Jan 29, 2022 23:45:00

How many trials can the English word guessing game 'Wordle' reach the answer on average?

'Wordle ' is a browser game that guesses five-letter English words based on the hints obtained by entering words. There are various restrictions such as one game that can be played per day and the maximum number of word input trials is 6, but on average, how many trials can be done to clear the game, and the results are It is open to the public.

Below, the article contains hints for 'Wordle' for the January 29, 2022 question.

Wordle-solving state of the art: all optimality results so far --Laurent's notes
https://www.poirrier.ca/notes/wordle-optimal/

The best strategies for Wordle --Things (various)
http://sonorouschocolate.com/notes/index.php?title=The_best_strategies_for_Wordle

The game screen of Wordle is as follows. First, enter a real five-letter English word.

This time, I entered the three words 'HINTS', 'MUSIC', and 'POWER'. For each word, the black background alphabet is 'not included in the answer', the yellow background is 'included in the answer but in a different position', and the green background is 'included in the answer and aligned'. Indicates what is '. In other words, in this case, the second letter of the answer word is confirmed as 'O'. It is confirmed that 'U' is located other than the second character and 'C' is located other than the fifth character.

Wordle has been analyzed based on the source code, and it is known that there are a total of 12,972 registered English words, of which 2315 are the daily 'answers'. The 'answer' starts with 'CIGAR' for June 19, 2021 and ends with October 20, 2027, which is common to all players around the world.

You can access the word list by clicking the link below.
・

All registered English words
・English words chosen as the answer

The key to solving Wordle with the minimum number of trials is determining the 'first word to enter'. Since the words that can be the answer are known, the solution that 'if you enter this word, this is the best word for the next word' is derived, and it is desirable that the first word you enter has a wider derivation. For example, the word 'HOUSE' has a maximum of three 'best words to enter a second time' depending on the hint, but the word 'FORGE' has a maximum of six.

It is better to use words that are as easy to derive as possible as the first input word, and it is known that there

are 105 types of words that are particularly broadly derived. Among them, the word 'SALET (medieval helmet)' has the least number of trials to reach the answer, with an average of 3.4212 times.

by Alex

A part of the chart when 'SALET' is entered first looks like this. B, Y, and G represent the background colors black, yellow, and green, respectively. For example, if you enter 'SALET' and all are black (BBBBB), the next word to enter is 'COURD'. If you enter 'COURD' and the result is black, black, black, yellow, and green (BBBYG), you should enter 'GRIND' .... If you type along this chart, you can reach the answer with an average of 3.4212 trials for any word.

Wordle also has a 'hard mode'. This mode is a rule that if the entered word has a yellow / green display, the alphabet must be used in the future. Furthermore, if it is green, the position is fixed as it is, so if you enter the word 'POWER' and the last 4 letters (OWER) turn green, you can enter 'TOWER' and 'COWER' after that. Limited to words ending in OWER, such as 'LOWER'.

The charts are very different in hard mode, but the minimum number of trials is still 3.5085 on average. However, in the normal mode, the answer can be derived in 4 trials at the worst, while in the hard mode, the answer can be derived in 6 trials at the worst. This chart is flawed due to the rule that you must enter the correct word when you enter it the sixth time. In addition, although the average number of trials is 3.5448, which is not 'optimal', you can check the chart that can derive the answer in 5 trials even in the worst case from this link.

In addition, all the above charts are about 'when you know the answer 2315 words'. If you try to derive an answer from all 12,972 words, it seems impossible to build a chart with just 5 trials.