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Optimize Production tf2
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so i don't really know what to do with this blog but like a month ago i optimized wordle so i'll write about that
so the best first word in wordle is ROATE which according to dictionary.com means "the cumulative net earnings after taxes available to common shareholders, adjusted for tax-affected amortization of intangibles, for the calendar quarters in each calendar year."
i calculated this using python (my beloved). you want to eliminate the most words on average in your guess, so that's what i'm optimizing.
before i go deeper i want to clear up some terminology
a guess is a word that you can type in to wordle. there are more than 12,000 possible guesses you can make in the game.
an answer is a word that can actually be the answer, the word that you are looking for. there are only 2315 possible answers in the game.
a result is some collection of greys, yellows, and greens. when you type in a guess you get a result
by the way all the wordlists that i used in these calculations are the actual wordlists that they use in the wordle game
so, basically my program takes a word that you can guess and sees what the result would be if you guessed that word for every single possible answer (of which there are 2315). in this way, each possible answer is assigned a result.
so your goal is for these answers to be as spread out as possible between the results. if 99% of the time your guess gets all greys, than you're revealing very little information. ideally every possible answer is spread out perfectly between the different possible results. there are 243 possible results in wordle (3^5), and 2315/243 is around 9.5, so in your ideal world no matter what happens after your first guess you have narrowed it down to 9.5 different words.
we of course don't live in this ideal world, so we have to do with ROATE. how do i calculate how good a word is? take the number of answers assigned to a result, divide by the total number of answers (2315), and square that. repeat for every result and sum all the numbers you get.
let's say there were 3 possible results and 6 possible answers. a word that had the answers split evenly would get:
(2/6)^2 + (2/6)^2 + (2/6)^2 = 0.33
meanwhile, a word that had most of the answers assigned to only having one result would look more like:
(5/6)^2 + (1/6)^2 + (0/6)^2 = 0.72
lower numbers are better, with 1 being the worst possible score. these numbers actually tell you the average amount of elimination for the words. so the first example with 0.33 on average reduces the possible answers to 33% of it's original size (obviously), from 6 to 2. less obviously, the second example on average reduces the answers to 72% of it's original size, from 6 to 4.32.
SO, i did this calculation for each word that you can guess, and the best was ROATE. ROATE's score was 0.0262. this means that when you guess ROATE, on average the possible answers are cut to 2.62% of the original possible answers, which means on average after getting ROATE you are narrowed down to 60 words. that's pretty good for just one guess. (as I said earlier, the theoretical best would be 9.5). a very rough estimate tells me that a second guess would probably narrow you down to three answers, so with ROATE (if you play tactfully) you will hopefully usually get the wordle in three or four.
one other thing to keep in mind is that although ROATE is a valid guess, it isn't a valid answer. would a valid answer (such as the word RAISE) be better? i did the math and it is very close but ROATE is still better either way.
thanks for reading, i'm not even done because i calculated the best possible second words as well, ill talk about that later
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