After my previous video showing AROSE as the best first guess in Wordle, I started doing some more cool Excel formulas to test all Wordle words. This is a long video for the weekend, mostly of me geeking out about Excel and doing 1.5 billion calculations with a $10 spreadsheet.
For a great Wordle Analysis from Laurent Lessard: Solving Wordle - Laurent Lessard
Table of Contents
(0:00) Introduction
(1:15) Colors in 53 formulas
(6:10) Laurent Lessard or 3Blue1Brown
(7:25) The 2315 words
(8:50) Solving for 5.3 Million with 284 MM formulas in Excel
(10:40) The 10,972 words
(11:57) 2315 x 12972 x 53 of 1.3 billion
(13:00) Wordle Universe 1.596 billion calcs
(14:25) Can be the answer?
(14:59) Count unique constellations per guess
(17:17) It is not 3^5 possible answers
(18:10) Show 10 largest using LARGE in Excel
(18:30) Using Ctrl+Right Arrow in Excel
(18:46) TRACE, CRATE, or SALET starting words
(19:38) 10 words with most constellations
(20:14) Max words in play after any guess
(20:36) COUNTIF for each in array in Excel
(21:30) What's the most words still in play
(22:20) RAISE or ARISE for less words in play
(23:00) Is Wordle a hostile opponent?
(23:34) Solving methodology
(25:05) Filtering to find 10 words still in play
(26:00) Sheet2 for words still in play
(26:38) Evaluating the best for 2nd word
(28:45) Guessing a wrong word narrows it for the win
(29:16) Which words will minimize words in play
(30:00) Having 221 after first guess
(30:25) Using Excel Advanced Filter from another sheet
(32:05) End game strategy wins 2nd guess from now
(34:10) Increase chance of less than 100 words after first guess
(35:30) Maximize winning in 2 PARSE, CRATE, TRACE
(36:50) The worst first guesses in Wordle
(37:15) TARES, SANER, AISLE, ALONE as best words
(38:40) Over 1000 words in play after first guess
(39:10) AISLE ALONE for less than 200 words
(39:20) PARSE or CRATE or TRACE
For a great Wordle Analysis from Laurent Lessard: Solving Wordle - Laurent Lessard
Table of Contents
(0:00) Introduction
(1:15) Colors in 53 formulas
(6:10) Laurent Lessard or 3Blue1Brown
(7:25) The 2315 words
(8:50) Solving for 5.3 Million with 284 MM formulas in Excel
(10:40) The 10,972 words
(11:57) 2315 x 12972 x 53 of 1.3 billion
(13:00) Wordle Universe 1.596 billion calcs
(14:25) Can be the answer?
(14:59) Count unique constellations per guess
(17:17) It is not 3^5 possible answers
(18:10) Show 10 largest using LARGE in Excel
(18:30) Using Ctrl+Right Arrow in Excel
(18:46) TRACE, CRATE, or SALET starting words
(19:38) 10 words with most constellations
(20:14) Max words in play after any guess
(20:36) COUNTIF for each in array in Excel
(21:30) What's the most words still in play
(22:20) RAISE or ARISE for less words in play
(23:00) Is Wordle a hostile opponent?
(23:34) Solving methodology
(25:05) Filtering to find 10 words still in play
(26:00) Sheet2 for words still in play
(26:38) Evaluating the best for 2nd word
(28:45) Guessing a wrong word narrows it for the win
(29:16) Which words will minimize words in play
(30:00) Having 221 after first guess
(30:25) Using Excel Advanced Filter from another sheet
(32:05) End game strategy wins 2nd guess from now
(34:10) Increase chance of less than 100 words after first guess
(35:30) Maximize winning in 2 PARSE, CRATE, TRACE
(36:50) The worst first guesses in Wordle
(37:15) TARES, SANER, AISLE, ALONE as best words
(38:40) Over 1000 words in play after first guess
(39:10) AISLE ALONE for less than 200 words
(39:20) PARSE or CRATE or TRACE
Transcript of the video:
Holy smokes, 1.5 billion calculations in Excel.
This is an insanely long video, and let me just save you some time.
I geek out, because I can run one and a half billion calculations in Excel without crashing.
You already know this: the new dynamic array formulas are wildly helpful. You probably don't know, when you get an email from Larry Robinson, it can turn into an obsession.
And just for any of you who are still playing AROSE as your first Wordle word, there's better words, TRACE.
But there's other better words depending on your strategy.
I never know what Excel video is going to take off, right?
And that Wordle video where I chose AROSE has now have people calling me a CNN-cited Wordle expert, which is just insane.
There's people who are doing this much better than I am, and I'll send you links to those.
This is a weekend.
If it's snowing where you're at, and you hate the Super Bowl, and you need a video to put you to sleep, this is it.
For all of my regular viewers who are looking for something cool in four or five minutes, I'm not offended. Skip this one.
I'll see you on Monday.
Excel is a miraculous program for its ability to deal with large amounts of calculations without any problem.
One of the earliest things I wanted to do was to build a little model here where if I typed in the Wordle word of the day and made a guess, could I generate the green, gray and yellow tiles?
Now, Wyn Hopkins had already solved this, and I could have downloaded Wyn's workbook to try and look at his code.
But I just started out here, and just to solve this simple little problem, with 53 formulas, there is some cool Excel stuff going on here, right?
So I have a five-letter word here, and I want to break that out into five horizontal cells.
So the mid-function with the sequence of five would give me five vertical cells, but I want horizontal cells.
So rather than use transpose, check this out in the sequence here.
I ask for one row of five columns, and that forces it to go across. Same thing here for trace, which are green.
This is easy.
If the letter here is equal to the letter here, then I have a green cell. Otherwise, it's not green.
Which, do we still have to score? In other words, so we know that R and A are in the correct spot.
We don't have to worry about those anymore, but I still have to worry about this one, this one.
Simple little formula there, right? And then I was really happy with this.
If we still have to score it, I want to bring that letter down.
But if we don't have to score it anymore, I want to put something there that's not going to be found as a match. And rather than a letter, I put a number.
And instead of just any number, I use the column function.
That way, it'll generate three, four, five, six, seven here, and that will never match to T-R-A-C-E.
What are the guess letters that are not scored yet? Same basic logic there, okay?
And then for which letters are gray, this was going to be easy, I thought.
I'll look for a T somewhere in here, and if there's none then this is a gray cell, right?
And that was all good, and I used this for about two weeks, and Dan Mayoh from Fintega used this. And then he wrote to me.
He said, "Hey, your algorithm just threw out a word that was the right word".
Dan had done some drilling down, and he figured out that the problem was when the guess had two or more of the same letter, MOMMA being the extreme example of three.
