Effective Wordle Heuristics
This paper demonstrates that simple heuristics can efficiently generate effective daily Wordle strategies by prioritizing possible solution words, thereby avoiding the computational cost and obscurity associated with exhaustive search methods.
Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Imagine you are playing a game of Wordle, where you have to guess a secret five-letter word in six tries. Every time you guess, the game gives you clues: green for the right letter in the right spot, yellow for the right letter in the wrong spot, and gray for letters that aren't there.
For years, computer scientists have tried to find the "perfect" way to play this game. They built super-computers to check every single possible combination of words. The result? They found a strategy that is mathematically perfect, but it requires you to start with weird, obscure words like "salet" or "tarse"—words most people have never heard of. Plus, running these calculations takes days of computer time.
This paper, written by Ronald Greenberg, asks a simple question: Can we find a strategy that is almost as good, uses normal words people actually know, and can be calculated in a few seconds?
The answer is a resounding yes.
Here is the breakdown of the paper's findings using some everyday analogies:
1. The "Super-Computer" vs. The "Smart Human"
Think of the old "optimal" strategies as a super-computer trying to solve a maze by checking every single path. It finds the absolute shortest path, but it takes forever to calculate, and the path starts with a door you've never seen before (like the word "salet").
Greenberg's approach is like a smart human looking at the maze. Instead of checking every single path, they use a few simple rules of thumb (heuristics) to make a very good guess almost instantly.
- The Result: The "smart human" strategy is only slightly less efficient than the super-computer, but it uses words like "raise" or "trace"—words you actually know.
- The Speed: While the super-computer takes days to plan, the smart human strategy takes seconds. This means the computer can re-calculate the best strategy every single day to account for words that have already been used.
2. The "Filing Cabinet" Analogy
How does the computer decide which word to guess? Imagine you have a giant filing cabinet containing all 3,158 possible secret words.
- The Goal: You want to pick a guess that splits these files into the most distinct piles (bins) possible.
- The Old Way: Some strategies tried to guess words that would make the piles as small as possible on average.
- Greenberg's Discovery: The best strategy is actually to guess the word that creates the highest number of different piles, regardless of how many files are in each pile.
- Analogy: Imagine you are sorting a deck of cards. Instead of trying to sort them perfectly by suit immediately, you just want to make sure you have the most different groups of cards possible after your first move. This gives you the most information to work with next.
3. The "Tie-Breaker"
Sometimes, two words seem equally good at splitting the files. Which one do you pick?
- Greenberg found that when two words are tied, you should pick the one that leaves you with the smallest average pile size for the next guess.
- Analogy: If two doors look equally promising, pick the one that leads to the room with the fewest people, just in case you have to search that room next.
4. The "Hard Mode" Challenge
Wordle has a "Hard Mode" where you must use the green and yellow letters you've already found in your next guess.
- This is like playing chess where you are forced to move a specific piece every turn. It makes the game much harder for computers because they can't just look ahead freely.
- Greenberg found that for Hard Mode, you need a slightly more complex strategy (combining a few rules), but even then, the computer struggles to match the "perfect" strategies found by the super-computers. However, the strategies found are still very good and much faster to calculate.
5. The "Used Up" Advantage
Here is the best part: Since Wordle (usually) doesn't repeat words, the game gets easier over time as you eliminate words you've already seen.
- Because Greenberg's strategy is so fast (taking only seconds), the computer can update its list every day, removing the words that have already been used as solutions.
- Analogy: It's like playing a game of "Guess Who?" where you can cross off faces you've already eliminated. By doing this daily, the average number of guesses needed drops slightly, making the game even easier for you.
The Bottom Line
You don't need a super-computer or a dictionary of obscure words to win at Wordle.
- Don't guess "salet." Guess "raise" or "trace."
- Don't wait days for a plan. A simple rule that tries to create the most "buckets" of possibilities works almost perfectly.
- The Future: The author even provides a website where you can get a fresh, daily strategy that adapts to the words already used, ensuring you always have the best possible chance of winning in six tries or fewer.
In short: Keep it simple, use common words, and let the computer do the quick math every morning.
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