pywt.py

A python based Wordle game helper

• Main Window:
• In Use Main Window Shown Next to NYT Results:
• Information Window: The information window explains the Helper features in detail. Its content is included at this Readme's end section. The previous two images are intended to show what the Helper does.

What To Expect From This Helper

• Expect nothing more than a helper with a thorough vocabulary that presents words only matching the letters you specify.
• The Helper was created for investigating Wordle word pick strategies. Using the Helper removes the task of thinking up five-letter words to allow one to focus only on play strategy.
• The Helper "knows" the words but not which word is the solution. As such the Helper ruins the game for those where thinking up words is the attraction to Wordle.
• The Helper can calculate the entropy or information bits for every guess applied to the current words showing. The guess having the highest entropy is the best guess baring any additional information regarding the words showing.
• A companion to the Helper is the word groups analyzer Groups Driller. The Helper's Highlight Group Optimal button runs an instance of the Groups Driller's output in context with the words the Helper currently shows. The Groups Driller button runs a separate Groups Driller word groups analyzer instance. Its purpose is for examining groups properties in a manor independent of the Helper and without disturbing the Helper's current state. Groups can be used to calculate the expected number of steps associated with any guess word. See EXPECTEDSTEPS_Readme.md for more information.
• A side show to the Helper is fmwm.py, the Finite Monkey Wordle Machine (FMWM). FMWM dispatches a machine, the monkey, to perform Wordle related tasks, like how many random guesses are required to solve Wordles. It can also find all the Magic Words present in the vocabulary for a given word. Magic Words reduce the selection guess pool to contain just the solution word. See FMWM_Readme.md for more information.

Running the Wordle helper

• Open a Terminal window
• Change to the folder where you placed pywy.py and the other files and folders.
• Enter the command: python3 pywt.py
• For Apple OSX and Linux systems double-clicking the start-pywt.command file in the Finder also starts the Wordle helper.

Running the Wordle Helper with start-pywt.command

• start-pywt.command is a shell script intended for launching the Wordle helper from a computer's file browser. It should run the helper with a double click after being properly setup.
• Setting up start-pywt.command requires marking it an executable file. This is later described in Installing the Wordle Helper
• start-pywt.command checks for required components before launching the Wordle helper. It reports what components are missing and will not launch the Wordle helper when critical components are missing.
• start-pywt.command output looks like this when it is launching the Wordle helper:

Requirements

• Linux, Apple OSX or Microsoft Windows running a Linux subsystem
  • It should be possible to have the Helper running in a Linux subsystem running in Microsoft Windows, but these instructions do not explain how. The Linux subsystem would need to have OS components, like 'cat', 'grep' and 'bash' typically present on any Apple OSX or Linux system in addition to the python3, pip and customtkinter installs.
• python3: (https://www.python.org/downloads/)
  • As of this writing Python 3.10 is recommended.
    • Customtkinter will have a problem with Python 3.12.
    • There is an annoying graphical user interface focus bug when using Python 3.12 where the controls on the Helper window do not activate unless the window background is first touched. Using Python 3.10 avoids the problem. Using the command python3.10 pywt.py runs the Helper in Python 3.10 when other Python3 versions are present on your system.
• pip: pip is a package installer for python3.
• customtkinter

'tkinter' provides graphical user interface support for python applications. It should automatically install with python, but be aware you might need to manually install it. 'customtkinter' is an expansion to 'tkinter'. This Wordle game helper uses some customtkinter features and so it needs to be installed along with python3. 'pip' is python's utility for installing components like 'customtkinter'. 'pip' needs to be installed in order to install customtkinter.

Installing python3, pip and customtkinter

• First, install python3 by using the standard install package provided at https://www.python.org/downloads/. Be aware Python3 can be installed by using many different methods. Each method may install python3 and its versions at different locations on your system. This can cause complications for you if you are not aware of it. Each of the next two requirements pip and customtkinter will be installed at the specific python3 version and location that corresponds to the python3 version used to install them. For this reason using the standard install package provided at https://www.python.org/downloads/ is recommended.

• Second, install pip by using the command python3 -m ensurepip --upgrade entered in a Terminal window. Not all python3 installations are equal. It is possible for the ensurepip feature to not exist, in which case you will need to search the web for the method that works for your situation to install pip.

• Lastly, install customtkinter by using the command pip3 install --upgrade customtkinter==5.2.2 entered in a Terminal window.

• Note: customtkinter is in active development. Changes to it might cause Wordle Helper to fail running. When using the convenience script start-pywt.command to start the Wordle Helper there is no failure feedback other than not seeing the Helper. As of this writing the Helper runs with customtkinter versions 4.6.3 and 5.2.2. Version 4.6.3 and 5.2.2 with this Helper in Apple OSs: Ventura 13.0, Monterey 12.6 and Catalina 10.15.7.

Installing the Wordle Helper

• Download the pywtpackage.zip release file from the repository releases link.
• Unzip the pywtpackage.zip release file. It should unzip to be a folder named pywtpackage.
• Rename the pywtpackage folder as you wish and place the folder with its contents to where you would like to keep it.
• A file privilege for the start-pywt.command double-click-to-run convenience file needs to be changed for it to work. Use the command: chmod +x start-pywt.command executed in Terminal, at the file's folder, to make the change. The same applies to the other convenience files: start-fmwm.command and start-groupdrilling.command. For these use the commands: chmod +x start-fmwm.command and chmod +x start-groupdrilling.command executed in Terminal, at the file's folder, to make the changes.
• In the zip package, this README.md file, the images it uses and a couple of files in the worddata folder regarding letter ranking may be deleted if desired. The only required files, and their associated folder, that are in pywtpackage.zip are:
  • start-pywt.command (the double-click-to-run convenience script file)
  • pywt.py (the wordle helper app.)
  • helpers.py (a helper to the app.)
  • groupdrilling.py (a helper app for groups analysis)
  • start-groupdrilling.command (convenience script file)
  • fmwm.py (a command line application to measure strategies)
  • start-fmwm.command (convenience script file to run fmwm.py)
  • helpinfo.txt (help information)
  • letter_ranks.txt (letter ranking data file)
  • nyt_wordlist.txt (wordlist - shuffled)
  • wo_nyt_wordlist.txt (wordlist - shuffled)

Word Ranking

• Word ranking based on letter occurrence frequency is part of what this Wordle Helper was initially developed to investigate and then automate as a selection strategy for the FMWM. This is why the word lists are shown ranked in this way and why these instructions appear to emphasize Word Ranking even though the Helper has evolved to perform the more effective Groups analysis method.