The actual word itself has not that many, like just one M, so I'll go with A-M-E-E-E.
I was reporting those extra Ms as not gray, which was forcing them to show us as yellow, right? So thanks to Dan for figuring this out.
I had a simple little formula there, but then three more rows of formulas to look for that weird situation where the guess has multiple duplicate letters and the answer doesn't, and to detect that and to correct the gray.
So in this case here, guessing MOMMA, it would have given me not grays for the second and third M, but in fact it should be gray for the second and third M because there is only one M in the word.
The yellow one was the one I thought was going to be really hard, and that was the one I actually thought I was going to have to download Wyn's spreadsheet to take a look.
But it's really easy.
If the cell is not gray and not green, then guess what? It's yellow, right?
So this was really easy, just one minus, is it gray, minus is it green? And that gives me the yellow cells.
To convert these series of ones and zeros, well, instead of just an if formula that was nested, I used the ifs function, which is cool. So if C7 is one, then it's green.
If C20 is one, then it's gray, and I used a dash for gray.
If C22 is one, then a yellow.
And you have to finish out the ifs with this thing that is always true in what to happen. And this is good.
The Z should never show up.
When I was working on this fix for the Dan Mayoh discovery, it came up Z a few times. I'm like, "Okay, I need to fix that".
And then finally, the very last formula is a little CONCAT formula.
You know, I love TEXTJOIN, and I say TEXTJOIN is superior to CONCAT in every way, except for when we just need to take five cells and smash them together.
Then that works out really great.
Okay, now before we get to the million cells, I want to thank Larry Robinson at the MrExcel message board.
He prompted all of this.
He started asking me questions about my first Wordle video.
But since then, we've both watched and studied at GitHub, Laurent Lessard and his amazing analysis, and then the beautiful YouTube video, 3Blue 1Brown. So this is not a Wordle video.
I defer all Wordle logic to those two gentlemen, because they have figured it out, right?
This is an Excel video, right? I'm just geeking out about how amazing the Excel-ness is here, okay?
So what did I say? Was it 53?
To get down to the point where I can put in a word frame and my guess, D-U-M-B-S, and it correctly will score this as gray, gray, yellow, gray, gray, which matches the Wordle website itself.
Down the left-hand side here, instead of the Scrabble dictionary that I used in the last video, 8,000 words, I've used the actual word list, 2,315 words that Wordle might use someday.
This is the whole population of five-letter English words.
Josh Wardle, who created Wordle, his girlfriend went through those words and chose ones that she thought were valid answers, right?
So there's only 2,315 words that can happen, and down the left-hand side here, I have all 2,315 words.
Across the top, I have all 2,315 words going across.
The theory is, if the actual Wordle word is this going down the left-hand side, and this is the word that I guess, what will the constellation be? That's Laurent's term for the answers.
And like you'll see here, if you get G-G dash, dash, dash, then that means that it could be any of these, or probably many others that are further down, right?
So the worst thing that can happen, and it actually happened earlier today, is you put in a guess and instead of narrowing it down to 10 words, it narrows it down to 220 words.
This morning, it went from 2,315 words down to 221, which is not a great improvement.
I mean, it's a tenfold improvement but it's not getting it down to 10.
All right, here's the amazing thing.
I'm going to choose this whole range, and control backspace to bring that top left corner cell back into view.
From data, what-if analysis data table, across the top is the word that's guessed.
I'm going to take each of these 2,315 words across the top, and plug them into B5.
And down the left-hand side, the actual Wordle word ...
If you keep playing Wordle long enough, all 2,315 of these will come up sooner or later.
That would go into here, right?
Now, I'm not going to press okay, because it takes a few minutes.
What happens here is, this generates a table formula.
And in this table formula, if you let it calculate, there are 5,359,225 possible combinations of, this is the Wordle word and this is your guess.
Those are the constellations that you're going to get. I actually walked away.
I figured this would take an hour.
When I came back five minutes later and it had finished calculating, I was pretty astounded. Five million sets of calculations ...
It's 5,359,225 cells that are populated down here, and each one of those cells required 53 formulas.
Every intersection here, they do all 53 formulas to come up with this answer in the yellow cell.
That's 284,038,925 calculations in about five minutes or so.
It's really amazing.
Now, before Laurent and 3Blue 1Brown posted their solutions to Wordle, the question came up.
"Do I only have to look at the 2,315 words that it could be?" There's a second list of 10,000 and some words that will never be the answer, but you are allowed to guess.
Are there times where it helps to make a guess that's not an actual Wordle solution?
And this actually happened with this puzzle, right? The correct word was frame.
After trace, I had it down to 10, and that was beautiful.
But there was a lot of duplication within the 10, and I actually ended up choosing a word that can't be the Wordle word, dumbs.
Because after choosing dumbs, I was guaranteed to get it down to just one or two possibilities.
I'll show later how we came up with that, right? So I really pushed back on this.
I said, "I'm always going to guess words that's the correct word". But I've since learned ...
It was Larry and Dan both said, "You need to test it both ways.
You need to test the possibility of answering a word that won't be the answer, just in order to knock a whole bunch of other letters out.
Sometimes that will be the best strategy". Hey, this is a new file.
They convinced me that I had to consider the 2,315 possible Wordle words against the larger population of 10,657 words that will never be the Wordle answer, but are valid.
Exact same logic, the same 53 formulas there, but now it's 24,670,955 cells times the 53 formulas.
That is an astounding 1,307,560,615 cells. I can't tell you how long this took.
It was longer than I could stand to watch, but it was less than an hour.
It didn't crash the computer, which I think is impressive, although I very definitely copied and pasted those values so it would never have to calculate again.
Well, I thought it would never have to calculate again, until Dan Mayoh found my logic error, and then I had to calculate it one more time.
Welcome to this range, which I call the Wordle universe.
So from the first workbook that did 284,000,000 calculations, and the second workbook with 1,307,000,000 calculations, that means this is 1,596,950,818 calculations all represented right here, down the left-hand side.
2,315 words that the actual Wordle could be on any given day.
Across the top, those same 2,315 words followed by 10,657 words that you are allowed to guess but will never be the Wordle word.
So that's 2,315 times 12,972.
That means that in this spreadsheet right here, not counting the words at the top or the side, the number of constellations here is 30,030,180.
It's like this whole thing, and there's the count down there.
And again to get this, it's the result of 1,596,000,000 calculations, all in a spreadsheet that I'm paying $10 a month for.
With kudos to the better solvers, who are using high-end programming languages, my $10 spreadsheet is getting me really far along this path.
This can be up here. This is really important.
