Sudoku Players' Forum (clone)

by **Mathimagics** » Wed Jan 19, 2022 3:13 am

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WORDLE, of course, refers to Josh Wardle's game (Wordle), but the observations below are probably applicable to the many clones that have appeared.

The standard elements are:

DICT words: the dictionary, ie word list, the set of all 5 letter words that are allowed for any guess.

GAME words: a subset (~20% of the DICT) of words that can be selected by the app as the code word (target word).

The questions that interest me are these:

Q1: What are the best word(s) to use for the initial guess?

Q2: Would a 6-letter WORDLE be harder?

To investigate these questions, I created a simple robotic player, which I call Marvin.

The approach is quite simple. Each game simulation involves fixing a target word, and one or two initial guess words, and then:

tests the initial guess(es), obtaining a result code (Yellow, Green, Grey) (eg: [YXXGX])

enters the guess loop:
- from the result codes identify the implied constraints implied (letters present, letters excluded, etc)
- find all words that satisfy these constraints
- select one at random as the next guess
- rinse-n-repeat until only one possibility remains

A simulation run was done for various initial guess choices. Each run fixed 1 or 2 initial guess words, and ran the simulator against all the GAME words. This was done 5 times for each initial guess and the results aggregated. I give 3 measures for comparison:

GPW = average guesses per game

total game score: 5 points for solved at guess #2, 4 points for guess #3, etc. No points for failure to solve in 6 guesses.

weighted score: 16 points for solved at guess #2, 8 points for guess #3, 4 points for guess #4, etc.

I will report the results in the next post.

by **Mathimagics** » Wed Jan 19, 2022 4:06 am

I tested various 1-guess and 2-guess approaches. In the table below, GPW is average guesses to finish the game, S is the linear score, WS is the weighted score. Simulation ran 5 x 2315 = 11575 games for each initial guess choice.

Code: Select all: # guesses => 2 3 4 5 6 7+ GPW S WS -------------------------------------------------------------------------- RAISE 647 1655 3503 2956 1684 1125 5.135 27960 45200 CRATE 755 1801 3582 2957 1502 973 4.949 29141 48232 TRACE 734 1776 3643 2948 1519 950 4.933 29118 47939 TRAIN 665 1711 3529 3073 1624 968 5.000 28526 46214 RAISE CLUMP 4351 3141 2474 1041 558 4.393 32841 53441 SATIN HORDE 4723 3066 2224 983 569 4.336 33546 55559 TRIPE COALS 5093 3129 2025 845 478 4.201 34654 58155

RAISE and CREATE both appear regularly in other people's recommended words list.

Guardian article wrote:Ian Gowers, a mathematics professor at Cambridge, suggested choosing two words with a lot of commonly used letters where none are reproduced, for example “tripe” followed by “coals”.

And this in fact was the overall best performer for Marvin.

6-letter results

I naively assumed that a 6-letter game would be harder, after all, the DICT size is almost doubled. So I was somewhat taken aback by Marvin's report:

Code: Select all: # guesses => 2 3 4 5 6 7+ GPW S WS -------------------------------------------------------------------------- RAISED 166 2292 3621 1983 773 780 4.801 25600 40215 TRACED 216 2374 3727 1967 682 649 4.624 26373 41972 DECANT 226 2327 3844 1889 688 646 4.621 26436 42074 BANGED PURIST 3339 4154 1420 432 270 4.109 29090 46600 COMING PASTER 2988 4233 1524 487 383 4.266 28186 44371 CHINOS GARBLE 3081 4301 1544 426 268 4.146 28741 45366 LASTED PORING 2940 4200 1562 511 402 4.296 27995 43955 RINGED COSTAL 3202 4161 1388 474 395 4.236 28541 45510

I should point out that my target pool for 6-letter words has only 1924 words in it (and 23033 words in the DICT), so the scores look lower because I didn't scale them.

In any case, it's the GPW results that are interesting. Marvin finds the target with fewer guesses on average than for 5-letter Wordle.

This highlights a fundamental truth, I think - that the more letters there are in the game words, then the more information content there is to be had from the initial guesses.

My conclusion: 6-letters is in fact easier than 5, and if I were to build a game app for 6-letter play, I would seriously consider making 5 guesses the cutoff point!

by **Mathimagics** » Wed Jan 19, 2022 6:51 am

.
Some sample games (6 letters) from Marvin, with 2 fixed guesses. This numbers on the right are the number of possible words (NPW) after each guess.

Code: Select all: M A N G L E . Y G . . . 80 P U R I S T . G Y . . . 2 K U N K A R . G G . G Y 1 R U N W A Y M A N G L E . Y G . . . 80 P U R I S T . G Y . . . 2 R U N W A Y G G G G G G 1

Code: Select all: M A N G L E . G . . . . 532 P U R I S T . . . Y Y . 26 Z A I D A S . G Y . Y Y 3 F A S C I A . G G Y G G 1 C A S S I A M A N G L E . G . . . . 532 P U R I S T . . . Y Y . 26 H A I C K S . G Y Y . Y 1 C A S S I A

by **coloin** » Thu Jan 20, 2022 7:25 pm

Greetings Oh My !

