> I was thinking to calculate the average amount of money, say for the
> last ten transactions, and check how far is the next transaction
> amount from the average. Too much deviation would signal an anomaly.
> But this does not sound much, does it?

A typical outlier detection approach. This would work in most cases. But, as the problem statement deals with credit card fraud detection, the detection technique/algorithm/implementation should be more robust.

You might want to have a look at the [**Mahalanobis Distance**][1] metric for this type of outlier detection.

Coming to the algorithms for fraud detection, I would point out to the standards used in the industry (as I have no experience in this, but felt these resources would be useful to you).

Check [my answer][2] for this question. It contains the popular approaches and algorithms used in the domain of fraud detection. The [Genetic Algorithm][3] is the most popular amongst them.


  [1]: https://en.wikipedia.org/wiki/Mahalanobis_distance
  [2]: https://datascience.stackexchange.com/questions/8099/classifying-transactions-as-malicious/8100#8100
  [3]: https://en.wikipedia.org/wiki/Genetic_algorithm