The first 2,315 cells here have a one, and then after that it's a zero.
As I'm playing Wordle each day, that becomes an important factor.
Like, "Do I want to make a guess that could be the answer?
Is there some chance that I'm going to win on the next guess, or am I playing to solve it in the second guess?" Sometimes it seems better to play it where you're solving it in the second guess.
Now that I have the Wordle universe, the question is what's the best first word?
And last time, I said it was AROSE or arise, and that's not my best word anymore.
The range that we have up here is 30,030,180. It's a lot of cells.
It's very wide.
It's very frustrating when I want to copy this formula to the right. It's hard to get out here to S-E-A.
So I'm going to cruise down here, 2,315 words down the left-hand side.
These are the Wordle words that could be. Here's all the words we're allowed to guess.
I'm going to control down arrow and cruise down a little bit here to this range.
This range is 12,972 columns wide and there's only 12,972 formulas here.
It basically asks the question of, "What are the unique constellations that we might guess, had we guessed aback?" And what I've determined is the more constellations you get, the more information you're going to have, right?
So if there's a word that only gives us 20 constellations, that means that 2,315 divided by 20, you're going to end up with hundreds of possibilities.
But if you had 150 possibilities, then that's a better variability, which means that there's going to be less words that are going to match any given constellation.
All right, so I copied this across for all 12,972, all right?
So that's impressive that there's 12,000 unique functions there, that are analyzing 2,300 cells each, and it all calculates pretty quickly.
And then the count, and this is counting using the array indicator there, the hash to say, "Count how many answers we had from there".
And so here if I'd guessed aback, there's 57 possible answers that I'm going to get.
What's the best, right? So if I look through this, the max.
What's the most number of constellations that I can get?
In theory, some would say that this could be green, yellow or gray, so it's three to the fifth power, 243 possible combinations.
So getting 150 of the 243 possible, that's impressive, but it's not possible to get all 243.
For example, if you had a word that was G-G-G-G, four greens in a row, it can't possibly be a yellow.
Thanks to Larry Robinson for pointing that out to me.
So several of the 243 just simply aren't possible. I'm interested in which ones might have 150.
Now normally, what I've been doing is not just asking for the max, but ask for the large.
I want to see the 10 largest, so the sequence of 10, that little formula there, right?
There's only one word that has 150 constellations, then after than 148, 148, 147, 147.
Down here, I put a sequence of 150 and I cruise down to the 150.
If I would control right arrow from here, I'm going to end up at that one word, that one magic word, that has 150 constellations.
That word is trace. Trace is now my new favorite word.
But there are other possible favorite words, like let's look at the 148s.
So I come down here to 148.
There should be three of them now, and the first one is crate, and then trace, and then this one is salet.
Now, I'm not sure I like salet because it can't possibly be the right word.
But what I do like is an anagram of salet, which is slate.
There's slate, and slate unfortunately only gives us 147 constellations.
But some days, that feels okay. Like this morning, I guessed slate.
All right, I transpose those other results, input it here.
So these 10 words are the words that return the most constellations.
I want to have that one-in-2,315 chance that I'm going to solve it on the first guess.
Sooner or later, that is bound to happen.
And so I really think that out of these, it's trace, crate, slate and parse that are probably the words that I'm going to choose on any given day.
But wait, there's another way to look at this.
So one of these constellations here, like G, dash, dash, Y, dash; how many times does that constellation appear, right?
So I'm going to come down here below my 150 rows, where I repeat all 12,972 columns. And this time, the calculation is much harder.
I'm doing a COUNTIF of the original 2,315 constellations, had I guessed aback.
And then the question is, how many times is it each of these answers returned by this array?
So in this case, I'm running the COUNTIF essentially 57 times down here, right? And so let's just look.
Had I guessed aback, there's one combination that's going to appear 925 times.
That would be terrible.
That would be a terrible first guess, to come up with number 44. Let's come up and see what that is.
It's probably no hits at all.
Yeah, so if I get five gray tiles and I guessed aback, I've only gone from 2,315 words down to 915 words.
That would be a very disappointing first word, right?
So I asked the question of, what's the worst thing that could happen?
What's the most number of words that will still be in play after this first guess?
And that's a column up here called max, max. And in this case, high numbers for max are bad.
I want the lowest numbers for max, so we ask for the small of all the maxes, comma, sequence of 10.
And there's some words where the worst thing that can happen to you is it gets narrowed down to 168.
So, that's taking the max column. This time we're going to sort smallest to largest.
Raise, arise, which in my other video was my second choice, these next several cannot be the right word, right?
So depending on your strategy, is it that you want to have the most unique combinations, or you want to have the lowest possibility of having a whole bunch of words after the first guess?
You might come up with raise or arise, trace, crate, slate, parse, raise, arise. Those are great words to choose from.
Now when I was talking to Dan Mayoh I said, "Well, we should really choose a different word every day.
Because when Josh Wordle becomes aware that Laurent and the others have pronounced trace as being the best word, he might start throwing words in that will make it more difficult for us to win".
And Dan said, "Well, yeah. You're putting emotions in there.
The 2,315 words have already been determined. The order's already been determined.
Each one's going to appear once, and so there's no evil actor trying to make it harder for you".
All right, part three.
This one, two, three, four ... Four worksheets in this workbook.
This first worksheet ... I never come here.
It's just simply used by formulas on the other sheets ... It's the universe.
It's every possible word that could be the Wordle answer today, with every possible guess, the 30 million combinations with a great name of universe.
Bill best; this is a very small sheet, 2,315 rows down the side, just the words that are possible good words across the top.
Out here, just for completeness, I've included the words that a lot of people were using as their first words.
AROSE, ADIEU ... which by the way, that's a horrible first word.
It will never hit.
A Tweet that said, "The day that ADIEU is the word, Twitter will break. It's never going to happen.
It's not in the 2,315 words".
So I just put these out here for completeness, and the idea is that every day I'm going to choose which word from these.
Preferably not the gray columns, because those are words that will never appear, right?
So trace or crate or slate or parse or raise or arise, whatever mood strikes me that day.
I put that into the Wordle website, so I guessed trace, and I came back with gray, green, green, green, gray, green.
So then whichever word that I had chosen that day, I apply a filter just to that column, and I look for this result.
So, dash, green, green, dash, green, click okay. Oh, what a great day this was.
There are only 10 possible answers. I went from 2,315 answers down to 10.
What a beautiful, beautiful day that is, all right?
So now, I don't have to worry about the 2,315 words.
The question is, given this population of 10, what's the best guess?
Welcome to the sheet called step two, across the top, 12,972 words.
Down the left-hand side, the words that are still in play.
On this particular day, there's only 10 rows.
