Wordle Strategy – Eliminate not enumerate (Post #1)
Preamble
It is routine to end up in a position where 3 or more possible answers exist. This can happen after the 1st guess, though the probability is small. It usually happens after the 2nd or 3rd guess. There are at least 2 ways of playing at this juncture – 1) enumerate and 2) eliminate.
Enumerate: try one possible solution at a time. If there are N possible solutions, then the probabilities of guessing the correct word are 1÷N, 2÷N……N÷N in 1st , 2nd, …. Nth try. Due to the constraint of the game, N can’t be higher than 6.
Eliminate: enter a guess that eliminates all but 1 possible solution. This way the puzzle can be solved in 2 guesses. There is a special case of the eliminate strategy. Sometimes one of the possible solutions itself works as an elimination word. Under this scenario, it is possible to solve the puzzle in one guess. If the possible solutions are “too many”, then it may not be possible to find one word to eliminate all but one possible solution. In such a case the goal has to be to narrow down the possibilities to a “few”.
Eliminate not Enumerate examples
Example #1: Elimination possibility after the first Guess
Wordle # 414 (August 6, 2022): Seed word SOARE
Discovery of the letter S as the first letter of the final answer made it possible to begin the elimination strategy from the second guess. This is not always a possibility.
After the first guess (SOARE), there were eight possibilities grouped into two groups:
- Group One: SHEAR, SPEAR, SMEAR, and SWEAR
- Group Two: SANER, SAFER, SAVER and SABER
This is an example where the possible solutions differ only in one position (#2 in the first group and #3 in the second group). It is not always the case.
I could not come up with a single word to eliminate all but one possibilities. I chose the word NYMPH as the elimination word. It is worth noticing that I had to “waste” one space (for the semi-vowel Y) in order to form a valid word. I am sure a better word exists. NYMPH had the potential of eliminating four of the eight possibilities spread across the two groups: Group #1: SWEAR and Group #2: SAFER, SABER, and SAVER.
Luckily for me, NYMPH confirmed the presence of the letter M there by pointing to SMEAR as the answer.
Had NYMPH failed, i.e., the answer didn’t have the letters N, M, P and H, I would have picked FABLE as the next elimination word. It would have eliminated SAFER and SABER due to the presence of the letters F and B in FABLE. Also, it would have eliminated SWEAR since the letter E in FABLE is in spot #5 vs. #3 in SWEAR.
Impact of the elimination strategy (vs. the enumerate strategy)
For this puzzle, with the selection of SOARE as the first word, the “apriori” odds for the two strategies (Eliminate and Enumerate) from third guess onwards compare as follows:
- Eliminate strategy: the odds are 50/50 that it would take 3 guesses or 4 guesses.
- Enumerate strategy: the odds are 1 out of 8 that it would take 3 or 4 or 5 guesses and 3 out of 8 that the puzzle will not be solved in six guesses.
Finally, the probability of solving the puzzle in four guesses or less are 100% for the elimination strategy and 25% for the enumerate strategy.