are absolutely the same thing. They are just synonyms of each other...? Unless you are alluding to the difference between expected winnings and observed winnings?

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Another thing about averages is that it is sometimes rare for the average to ever occur. Often there is a considerable spread above and below but nothing on the average. Bonds will be no different and some people will get much more than expected and others will get less.

Originally posted by **Terry Towelling**
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Without boring you too much and getting too technical, but this is not entirely accurate either, particularly with respect to premium bonds. The mean is a useful summary statistics at denoting the central tendency of any data. That is, it represents the data point that occurs at the highest frequency.

The mean is only really suitable when the data follow a Gaussian distribution (otherwise known as 'normal' or 'the bell curve'). If the mean does not accurately represent the central tendency (i.e. the value that occurs most frequently), then other summary statistics should be used, such as the median. This is often seen with things like salaries (and indeed the number of legs

), as this tends to be quite highly positively skewed, with large dispersion due to high value outliers. The mean will tend to overestimate the central tendency point, and the median can be more meaningful.

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Perhaps it should also say that such expectation is most likely to be observed in the longer term - i.e after several years (as you stated, Eskbanker). Is it perhaps a little improper of NS&I to suggest it is likely from the outset? (if it still does, that is).

Originally posted by **Terry Towelling**
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I agree, the quote of the rate could be misleading. It states 1.4% is the 'annual prize fund interest rate". Now I take this to mean that when the look at the entire holding over a year, and the entire amount paid out, it would equal a rate of 1.4%...? As you and Eskbanker say, the longer a person holds the bonds, the closer to this 1.4% rate they will be (in essence they have greater amounts of data, and the more data there is, the more likely it will represent the 'true' estimate). Of course knowing the spread of the data around this mean estimate would show you where you could lie in the extremes.

The MSE premium bond calculator I believe just looks at the expected return at any given month, given the amount of bonds you hold. There is a saying in statistics, most models are wrong, but some are useful...that is to say that while the 'model' from the MSE premium bond checker can often be wrong in trying to predict the exact amount you will win (and in very rare cases, can be extraordinarily wrong..) it is helpful it gauging what you are likely to expect to get with a certain holding at any given month, and whether other savings may be more suitable.

To go off on a bit of tangent, but the same applies in my field of medical statistics. We use large amounts of clinical data to model things, like risk of heart attack. We can look at things like age, cholesterol and diet to see what impact it has on the probability of having a heart attack. However, these models are generally pretty poor at predicting any one individuals risk of having a heart attack to a precise point in time..! Nevertheless, it's still useful in providing health advice and reducing the risk of heart attacks in the population in general.