Down here, I repeat those formulas. Here's the unique.
Here's the count of the unique. Further down, here's the count of each unique.
What's the worst possible thing that could happen?
What's the best worst thing that could happen, right?
So on this particular day, there were four possibilities that had a max of seven, right?
So as I'm cruising through to look for these, so starting here from the seven, I'm going to press control right arrow four times, and analyze the four possible words.
First one is damps. Damps is not a word that it could be.
There's seven unique constellations, and the worst possible case is that I get an item that appears four times, blank, Y, blank, blank, blank.
Control right arrow again, dimps, same number, seven and four.
Control right arrow again, dumps, seven and four. Control right arrow again, kedge, seven and three.
Control right arrow again, that's it.
I didn't like any of those, and we know that there's several additional words that provided six.
So control right arrow, and again I'm looking for something that might possibly be the word, right? But I didn't like that five, the max.
There's a chance there that I would only narrow these seven words down to five words.
Dusky, pudgy, spade ... Wow, there's too many.
I think that's why I came back up here and said, "What's the best thing that could happen?
The best worst thing that could happen?" And I ended up here at dumbs, D-U-M-B-S, six possible constellations.
The worst possible outcome would be that I would have three words to choose from. So I plug that in.
I got gray, gray, yellow, gray, gray.
I'm applying a filter here, gray, gray, yellow, gray, gray, and victory, because there's only one possibility.
I lucked out that the word that day was frame, and I'm done. Isn't that crazy?
That guessing dumbs, which can't possibly be the right word, allowed me to solve this in three.
I went back to my other solver, the AROSE solver, guessing AROSE.
And on that particular day, it required four answers.
But what I've learned is, this method is not always going to be better than the AROSE solver.
But it will be better than AROSE, statistically I'll end up with better answers, by using this method instead of the letter frequency method that I was using before.
Now, the others are going to tell you that trace is the best word.
Statistically, trace is a really good word.
But there will be some days, there will be some Wordle words, where trace could potentially give you only narrowing it down to 246, from 2,315 to 246.
So I woke up this morning and I said, "I'm going to try something else other than trace," right?
So fewest constellations, but I was looking for something that had a better worst possible, and slate came up like instead of 246, maybe 221.
And so I guessed slate, and to my shock I ended up at that 221.
So whereas yesterday I was able to after the first guess narrow it down to 10, today I narrowed it down to 221, which was not exciting.
So now, the 221 words here ... And actually, I love the way that I generate this.
Roger in Wales is a huge fan of the advanced filter, and I have to tell you it works beautifully here.
Because what I learned is these are the 221 words, and I want to pull those 220 words forward from the universe, right?
And the amazing way to do this is just to come up here to a blank cell, data, filter, advanced, and I want to copy to another location.
I'm going to copy from the name range of the universe.
My criteria range are all the words today, all 221 words.
And my CopyTo are all 12,972 words plus the word word.
Click okay.
Now, this is not instantaneous because it's returning 12,973 columns, but that wasn't bad.
That was five or six seconds to get my universe narrowed down to just these words.
Okay, so repeating the same steps again from these 221 words, the best case would be 72 unique constellations that happen three times.
The best worst situation would get me down to 14 letters, and the word round matched both of those, right? So it had a 72, it had a 14.
It had the advantage of being a word that it could be.
So I guessed round. I got yellow, yellow, yellow, gray, gray.
That cut me down to these seven words.
And this time when I looked for the results of how many unique constellations I could get, there were seven words.
There were two words that I could guess that had seven unique constellations.
This is the end game strategy where you're not trying to get it on the next guess.
You're trying to make sure, for sure, that you're going to get it on the second guess from now, all right? So starting here at the seven, control right arrow, we see two.
It gives us seven constellations, and it can't possibly be the word.
Control right arrow, and curfs gives us seven constellations.
If I guess either of those, then it's going to be narrowed down to exactly one word.
Now if I would have just guessed one of these seven words, then it's a one in seven chance, 14% chance, I'm going to get it right on three, but an 86% chance that I'm not, right?
And for those 86% chance, I wanted to make sure that I absolutely knew for sure what the answer was going to be in the fourth guess. So choof, and then the only thing left was humor.
Every few days I report back to Larry Robinson, who encourages me.
I said, "Larry, I love the Excel that's happening here, some amazing Excel, but there's nothing for anyone to download.
There's no easy set of steps that you can go through every day.
You kind of have to be a little OCD in order to go through these steps each day, or really just love Excel.
I don't know".
And what's worse is, after solving the puzzle each day using this method, I then go back and use the old method with AROSE and letter frequency.
It just so happened that today, using AROSE, I did solve it in three, right?
So this method isn't better every time, but it's better more times. Here's another approach.
I'm taking that last analysis, and so if I guess aback, there's some chance that I'm going to end up with 288 possible words.
Oh geez, there's a chance I'm going to end up with 925 possible words.
That means there's 925 Wordle words that would return the exact same constellation of answers.
So I took those numbers up there, and I used the sort function to sort descending, right?
And a couple things that we're interested in here, like if you guessed aback, it had 925 possible words instead of 2,315.
Yeah, you eliminated a bunch of words, but it's not as good as getting down to 10, right?
And so I copied that across, yeah, and then kind of tried to bucket this, right?
Like, is there ever a word that I could guess that I would end up with more than 1,000 words? And there are.
Here in this case, aback; if I would guess aback, there's 925 possible Wordle words where I will end up with 925, and so on down here. So I have a couple of metrics.
One, what are the percentage of days, of the first 2,315 Wordle puzzles, where I'm going to end up with more than 100 words? And then this guess-in-two is kind of an interesting thing.
So nine times out of 2,315 I'll know for sure. 100% times nine, divided by 2,315.
And then there will be 16 times out of 2,315 where I'll have a 50/50 guess for word two, and nine divided by 2,315, where I'll have a 33% guess.
So this kind of totals that whole thing up, right?
On the top end, I can get to the point where I'll be able to guess in two, 4.45%. On the bottom end, it's only like 0.38, a third of a percent.
So you might want to maximize in two, or minimize the percent of the time that you're stuck with more than 100 words after the first guess.
Looking down here, the max of that is 94.6. The min is 16.2.
You definitely would, I think, rather have the 16.2 instead of the 94.6.
So, let's take a look at all of the possible guesses.
If I want to maximize the chance of being able to guess in two, parse, crate, trace; trace comes up again on the bottom end of this.
This is again, if you're in a bar bet with your friend and you say, "Hey, I bet you can't guess it in five, but I get to choose the first word".
Kukus, jujus, these are really bad first words, yeah.
