I implemented Donald Knuth 1977 algorithm for Mastermind https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf
I was able to reproduce his results - 5 guess to win in the worst case and 4.476 on average.
And then I tried something different. I ran Knuth's algorithm repeatedly and shuffled the entire list of combinations randomly each time before starting. I was able to land on a strategy with 5 guesses to win in the worst case (like Knuth) but with 4.451 guesses to win on average. Better than Knuth.
Are there any previous work trying to outperform Knuth algorithm on average , while maintaining the worst case ? I could not find any indication of it on the web so far.
Thanks!
Alon
As far as I know, up till now there is no published work about this effect yet. I have made this observation some time ago, one can get better results by not always choosing the (canonically) first trial out of the "one-step-lookahead-set". I observed the different results by not starting with 1122 but with e.g. with 5544. One can also try to choose randomly and not use the canonically first. Yes, I agree with you, that is an interesting point - but a very, very special one.