Best First Wordle Guess

In Wordle there are 2,315 words that are valid answer to the puzzle and there are 10,657 words that are valid guesses that are not potential answers. As a result there are 12,972 valid guess words. The most popular letter in the set of 2,315 answer words is 'e' which occurs in 1,056 of the answer words or about 46% of potential answer words. Unsurprisingly, half of the ten most common letters are vowels while 'r' is by far the most common consonant. 

The most common first letter is 's' which is the first letter in 366 of words. 'a' is the most common second and third
letter with counts of 304 and 307, respectively. Likewise, 'e' is the most common fourth and fifth letter occurring as the fourth letter 318 times and as the fifth letter 424 times. The only letters that rank in the top five by position that are not in the most ten frequent letters are in the first position ('c', 'b', 'p') and in the fifth position ('y'). 

If the goal of the first guess is to get as many matches as possible, with both letters contained in a word (letter tiles) and the correct location of said letters (green tiles) then it would appear that a word containing 'e', 'a', 'r', 'o', and 't' would be best, potentially with an 'o' in the second position, 'a' in the third position and an 'e' in the fifth position. However, merely matching (or not matching) in the first turn is not necessarily the best strategy to solve the puzzle in the fewest turns.

The most accurate way to determine the best first guess would be to play the game to completion with each answer word and each valid guess word. However, this is extremely difficult computationally, iterating over each of the 2,315 answer words and 12,972 valid guess words for the first guess results in 30,030,180 combinations alone. Iterating over a second guess would result in 390 billion possible permutations. The table for the 30 million combinations is below, which shows that 'roate' is the first guess that eliminates the most possible answers after one guess. On average the potential number of answers is reduced form 2,315 to 60.4, a 97% reduction. 'roate' is a valid guess word, but it is not a potential answer, if one wished to use a valid answer word for the first guess then 'raise' is the best first guess word. On average, a first guess of 'raise' results in 61.0 average words remaining.

The best ten first guess words all contain the most frequent letters without multiple instances of the same letter in the word suggesting that choosing words based on letter frequency is important. Likewise, of the two words that contain each of the five most common letters, 'roate' and 'orate', 'roate' results in fewer remaining words. This would indicate that letter positioning is import as well, given that 'o' is the second most common second letter and 'r' is the third most common second letter. Additionally, 'r' is the 11th most common first letter whereas 'o' is the 17th most common first letter.