All right, then let's look at the, what are the chances I'm going to be over 100 after the first guess?
So tares, T-A-R-E-S, or saner, aisle, alone, all seem to minimize that chance of being over 100.
I seem to have this obsession with guessing a word that it could be.
But is tares at 16% good enough that I give up the one in 2,315 chance of getting it in one word, in order to drop down to saner?
Especially, we could go back and see if saner was ever a word yet, in which case this little one here isn't important, because they're not going to repeat words.
On the bottom end of this, there are some really bad words.
Yukky, jeeze right? You guess those, you have more than a 90% chance of having more than 100 words.
So depending on your strategy, if you're trying to minimize the chance of having over 100 words, maybe some of these green words will work.
If you're trying to maximize the chance of winning in two, then parse or crate or even trace isn't bad.
All right, so this table here; 10 interesting words, really bad words, really good words.
How many times out of 2,315 games will you end up with more than 1,000 words? Kukus, 1,258, jujus, 1,353, kudzu, 1,369, yukky, 1,368, jeeze, 1,226.
If you would guess these words, you're never going to have more than 1,000, never 500 to 999, but there are chances here. Trace, crate and parse, you'll be 246.
If you want to make sure that you always have less than 200 words, then aisle or alone would be the words that make sure you never fall into that category.
And then down here on this other end, what are the chances that after one guess, there's only going to be one possible word? And so parse or crate are there.
If you're just trying to make sure that you can win in three, the chances of two possible words, same sort of numbers there. So that's where we stand.
The others have written programs that look through every possible combination, do a lot more higher-order math, but I'm doing some really fun Excel things.
Being quoted in that CNN article ... It's funny, they never called me.
I didn't know I was going to be in that article, but a lot of people have seen that.
My friends at Florida Citrus Sports did their member spotlight on me, calling me a Wordle expert who's also known as MrExcel.
That's funny. Yeah, so here we are.
It's a lot of great Excel.
If you have any thoughts, please, down in the YouTube comments, let me know.
You know, maybe there's somewhere else to take this. I'm not sure.
This is an insanely long video, and let me just save you some time.
I geek out, because I can run one and a half billion calculations in Excel without crashing.
You already know this: the new dynamic array formulas are wildly helpful. You probably don't know, when you get an email from Larry Robinson, it can turn into an obsession.
And just for any of you who are still playing AROSE as your first Wordle word, there's better words, TRACE.
But there's other better words depending on your strategy.
I never know what Excel video is going to take off, right?
And that Wordle video where I chose AROSE has now have people calling me a CNN-cited Wordle expert, which is just insane.
There's people who are doing this much better than I am, and I'll send you links to those.
This is a weekend.
If it's snowing where you're at, and you hate the Super Bowl, and you need a video to put you to sleep, this is it.
For all of my regular viewers who are looking for something cool in four or five minutes, I'm not offended. Skip this one.
I'll see you on Monday.
Excel is a miraculous program for its ability to deal with large amounts of calculations without any problem.
One of the earliest things I wanted to do was to build a little model here where if I typed in the Wordle word of the day and made a guess, could I generate the green, gray and yellow tiles?
Now, Wyn Hopkins had already solved this, and I could have downloaded Wyn's workbook to try and look at his code.
But I just started out here, and just to solve this simple little problem, with 53 formulas, there is some cool Excel stuff going on here, right?
So I have a five-letter word here, and I want to break that out into five horizontal cells.
So the mid-function with the sequence of five would give me five vertical cells, but I want horizontal cells.
So rather than use transpose, check this out in the sequence here.
I ask for one row of five columns, and that forces it to go across. Same thing here for trace, which are green.
This is easy.
If the letter here is equal to the letter here, then I have a green cell. Otherwise, it's not green.
Which, do we still have to score? In other words, so we know that R and A are in the correct spot.
We don't have to worry about those anymore, but I still have to worry about this one, this one.
Simple little formula there, right? And then I was really happy with this.
If we still have to score it, I want to bring that letter down.
But if we don't have to score it anymore, I want to put something there that's not going to be found as a match. And rather than a letter, I put a number.
And instead of just any number, I use the column function.
That way, it'll generate three, four, five, six, seven here, and that will never match to T-R-A-C-E.
What are the guess letters that are not scored yet? Same basic logic there, okay?
And then for which letters are gray, this was going to be easy, I thought.
I'll look for a T somewhere in here, and if there's none then this is a gray cell, right?
And that was all good, and I used this for about two weeks, and Dan Mayoh from Fintega used this. And then he wrote to me.
He said, "Hey, your algorithm just threw out a word that was the right word".
Dan had done some drilling down, and he figured out that the problem was when the guess had two or more of the same letter, MOMMA being the extreme example of three.
The actual word itself has not that many, like just one M, so I'll go with A-M-E-E-E.
I was reporting those extra Ms as not gray, which was forcing them to show us as yellow, right? So thanks to Dan for figuring this out.
I had a simple little formula there, but then three more rows of formulas to look for that weird situation where the guess has multiple duplicate letters and the answer doesn't, and to detect that and to correct the gray.
So in this case here, guessing MOMMA, it would have given me not grays for the second and third M, but in fact it should be gray for the second and third M because there is only one M in the word.
The yellow one was the one I thought was going to be really hard, and that was the one I actually thought I was going to have to download Wyn's spreadsheet to take a look.
But it's really easy.
If the cell is not gray and not green, then guess what? It's yellow, right?
So this was really easy, just one minus, is it gray, minus is it green? And that gives me the yellow cells.
To convert these series of ones and zeros, well, instead of just an if formula that was nested, I used the ifs function, which is cool. So if C7 is one, then it's green.
If C20 is one, then it's gray, and I used a dash for gray.
If C22 is one, then a yellow.
And you have to finish out the ifs with this thing that is always true in what to happen. And this is good.
The Z should never show up.
When I was working on this fix for the Dan Mayoh discovery, it came up Z a few times. I'm like, "Okay, I need to fix that".
And then finally, the very last formula is a little CONCAT formula.
You know, I love TEXTJOIN, and I say TEXTJOIN is superior to CONCAT in every way, except for when we just need to take five cells and smash them together.
Then that works out really great.
Okay, now before we get to the million cells, I want to thank Larry Robinson at the MrExcel message board.
He prompted all of this.
He started asking me questions about my first Wordle video.
But since then, we've both watched and studied at GitHub, Laurent Lessard and his amazing analysis, and then the beautiful YouTube video, 3Blue 1Brown. So this is not a Wordle video.
I defer all Wordle logic to those two gentlemen, because they have figured it out, right?
This is an Excel video, right? I'm just geeking out about how amazing the Excel-ness is here, okay?
