3 ms·
> From an information-theoretic perspective, the optimal initial guess is the one which is maximally informative about the target, given the resulting pattern.
by npinsker 5y ago
> From an information-theoretic perspective, the optimal initial guess is the one which is maximally informative about the target, given the resulting pattern.
This statement (which motivates the rest of the analysis) isn't correct, because it doesn't take into account the highly irregular search space of what you're actually allowed to guess. Sets of possible words can vary a lot in terms of how easily they can be further cut down: for example, if you're on hard mode and your set of possible words is [BILLY, DILLY, FILLY, HILLY, SILLY, WILLY], then you might be in trouble.
- canjobear 5y agoYeah, the analysis doesn't really work for hard mode as noted in a footnote.
- npinsker 5y agoI don't think it works for easy mode either. The overwhelming majority of 6-word sets can be distinguished in two guesses in easy mode (their EV is either 11/6 or 2), while this set has an EV that's around 3.
- canjobear 5y agoI think you're right. Although a first guess might reduce the set size a lot, it might lock you into a situation where all the possible second guesses are useless.
- pxx 5y agofor this specific set in easy mode doesn't (bawds, chefs) result in unique responses for all of them? so that's 2.5 guesses total? Where are you getting the EV for 6-word sets?
- npinsker 5y agoYou're right: the EV is 2.5 (my guess was pessimistic). For (almost all) 6-word sets, there's a single word you can use to delineate all six words, which gives an EV of 1.83 if that word is in the set and 2 if it isn't.