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Sam's avatar

I could be wrong and not thinking this all the way through, but I don't think this is optimal. Your trees handle bigrams and co-occurrence, but isn't it the case that a particular guess could seem to be be suboptimal at one step, but turn out to have been optimal at a later step?

Imagine (for some word list) that guessing "s" first narrows the range as much as possible in step one (say, it narrows the range of possible words 50%). The three branches from that guess (green, yellow, or black) lead to three new optimal guesses for your second guess. Let's say that green "s" means the next optimal guess narrows the field by a further 10%, yellow "s" means the next guess narrows the field by 5%, and black "s" means the next guess narrows the field by 3%. Taken together, the two guesses narrow the field by 60% ("s" was green), 55% ("s" was yellow), and 53% ("s" was black), which is an average of 56%.

Isn't it the case that, for that same word list, guessing "p" first might narrow the range by less (say only 49%), yet the three branches for the next guess might be better than they were for "s"? So "p" might seem like a worse guess at the moment, but it might be that the optimal guesses off each branch of that guess are better. Maybe the subsequent optimal guess after green "p" narrows by 9%, after yellow "p" by 8%, and after black "p" by 7%. So the sequence of guesses taken together give you 58%, 57%, and 56%, for an average of 57% (higher than 56%).

I don't think you can actually optimize this with a single tree at each step. I think you would need to actually build the full tree of trees (not just the trees you have here, but the tree of these trees for each subsequent guess, all the way to solutions). Your approach, looking at only one of those subtrees at a time, assumes a constraint of that larger decision tree that I don't think it has.

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Madeline's avatar

This is bugged for 213. RAISE>COUNT>BLOOD narrows the scripts possibility array down to [PROXY, GROOM, PROOF]. Since the 2nd O in BLOOD is grey it should exclude GROOM and PROOF but instead guesses both of them first before PROXY.

In fact it guesses GROOM before PROOF even though PROOF would be the better guess between the two.

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