So what did I say? Was it 53?
To get down to the point where I can put in a word frame and my guess, D-U-M-B-S, and it correctly will score this as gray, gray, yellow, gray, gray, which matches the Wordle website itself.
Down the left-hand side here, instead of the Scrabble dictionary that I used in the last video, 8,000 words, I've used the actual word list, 2,315 words that Wordle might use someday.
This is the whole population of five-letter English words.
Josh Wardle, who created Wordle, his girlfriend went through those words and chose ones that she thought were valid answers, right?
So there's only 2,315 words that can happen, and down the left-hand side here, I have all 2,315 words.
Across the top, I have all 2,315 words going across.
The theory is, if the actual Wordle word is this going down the left-hand side, and this is the word that I guess, what will the constellation be? That's Laurent's term for the answers.
And like you'll see here, if you get G-G dash, dash, dash, then that means that it could be any of these, or probably many others that are further down, right?
So the worst thing that can happen, and it actually happened earlier today, is you put in a guess and instead of narrowing it down to 10 words, it narrows it down to 220 words.
This morning, it went from 2,315 words down to 221, which is not a great improvement.
I mean, it's a tenfold improvement but it's not getting it down to 10.
All right, here's the amazing thing.
I'm going to choose this whole range, and control backspace to bring that top left corner cell back into view.
From data, what-if analysis data table, across the top is the word that's guessed.
I'm going to take each of these 2,315 words across the top, and plug them into B5.
And down the left-hand side, the actual Wordle word ...
If you keep playing Wordle long enough, all 2,315 of these will come up sooner or later.
That would go into here, right?
Now, I'm not going to press okay, because it takes a few minutes.
What happens here is, this generates a table formula.
And in this table formula, if you let it calculate, there are 5,359,225 possible combinations of, this is the Wordle word and this is your guess.
Those are the constellations that you're going to get. I actually walked away.
I figured this would take an hour.
When I came back five minutes later and it had finished calculating, I was pretty astounded. Five million sets of calculations ...
It's 5,359,225 cells that are populated down here, and each one of those cells required 53 formulas.
Every intersection here, they do all 53 formulas to come up with this answer in the yellow cell.
That's 284,038,925 calculations in about five minutes or so.
It's really amazing.
Now, before Laurent and 3Blue 1Brown posted their solutions to Wordle, the question came up.
"Do I only have to look at the 2,315 words that it could be?" There's a second list of 10,000 and some words that will never be the answer, but you are allowed to guess.
Are there times where it helps to make a guess that's not an actual Wordle solution?
And this actually happened with this puzzle, right? The correct word was frame.
After trace, I had it down to 10, and that was beautiful.
But there was a lot of duplication within the 10, and I actually ended up choosing a word that can't be the Wordle word, dumbs.
Because after choosing dumbs, I was guaranteed to get it down to just one or two possibilities.
I'll show later how we came up with that, right? So I really pushed back on this.
I said, "I'm always going to guess words that's the correct word". But I've since learned ...
It was Larry and Dan both said, "You need to test it both ways.
You need to test the possibility of answering a word that won't be the answer, just in order to knock a whole bunch of other letters out.
Sometimes that will be the best strategy". Hey, this is a new file.
They convinced me that I had to consider the 2,315 possible Wordle words against the larger population of 10,657 words that will never be the Wordle answer, but are valid.
Exact same logic, the same 53 formulas there, but now it's 24,670,955 cells times the 53 formulas.
That is an astounding 1,307,560,615 cells. I can't tell you how long this took.
It was longer than I could stand to watch, but it was less than an hour.
It didn't crash the computer, which I think is impressive, although I very definitely copied and pasted those values so it would never have to calculate again.
Well, I thought it would never have to calculate again, until Dan Mayoh found my logic error, and then I had to calculate it one more time.
Welcome to this range, which I call the Wordle universe.
So from the first workbook that did 284,000,000 calculations, and the second workbook with 1,307,000,000 calculations, that means this is 1,596,950,818 calculations all represented right here, down the left-hand side.
2,315 words that the actual Wordle could be on any given day.
Across the top, those same 2,315 words followed by 10,657 words that you are allowed to guess but will never be the Wordle word.
So that's 2,315 times 12,972.
That means that in this spreadsheet right here, not counting the words at the top or the side, the number of constellations here is 30,030,180.
It's like this whole thing, and there's the count down there.
And again to get this, it's the result of 1,596,000,000 calculations, all in a spreadsheet that I'm paying $10 a month for.
With kudos to the better solvers, who are using high-end programming languages, my $10 spreadsheet is getting me really far along this path.
This can be up here. This is really important.
The first 2,315 cells here have a one, and then after that it's a zero.
As I'm playing Wordle each day, that becomes an important factor.
Like, "Do I want to make a guess that could be the answer?
Is there some chance that I'm going to win on the next guess, or am I playing to solve it in the second guess?" Sometimes it seems better to play it where you're solving it in the second guess.
Now that I have the Wordle universe, the question is what's the best first word?
And last time, I said it was AROSE or arise, and that's not my best word anymore.
The range that we have up here is 30,030,180. It's a lot of cells.
It's very wide.
It's very frustrating when I want to copy this formula to the right. It's hard to get out here to S-E-A.
So I'm going to cruise down here, 2,315 words down the left-hand side.
These are the Wordle words that could be. Here's all the words we're allowed to guess.
I'm going to control down arrow and cruise down a little bit here to this range.
This range is 12,972 columns wide and there's only 12,972 formulas here.
It basically asks the question of, "What are the unique constellations that we might guess, had we guessed aback?" And what I've determined is the more constellations you get, the more information you're going to have, right?
So if there's a word that only gives us 20 constellations, that means that 2,315 divided by 20, you're going to end up with hundreds of possibilities.
But if you had 150 possibilities, then that's a better variability, which means that there's going to be less words that are going to match any given constellation.
All right, so I copied this across for all 12,972, all right?
So that's impressive that there's 12,000 unique functions there, that are analyzing 2,300 cells each, and it all calculates pretty quickly.
And then the count, and this is counting using the array indicator there, the hash to say, "Count how many answers we had from there".
And so here if I'd guessed aback, there's 57 possible answers that I'm going to get.
What's the best, right? So if I look through this, the max.
What's the most number of constellations that I can get?
In theory, some would say that this could be green, yellow or gray, so it's three to the fifth power, 243 possible combinations.
So getting 150 of the 243 possible, that's impressive, but it's not possible to get all 243.
For example, if you had a word that was G-G-G-G, four greens in a row, it can't possibly be a yellow.
Thanks to Larry Robinson for pointing that out to me.
