[svat]

IMO, never losing the game is the bare minimum for any reasonable cost function: never take > 6 guesses. Beyond that, you can have different optimization functions based on whether you're trying to minimize the worst-case depth of the decision tree (number of guesses) for each position, or the average depth, or some other reasonable function of the distribution over number of guesses.

Although you could have arbitrarily many cost functions, a fairly general class is the following: pick some nonnegative constants (w1, w2, w3, w4, w5, w6, w7), and for a certain strategy, define the cost as:

    w1*n1 + w2*n2 + w3*n3 + w4*n4 + w5*n5 + w6*n6 + w7*n7

where nk (for 1≤k≤6) is the number of hidden (solution) words for which the strategy takes n guesses, and n7 is the number of words for which the strategy loses the game. Then,

• Setting w7 infinite / very high is a way of encoding the condition that you not lose the game. (You can set it finite/small if you don't mind occasionally losing the game for some reason!)

• Setting w1 = 1, w2 = 2, …, w6 = 6 will simply minimize the average number of guesses,

• Having them grow exponentially, e.g. setting wk = c^(k-1), where c is some constant larger than 12972 (the number of acceptable guess words) will make sure that the minimal-cost strategy first minimizes the maximum number of guesses, then break ties by having the fewest words take that many guesses, and so on.

[tshaddox]

> IMO, never losing the game is the bare minimum for any reasonable cost function: never take > 6 guesses.

I wouldn’t think so. If I get 99.9% of rounds correct with 3 guesses (and fail to find a solution to 0.1% of the rounds), and you get 100% of rounds with 6 guesses, I’d say I’ve soundly defeated you 99.9% of the time.

[svat]

Right, that point of view makes sense if you imagine two players separately playing Wordle and comparing their results, and indeed that's what the OP may have been thinking. But as far as I know, Wordle is primarily a game for one player to play against the computer, where eventually getting to the word (or not) is the most prominent outcome (the only notion of "win" or "defeat" in the game itself), and solving it in fewer guesses is just a bonus. But sure, if you don't care about occasionally losing, you can just set an appropriate weight for w7 within the same family of cost functions.

[tshaddox]

Indeed, it’s essentially a single player game, but we’re talking about which bot a player would want to use which is inherently a notion of bots competing against each other.

[rob74]

If you look at the failed attempts in the article, you'll see it's not so easy to get 100% correct with 6 guesses. For example:

SLATE, CRONY, HOUND, BOUND, POUND, MOUND (correct: WOUND)

SLATE, SHARE, SHAME, SHAPE, SHAKE, SHADE (correct: SHAVE)

...so sometimes even if it gets 4 of 5 letters right on the second try, it still has too many options left. Of course in cases like this it could go "one step back" and try a word with (most of) the letters that are different between these words (HBPMW or MPKDV). So try different words until the number of options is narrowed down sufficiently.

[balls187]

> I’d say I’ve soundly defeated you 99.9% of the time.

Except it wouldn't be 99.9% of the time. Just the games were you guessed fewer than GP.

GP's solver would expect to guess the correct word 100% of the time in fewer than 6 guess, but not that it would always take 6 guesses.

[tshaddox]

I was saying if you hypothetically got every correct guess in exactly 6 tries. You would pass the suggested “bare minimum” while my 99.9% strategy doesn’t, yet I claim my strategy is better.

[guipsp]

For some value of better, sure.

[tshaddox]

Sure, where "some value of better" is "wins in the overwhelming majority of rounds."

[divbzero]

> never take > 6 guesses

I suspect that with most languages it’s impossible to achieve 100% win rate for five or more letters. So w7 should be by far the largest weight but I don’t think it can be infinite.

[rik2]

I suspect the opposite. While the theoretical number of combinations is huge, the amount of information given by each guess grows faster than the number of real words of longer lengths.