Wednesday, June 29, 2022

# Introducing WordleBot, the Upshot’s Daily Wordle Companion

WordleBot is a tool that will take your completed Wordle and analyze it for you. It will give you overall scores for luck and skill on a scale from 0 to 99 and tell you at each turn what, if anything, you could have done differently — if solving Wordles in as few steps as possible is your goal.

It’s very easy. First, play Wordle. Then visit the Wordle Companion, ideally using the same device and web browser.

Every Wordle game starts with one of 2,309 possible solutions as the hidden word. At each turn, WordleBot chooses the word that will allow it to solve the game in as few steps as possible, assuming any of the remaining solutions are equally likely. It keeps doing this until only one solution remains — the right answer.

Months ago, before The New York Times bought Wordle, we, like many others, began wondering about the best starting word. It seemed like a straightforward mathematical question — yet everyone who approached the problem seemed to come up with a different answer.

WordleBot started as an attempt to settle this question once and for all. But along the way we realized that (a) the answer was more complicated than it seemed; and that (b) we were more interested in how closely our guesses matched those that would be chosen by a machine designed to solve Wordles.

Thus, WordleBot was born.

In addition, it may serve as a tiebreaker of sorts for those of you involved in competitive text chains with friends and family. If a Wordle took you five turns but you answered more efficiently than your friends, WordleBot may provide some bragging rights. If you did everything right and were simply unlucky, it will tell you that too.

We’ll leave it to you to decide which is more important.

WordleBot solves the 2,309 possible Wordles using the fewest number of guesses when it starts with CRANE in normal mode and DEALT in “hard mode.”

This may surprise some readers, who have seen, in various places across the internet, people claim that words like IRATE, SALET or RAISE are the best openers. The truth is that it depends exactly how you’re playing and whether you are a human or a computer.

The various Wordle algorithms all take slightly different approaches in how they solve the puzzle. Some start with knowledge of the solution list; others do not. Some allow any of the almost 13,000 five-letter English words as valid guesses; others (like WordleBot) use a smaller set. We restricted WordleBot to about 4,500 words that are more common among English speakers — it didn’t seem particularly helpful for a piece of software to recommend words like VOEMA, CUSSO, SKATT or ZEBUB,

Apart from all that, it’s worth noting that the perfect opening word for a computer isn’t necessarily the perfect opening word for you. WordleBot has perfect knowledge of the 2,309 solutions stored in its memory. It’s likely that you do not. So while the bot might know the precise optimal path to take from a given guess, it’s possible that you might not and that a different guess would be more likely to lead you to the answer.

More important, unless you’re playing in hard mode, every game of Wordle is solvable regardless of which word you choose first. So go ahead, start with FUZZY, we won’t stop you. (And note: WordleBot ignores your first guess when calculating your overall skill score. Be free.)

No. WordleBot will never analyze an incomplete game; it will give you advice only for completed Wordles.

By default, it will analyze whichever Wordle you’ve completed most recently on your device, if you have cookies enabled in your web browser. But you can also upload a screenshot of any completed Wordle — even if it’s from months ago, provided you’ve saved the screenshot — and it will analyze that for you instead.

No. It knows the full list of solutions, but nothing more. It also doesn’t know whether a Wordle solution has already been used.

No. The bot solves all Wordles in six turns or fewer.

Yes. The bot will give advice on your Wordle however you play. But hard mode presents a challenge.

It complicates things from a computational perspective: While eliminating the largest number of solutions with each guess is a tempting approach, it isn’t always the best idea. WordleBot needs to think several steps in advance to make sure that it’s eliminating solutions now and won’t get stuck in a losing position later.

For modern computers, this additional complexity is nothing to worry about, but we are somewhat constrained by the computing power of some smartphones and the amount of time we can reasonably expect you to wait for the bot’s analysis to load.

As a result, we did have to make some small shortcuts for the bot to analyze games in hard mode. In particular, it’s not always the best at knowing when it might be stumbling into a situation where there are more possible solutions than there are valid guesses remaining to differentiate them. In some cases, other guesses might have avoided these hard mode traps.