So several of the 243 just simply aren't possible. I'm interested in which ones might have 150.
Now normally, what I've been doing is not just asking for the max, but ask for the large.
I want to see the 10 largest, so the sequence of 10, that little formula there, right?
There's only one word that has 150 constellations, then after than 148, 148, 147, 147.
Down here, I put a sequence of 150 and I cruise down to the 150.
If I would control right arrow from here, I'm going to end up at that one word, that one magic word, that has 150 constellations.
That word is trace. Trace is now my new favorite word.
But there are other possible favorite words, like let's look at the 148s.
So I come down here to 148.
There should be three of them now, and the first one is crate, and then trace, and then this one is salet.
Now, I'm not sure I like salet because it can't possibly be the right word.
But what I do like is an anagram of salet, which is slate.
There's slate, and slate unfortunately only gives us 147 constellations.
But some days, that feels okay. Like this morning, I guessed slate.
All right, I transpose those other results, input it here.
So these 10 words are the words that return the most constellations.
I want to have that one-in-2,315 chance that I'm going to solve it on the first guess.
Sooner or later, that is bound to happen.
And so I really think that out of these, it's trace, crate, slate and parse that are probably the words that I'm going to choose on any given day.
But wait, there's another way to look at this.
So one of these constellations here, like G, dash, dash, Y, dash; how many times does that constellation appear, right?
So I'm going to come down here below my 150 rows, where I repeat all 12,972 columns. And this time, the calculation is much harder.
I'm doing a COUNTIF of the original 2,315 constellations, had I guessed aback.
And then the question is, how many times is it each of these answers returned by this array?
So in this case, I'm running the COUNTIF essentially 57 times down here, right? And so let's just look.
Had I guessed aback, there's one combination that's going to appear 925 times.
That would be terrible.
That would be a terrible first guess, to come up with number 44. Let's come up and see what that is.
It's probably no hits at all.
Yeah, so if I get five gray tiles and I guessed aback, I've only gone from 2,315 words down to 915 words.
That would be a very disappointing first word, right?
So I asked the question of, what's the worst thing that could happen?
What's the most number of words that will still be in play after this first guess?
And that's a column up here called max, max. And in this case, high numbers for max are bad.
I want the lowest numbers for max, so we ask for the small of all the maxes, comma, sequence of 10.
And there's some words where the worst thing that can happen to you is it gets narrowed down to 168.
So, that's taking the max column. This time we're going to sort smallest to largest.
Raise, arise, which in my other video was my second choice, these next several cannot be the right word, right?
So depending on your strategy, is it that you want to have the most unique combinations, or you want to have the lowest possibility of having a whole bunch of words after the first guess?
You might come up with raise or arise, trace, crate, slate, parse, raise, arise. Those are great words to choose from.
Now when I was talking to Dan Mayoh I said, "Well, we should really choose a different word every day.
Because when Josh Wordle becomes aware that Laurent and the others have pronounced trace as being the best word, he might start throwing words in that will make it more difficult for us to win".
And Dan said, "Well, yeah. You're putting emotions in there.
The 2,315 words have already been determined. The order's already been determined.
Each one's going to appear once, and so there's no evil actor trying to make it harder for you".
All right, part three.
This one, two, three, four ... Four worksheets in this workbook.
This first worksheet ... I never come here.
It's just simply used by formulas on the other sheets ... It's the universe.
It's every possible word that could be the Wordle answer today, with every possible guess, the 30 million combinations with a great name of universe.
Bill best; this is a very small sheet, 2,315 rows down the side, just the words that are possible good words across the top.
Out here, just for completeness, I've included the words that a lot of people were using as their first words.
AROSE, ADIEU ... which by the way, that's a horrible first word.
It will never hit.
A Tweet that said, "The day that ADIEU is the word, Twitter will break. It's never going to happen.
It's not in the 2,315 words".
So I just put these out here for completeness, and the idea is that every day I'm going to choose which word from these.
Preferably not the gray columns, because those are words that will never appear, right?
So trace or crate or slate or parse or raise or arise, whatever mood strikes me that day.
I put that into the Wordle website, so I guessed trace, and I came back with gray, green, green, green, gray, green.
So then whichever word that I had chosen that day, I apply a filter just to that column, and I look for this result.
So, dash, green, green, dash, green, click okay. Oh, what a great day this was.
There are only 10 possible answers. I went from 2,315 answers down to 10.
What a beautiful, beautiful day that is, all right?
So now, I don't have to worry about the 2,315 words.
The question is, given this population of 10, what's the best guess?
Welcome to the sheet called step two, across the top, 12,972 words.
Down the left-hand side, the words that are still in play.
On this particular day, there's only 10 rows.
Down here, I repeat those formulas. Here's the unique.
Here's the count of the unique. Further down, here's the count of each unique.
What's the worst possible thing that could happen?
What's the best worst thing that could happen, right?
So on this particular day, there were four possibilities that had a max of seven, right?
So as I'm cruising through to look for these, so starting here from the seven, I'm going to press control right arrow four times, and analyze the four possible words.
First one is damps. Damps is not a word that it could be.
There's seven unique constellations, and the worst possible case is that I get an item that appears four times, blank, Y, blank, blank, blank.
Control right arrow again, dimps, same number, seven and four.
Control right arrow again, dumps, seven and four. Control right arrow again, kedge, seven and three.
Control right arrow again, that's it.
I didn't like any of those, and we know that there's several additional words that provided six.
So control right arrow, and again I'm looking for something that might possibly be the word, right? But I didn't like that five, the max.
There's a chance there that I would only narrow these seven words down to five words.
Dusky, pudgy, spade ... Wow, there's too many.
I think that's why I came back up here and said, "What's the best thing that could happen?
The best worst thing that could happen?" And I ended up here at dumbs, D-U-M-B-S, six possible constellations.
The worst possible outcome would be that I would have three words to choose from. So I plug that in.
I got gray, gray, yellow, gray, gray.
I'm applying a filter here, gray, gray, yellow, gray, gray, and victory, because there's only one possibility.
I lucked out that the word that day was frame, and I'm done. Isn't that crazy?
That guessing dumbs, which can't possibly be the right word, allowed me to solve this in three.
I went back to my other solver, the AROSE solver, guessing AROSE.
And on that particular day, it required four answers.
But what I've learned is, this method is not always going to be better than the AROSE solver.
But it will be better than AROSE, statistically I'll end up with better answers, by using this method instead of the letter frequency method that I was using before.
Now, the others are going to tell you that trace is the best word.
Statistically, trace is a really good word.
But there will be some days, there will be some Wordle words, where trace could potentially give you only narrowing it down to 246, from 2,315 to 246.
