How does it calculate the best target points . . . ?

The methods used by the Darts Assistant are described in “ Optimal Strategies for the Game of Darts ” by David Kohler, Journal of the Operational Research Society, Vol. 33, pages 871 to 884, 1982. (Incidentally, this paper has three minor typos )

(Before reading on, please read at least the first three pages (871 – 873) of this paper, including the first typo.)

Note the Darts Assistant uses the following simple formula to convert the DA Rating to the parameter σ of the bivariate normal distribution (the meaning of the parameter σ is given on page 872 of the paper) :

σ =  3.1 -  0.029  x  DA Rating

. . . and why should I trust it?

I don't think anybody who is familiar with dynamic programming and branch-and-bound techniques could question the theoretical basis of the paper. The paper won a special prize when it was published and has been used in case studies at university level. In the 30-odd years since it was published nobody has ever questioned its theoretical basis.

However, you could legitimately question whether there are any logic errors in the Darts Assistant’s program that could give rise to inaccurate results.

The Darts Assistant program was constructed in a very modular fashion, from the bottom up. Each function was meticulously checked and tested before being incorporated in higher-level functions. The program was written twice in different languages on different computers, separated by almost 30 years, and generated exactly the same results. So I am completely sure the results are accurate and correct.

However, you may not be willing to take my word for this so I can offer a couple of ways for you to partially validate the accuracy of the program. If you’re interested in doing this and have some familiarity with maths (especially probability concepts) and with a spreadsheet such as Excel, please click on either or both of the following links:

Validation # 1

Validation # 2