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# How To Win At Wordle Using Math

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There's a good chance you've come across Wordle already, the hot new game where you have six tries to guess a word.

In the game, you are asked to make a guess at what the word could be. You are then given information on whether the letters you have selected are in the word, and whether they are in the right place. Letters that are in the correct place are flagged as green, whereas letters that are in the word but in the incorrect position become yellow. If the letters are incorrect, they turn gray.

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The basic mechanics are similar to the board game Mastermind, in which you are asked to guess the colors of pins that an opponent has selected.

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In much the same way, the best strategy to beat the game is to maximize the information you learn with each turn. For instance, in Mastermind, it's best to use colors you haven't used in the first go on your second turn, to discover which colors are in play.

Unlike Mastermind, in Wordle there are 26 possible letters that could be in each position (thank the alphabet for this extra difficulty) but the principle remains the same: if you want to win, you should be trying to maximize the amount of information you learn in each turn. Since there are a finite number of allowable five-letter words (they are not placed in random order), it's possible to figure out which letters are more likely to show up.

Use letters that are more likely to show up, and you maximize your chance of learning information for your next guess.

Wordle has not announced (probably to stop people from cheating by using math) the word list that they use. However, that hasn't stopped people from trying to figure out the best opening moves. Redditor adeadhead analyzed the occurrences of letters in the Standford Graphbase five-letter words list for their analysis, and found out how many times each letter occurs in all the possible five-letter words, coming up with this:

S : 3033
E : 3009
A : 2348
O : 1915
R : 1910
I : 1592
L : 1586
T : 1585
N : 1285
D : 1181
U : 1089
C : 964
P : 955
Y : 886
M : 843
H : 814
B : 715
G : 679
K : 596
F : 561
W : 505
V : 318
X : 139
Z : 135
J : 89
Q : 53

As you can see, you would be some kind of wild maverick to open your game by playing the letters J or Q. They went on to put together a list of the best words to use as an opening, as you'll likely get more information from the letters, given their chance of occurring.

[word, score]
['arose', 12215]
['raise', 11892]
['arise', 11892]
['aloes', 11891]
['stoae', 11890]
['laser', 11886]
['earls', 11886]
['reals', 11886]
['tears', 11885]
['rates', 11885]
['stare', 11885]
['aster', 11885]
['tares', 11885]
['snare', 11585]
['earns', 11585]
['nears', 11585]
['saner', 11585]
['nares', 11585]
['aisle', 11568]
['least', 11561]

Basically, always put an "s" in there, although the best word they found without an S was "orate".

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Other Wordle fans have conducted their own analyses using different dictionaries, finding significant crossovers. According to one posted to GitHub, the best words to use are: arose, soare, aeros, serai, reais, raise, arise, aesir, aloes, and seral. The worst being "fuffy" and "xylyl".

On your second go, you should also try and maximize the information gained, rather than guess at the word directly (unless you think you've cracked it, of course). Try to use letters that you haven't used before, and you will get far more information than if you reuse any of the letters you've already had, and of course try to use letters that are more likely to come up, vowels being especially helpful.

Happy wordling.

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