So I woke up this morning and I said, "I'm going to try something else other than trace," right?
So fewest constellations, but I was looking for something that had a better worst possible, and slate came up like instead of 246, maybe 221.
And so I guessed slate, and to my shock I ended up at that 221.
So whereas yesterday I was able to after the first guess narrow it down to 10, today I narrowed it down to 221, which was not exciting.
So now, the 221 words here ... And actually, I love the way that I generate this.
Roger in Wales is a huge fan of the advanced filter, and I have to tell you it works beautifully here.
Because what I learned is these are the 221 words, and I want to pull those 220 words forward from the universe, right?
And the amazing way to do this is just to come up here to a blank cell, data, filter, advanced, and I want to copy to another location.
I'm going to copy from the name range of the universe.
My criteria range are all the words today, all 221 words.
And my CopyTo are all 12,972 words plus the word word.
Click okay.
Now, this is not instantaneous because it's returning 12,973 columns, but that wasn't bad.
That was five or six seconds to get my universe narrowed down to just these words.
Okay, so repeating the same steps again from these 221 words, the best case would be 72 unique constellations that happen three times.
The best worst situation would get me down to 14 letters, and the word round matched both of those, right? So it had a 72, it had a 14.
It had the advantage of being a word that it could be.
So I guessed round. I got yellow, yellow, yellow, gray, gray.
That cut me down to these seven words.
And this time when I looked for the results of how many unique constellations I could get, there were seven words.
There were two words that I could guess that had seven unique constellations.
This is the end game strategy where you're not trying to get it on the next guess.
You're trying to make sure, for sure, that you're going to get it on the second guess from now, all right? So starting here at the seven, control right arrow, we see two.
It gives us seven constellations, and it can't possibly be the word.
Control right arrow, and curfs gives us seven constellations.
If I guess either of those, then it's going to be narrowed down to exactly one word.
Now if I would have just guessed one of these seven words, then it's a one in seven chance, 14% chance, I'm going to get it right on three, but an 86% chance that I'm not, right?
And for those 86% chance, I wanted to make sure that I absolutely knew for sure what the answer was going to be in the fourth guess. So choof, and then the only thing left was humor.
Every few days I report back to Larry Robinson, who encourages me.
I said, "Larry, I love the Excel that's happening here, some amazing Excel, but there's nothing for anyone to download.
There's no easy set of steps that you can go through every day.
You kind of have to be a little OCD in order to go through these steps each day, or really just love Excel.
I don't know".
And what's worse is, after solving the puzzle each day using this method, I then go back and use the old method with AROSE and letter frequency.
It just so happened that today, using AROSE, I did solve it in three, right?
So this method isn't better every time, but it's better more times. Here's another approach.
I'm taking that last analysis, and so if I guess aback, there's some chance that I'm going to end up with 288 possible words.
Oh geez, there's a chance I'm going to end up with 925 possible words.
That means there's 925 Wordle words that would return the exact same constellation of answers.
So I took those numbers up there, and I used the sort function to sort descending, right?
And a couple things that we're interested in here, like if you guessed aback, it had 925 possible words instead of 2,315.
Yeah, you eliminated a bunch of words, but it's not as good as getting down to 10, right?
And so I copied that across, yeah, and then kind of tried to bucket this, right?
Like, is there ever a word that I could guess that I would end up with more than 1,000 words? And there are.
Here in this case, aback; if I would guess aback, there's 925 possible Wordle words where I will end up with 925, and so on down here. So I have a couple of metrics.
One, what are the percentage of days, of the first 2,315 Wordle puzzles, where I'm going to end up with more than 100 words? And then this guess-in-two is kind of an interesting thing.
So nine times out of 2,315 I'll know for sure. 100% times nine, divided by 2,315.
And then there will be 16 times out of 2,315 where I'll have a 50/50 guess for word two, and nine divided by 2,315, where I'll have a 33% guess.
So this kind of totals that whole thing up, right?
On the top end, I can get to the point where I'll be able to guess in two, 4.45%. On the bottom end, it's only like 0.38, a third of a percent.
So you might want to maximize in two, or minimize the percent of the time that you're stuck with more than 100 words after the first guess.
Looking down here, the max of that is 94.6. The min is 16.2.
You definitely would, I think, rather have the 16.2 instead of the 94.6.
So, let's take a look at all of the possible guesses.
If I want to maximize the chance of being able to guess in two, parse, crate, trace; trace comes up again on the bottom end of this.
This is again, if you're in a bar bet with your friend and you say, "Hey, I bet you can't guess it in five, but I get to choose the first word".
Kukus, jujus, these are really bad first words, yeah.
All right, then let's look at the, what are the chances I'm going to be over 100 after the first guess?
So tares, T-A-R-E-S, or saner, aisle, alone, all seem to minimize that chance of being over 100.
I seem to have this obsession with guessing a word that it could be.
But is tares at 16% good enough that I give up the one in 2,315 chance of getting it in one word, in order to drop down to saner?
Especially, we could go back and see if saner was ever a word yet, in which case this little one here isn't important, because they're not going to repeat words.
On the bottom end of this, there are some really bad words.
Yukky, jeeze right? You guess those, you have more than a 90% chance of having more than 100 words.
So depending on your strategy, if you're trying to minimize the chance of having over 100 words, maybe some of these green words will work.
If you're trying to maximize the chance of winning in two, then parse or crate or even trace isn't bad.
All right, so this table here; 10 interesting words, really bad words, really good words.
How many times out of 2,315 games will you end up with more than 1,000 words? Kukus, 1,258, jujus, 1,353, kudzu, 1,369, yukky, 1,368, jeeze, 1,226.
If you would guess these words, you're never going to have more than 1,000, never 500 to 999, but there are chances here. Trace, crate and parse, you'll be 246.
If you want to make sure that you always have less than 200 words, then aisle or alone would be the words that make sure you never fall into that category.
And then down here on this other end, what are the chances that after one guess, there's only going to be one possible word? And so parse or crate are there.
If you're just trying to make sure that you can win in three, the chances of two possible words, same sort of numbers there. So that's where we stand.
The others have written programs that look through every possible combination, do a lot more higher-order math, but I'm doing some really fun Excel things.
Being quoted in that CNN article ... It's funny, they never called me.
I didn't know I was going to be in that article, but a lot of people have seen that.
My friends at Florida Citrus Sports did their member spotlight on me, calling me a Wordle expert who's also known as MrExcel.
That's funny. Yeah, so here we are.
It's a lot of great Excel.
If you have any thoughts, please, down in the YouTube comments, let me know.
You know, maybe there's somewhere else to take this. I'm not sure.