All this means is that the version of WordleBot that’s powered by a supercomputer would probably differ slightly from the version that runs in your phone, but the differences are mostly minor and we don’t suggest worrying about them.

No. It does all of its calculations on demand, on your smartphone or computer.

Absolutely. It’s hard to solve more efficiently than the bot, but quite easy to be luckier.

No.

No. It may change how you play Wordle, but it’s completely independent of Wordle itself.

A skill score of 99 is what WordleBot assigns to its chosen word at any given step. In its view, this is the most efficient choice to make to solve the puzzle in as few guesses as possible, averaged over all possible remaining solutions.

A skill score of zero is what you get if you just skipped a turn altogether. (While it’s impossible to actually skip a turn in Wordle, you can get the same effect by guessing a word you’ve already guessed: You lose a turn and you don’t learn anything new about the possible solution.)

Your skill score measures how close you were to the bot’s chosen word relative to the worst word you could have picked for that turn.

Suppose, for example, you guess CRANE on your first turn. The best thing that could happen would be if the hidden word were actually CRANE — you would solve the Wordle in one guess. That’s obviously very lucky.

The worst result would be five gray squares; you would be left with 263 possible solutions to sift through. Considering that 89 percent of the solutions share at least one letter with CRANEthat result would be very unfortunate, despite a strategically sound choice.

Our luck measurements represent how unexpected the outcomes of your guesses are, conditional on what we’d expect, on average, given what we know about the solution at that time.

Maybe you’re familiar with the game Guess Who, a popular two-person board game in which players use yes-or-no questions to try to guess the identity of their opponent’s hidden character. A guess like “does your person wear glasses?” divides the remaining possibilities into two groups: people who wear glasses and people who don’t. You get only one piece of information with each guess.

It’s similar with Wordle, but guesses can reveal much more information: Each letter of each guess can turn green, yellow or gray. That means a guess could theoretically divide solutions into up to 243 different groups (three to the fifth power, or 3^5, for the mathematically inclined). Realistically, because not every combination of letters is a valid word in English, a guess can divide solutions into 150 different groups at most, found by guessing TRACE on the opening guess.

In general, as a solver, you want your guesses to divide the possible solutions into as many groups as possible.

Here’s an example. Suppose, with your previous guesses, you’ve narrowed the possible solutions to five: BATCH, CATCH, LATCH, MATCH or PATCH, What should you guess next?

If you guess BATCHyou’ll divide the remaining solutions into two groups:

If the hidden word is BATCH, great! But if it isn’t — which is the more likely outcome — you’re stuck with four possible solutions.

A smarter guess would divide these groups more efficiently, putting you in a position to solve the puzzle regardless of luck. Here, WordleBot would guess BLIMP, See how that changes the picture:

With this approach, you divide the solutions into five groups of one word each. You’d be guaranteed to get the answer on your next turn!

When Josh Wardle created Wordle, he and his partner, Palak Shah, picked a subset of the roughly 13,000 valid five-letter English words to be potential solutions, meaning that many guesses, while perfectly adequate words in English, are not Wordle solutions. (Many plural forms of nouns, for example, are excluded from the solutions list.) WordleBot knows the full solutions list, and if you guess a word that isn’t on it, it will tell you.

It may be because you’re using a different web browser to play Wordle than you are in using the Wordle companion. (When you complete a day’s Wordle, your guesses and preferences are stored in a small file on your device called a “cookie,” and the information in that cookie is not, at the moment, stored across different devices or browsers.) So you can either make sure to use WordleBot on the same device you play Wordle on, or upload a screenshot of your Wordle to WordleBot instead.

Many mathematicians and programmers have tackled this problem, but we’d recommend watching Grant Sanderson’s 30-minute video on solving Wordle with information theory.

His (shorter) follow-up video, where he lands on SALET as the optimal opener, is also worth watching.

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