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 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 for this question. It contains the popular approaches and algorithms used in the domain of fraud detection. The Genetic Algorithm is the most popular amongst them.

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 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 for this question. It contains the popular approaches and algorithms used in the domain of fraud detection. The Genetic Algorithm is the most popular amongst them.