I have my first word worked out .....
and then worked out before hand the next word options depending on vowels / consonants and how many letters ....
It depends if you want to try to do it in 2 [get lucky with first word] or play safe with an unrelated [to the first] word

scores
3-3
4-8
5-4
6-1

so my GPW average is 3.9 given that i have been improving as time goes....

by **Mathimagics** » Fri Jan 21, 2022 6:20 am

coloin wrote:so my GPW average is 3.9 given that i have been improving as time goes....

With no failures assumed, that's 16 games, so GPW should be 4.2 [ (3*3 + 4*8 + 5*4 + 6*1) / 16 = 4.1875 ]
Marvin thinks that you divided by 17 instead ... tsk, tsk, shame on you !

coloin wrote:I have my first word worked out ..... and then worked out before hand the next word options depending on vowels / consonants and how many letters ....

Is it like Quantian's method? For a fixed initial word (RAISE) he computed the next best word based on the YGx result and produced a table of next word choices.

Quantian wrote:Under optimal play, the hardest word to find is BOXER: you guess RAISE, then NOTED, then WHELM, then FARCE, then JOKER, and finally BOXER. Average word takes 3.56 guesses.

It is hard to know what "optimal play" refers to, as no details are given. I implemented his 2nd-guess table (based on first guess = RAISE), and for this option Marvin gets a GPW of 4.58, which is quite similar to the results for fixed 2 guesses like TRIPE + COALS, and is well short of Quantian's GPW = 3.56 !!

So, I am trying to work out what Quantian's "optimal play" method might be from the list of guesses he gives for BOXER.

by **1to9only** » Sat Jan 22, 2022 11:31 am

Interesting reading: https://medium.com/@tglaiel/the-mathematically-optimal-first-guess-in-wordle-cbcb03c19b0a
A quick summary:
- There are 2315 possible solutions, and 12972 words it accepts as guesses.
- ROATE is the optimal first guess, if the metric you’re measuring is “the size of the possible solution list after a guess”.

by **Mathimagics** » Sat Jan 22, 2022 2:12 pm

Thanks 1to9only, an interesting read.

I see further down that he eventually decides that RAISE is best ...

I want to evolve Marvin (he's so depressed) into a "true bot", and to evaluate which approaches are actually more likely to win in general play - see Wordle Botfight - where a bot needs the ability to perform well for ANY target word in the list of 12972.

I see that the competition is stiff, with the leaders obtaining getting close to 4 GPW ... that's pretty impressive.

by **coloin** » Sat Jan 22, 2022 2:14 pm

Thankyou will read it .... is IRATE up there too i wonder ?
And has anyone got the words .... asking for a friend !

by **1to9only** » Sat Jan 22, 2022 4:03 pm

I've saved the Wordle web page, made some modifications (getting rid of some analytics stuff), and I play the game locally (offline) - there is no saved game stats after solving a wordle.

Another interesting article: https://bert.org/2021/11/24/the-best-starting-word-in-wordle/.
This one has a link to a 'beautified' version of the javascript code that drives Wordle - the list of solution words and acceptable words are in the script.
Direct link to beautified script: https://bert.org/assets/posts/wordle/main-beautified.js (right-click on link and Save linked content as...)

by **Mathimagics** » Sat Jan 22, 2022 4:29 pm

Tyler Glaiel wrote:So there you have it, the ideal first guess for Wordle is ROATE. It means:

“The cumulative net earnings after taxes available to common shareholders, adjusted for tax-affected amortization of intangibles, for the calendar quarters in
each calendar year in a specified period of time divided by average shareholder’s tangible common equity”.

A simpler definition, according to my Collins Scrabble Dictionary (2019):

ROATE (Shakespeare) to learn by repetition, also ROTE

by **Mathimagics** » Sat Jan 22, 2022 4:41 pm

Oh dear, I was avoiding mention of those lists until it became clear that nearly everybody had them ...

... but its seems that the horse has long since bolted :lol:

by **coloin** » Mon Jan 24, 2022 10:14 pm

Is this better play than deep blue

analysis and comments please .....

spoiler alert though as its todays 25/1

Hidden Text: Show

by **Mathimagics** » Tue Jan 25, 2022 5:09 am

I have a WLD (Wordle Lie Detector) which sanalyses the # of possible words matching (NPW) after each guess, and then gives a carefully considered analysis of the results:

Code: Select all: I R A T E . Y Y . . 60 B O N U S . . . Y Y 1 S U G A R G G G G G WLD: Fail!

Code: Select all: T R I P E . Y . . . 123 C O A L S . . Y . Y 3 Possible words: 1: SUGAR 2: MARSH 3: HARSH WLD: Pass!

Note that WLD results are currently not admissible in court :lol:

by **coloin** » Tue Jan 25, 2022 6:33 am

Coloin Shawshank wrote: I stand here on the steps of justice and fully respect the statutes of the Wangmeroo Legal Directive. I will reflect on the decision by by the jury and will take the required 24 hours to consider going down the appeals process. Should I chose the BONUS again I will be safe in the knowledge that TRIPE is not served for breakfast in Alcatraz

by **Mathimagics** » Tue Jan 25, 2022 8:29 am

WLD Court wrote:Duly noted ...

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