# [Tutor] What's the best way to model an unfair coin?

Steven D'Aprano steve at pearwood.info
Sun Oct 24 18:22:40 CEST 2010

```Richard D. Moores wrote:

> Actually, I used the unfair coin model as the simplest example of the
> kind of thing I want to do -- which is to model the USD->Yen exchange
> rate. I want the next quote to vary in a controlled random way, by
> assigning probabilities to various possible changes in the rate. See
> <http://tutoree7.pastebin.com/mm7q47cR>. So I assign probability 1/40
> to a change of plus or minus .05; 3/40 to .04; 5/40 to .03, etc.

Another approach you might take is to model the change as a normal
distribution (bell curve probability) rather than uniform. This is
probably more realistic. It would make most sense to have it symmetrical
around zero, so you want a random number with a normal distribution, a
mean of zero, and a standard deviation yet to be determined.

To determine the standard deviation, use this rule of thumb: for a
normal (bell) curve, approximately 68% of events are plus or minus one
standard deviation from the mean; 95% are plus or minus two std
deviations; and 99.7% are plus or minus three std deviations.

So if you decide that 99.7% of the time the change in exchange rate
should be less than 1.00, for example, that corresponds to a std
deviation of 0.333.

You then generate a normally-distributed value using the random module,
round it to two decimal places to correspond to cents, and Bob's your uncle.

--
Steven
```