• Letter Ranking Information Window:

• Five-letter words are assigned a rank according to how common the letters are in the Wordle possible solution words list. Three different ranking methods are possible. Each method sums a rank associated with each letter in the word. The above image, which can be shown by pressing Letter Ranking in the Information window, shows the ranks associated with each letter. This data is read from the letter_ranks.txt or the letter_ranks_bot.txt text files found in the worddata directory. The letter_ranks.txt ranking file is based upon the Classic, original NYT Wordle solutions words list (The 2,309 word list.). The letter_ranks_bot.txt ranking file is based upon the Classic+ words list. The Classic+ words list is what the NYT Wordlebot uses for its possible solutions word list. The Helper defaults to using the Classic+ words list.

• The Occurrence method considers letters occurring at least once in the word. The RNK column is the letter associated rank value. This value is how many times greater the letter is found once in a word compared to the least frequently occurring letter in the Wordle words list. Occurrence does not consider letter position nor does it value multiple letter occurrence above single occurrence.

• The Position method considers the letter's position. The RNK-X column is the letter associated rank value for the letter being in the X word's letter position. This value is the fraction of the letter's RNK that occurs when the letter is at the X position.

• The Both method sums the Occurrence and the Position methods. The method first biases the word rank according to by letter occurrence ranking. Then it up promotes the rank according to letter position rank.

• These ranking method are of different scales. Do not compare their ranking for any particular word. Instead, compare the ranking between different words.

• Word rank represents relative occurrence probability; however, any word matching the filter could be the Wordle word regardless of its rank.

Optimals

• Optimals identifies from the words in the current words Showing, or in one of the vocabulary sources: Classic, Classic+ or Large, that when used as a guess against the current Words Showing word list result in likely less remaining possible solutions.
• Any word from the Words Showing list used as a guess has a chance of being the solution. That chance is related to the number of Words Showing. When the number of Words Showing is three or more words the best guess becomes more likely a word that is not the solution. The solution being one of three words might be solved in two steps by first guessing a word not of the three that eliminates two words no matter which of the three words is the solution.
• For any guess the Words Showing change relates to the unique ways that guess word is wrong for each of the Words Showing. Some guess words leave fewer remaining words to choose from. It is possible for a word to leave only a one word remaining for every which way that word was wrong. You would solve the Wordle in your next guess under that condition. Optimal guess words might be in the Words Showing but are more likely selected from the other vocabulary sources. Optimals identifies those words.
• Groups are words that share a unique clue pattern. Thus, a group is an abstract that is both the clue pattern and the group of words. A separate window opens to report all the group pattern information when the Verbose checkbox is checked.
• Assuming the various settings have not excluded the solution from the current words showing and considering the solution is a random list member, then dividing the list into many small choice groups will on average minimize the number of guess required to narrow down to the solution.
• Groups identified with Optimals or Groups Driller, in verbose mode, can be used to calculate the expected number of steps associated with any guess word. See EXPECTEDSTEPS_Readme.md for more information. Calculating the expected number of steps can augment understanding Wordle dynamics, but it is not necessary for selecting words.
• The play word having the most Entropy is the best Wordle play. Entropy calculated by this Wordle Helper assumes assigns equal probability to every word in the possible solutions list. The NYT WordleBot does not treat all possible solutions as equal for its entropy word scores. Entropy comparisons should be made within the same context. For example compare the Wordle Helper entropy difference between two words to the NYT WordleBot entropy difference between the same two words.
• The play word yielding the largest group quantity is not necessarily the play having the least expected number of steps to solve. However, it very often does have the least expected number of steps to solve.
• The min-max value is the minimum size of the maximum group sizes in guess words identified to yield the largest number of word groups. Many guess words can yield the same largest number of word group. But the word group sizes can vary. One wants to know the smallest maximum group size in the groups analysis summary. The min-max value also coordinates with the summarized p2 value.
• The ave is the average number of words in the word groups.
• The exp value is the guess' expected size for the resulting word group. Expected size is the sum of the probability weighted word group sizes.
• The p2 value is the groups size population variance. This value is useful. It is a measure of how variable the group sizes are resulting from a guess candidate. When candidates have the same number of groups, select the candidate that has the smallest p2. Doing so removes the chance the solution will be a member of the larger groups because the group sizes vary less in size. When candidates vary in p2 you will see they have differing maximum group sizes.
• Larger Entropy values typically, but not always, go with the largest group qty having the smallest min-max value and smallest p2 value. The NYT WordleBot selects by its Entropy value.
• Optimal group analysis should always be performed on the total selection list that contains multiple letters. The analysis is for selecting words that puts the solution into smaller remaining word sets. The larger candidate selection pool provides more grouping opportunities.

• The Verbose Report Find button scrolls the report window to the last found search text instance, which will be highlighted. Include 'for: ' in the search text when searching for a guess word's pattern. Include 'qty: '' when searching for guesses having the same group quantities. To avoid finding to many text instances the search text must have five or more characters, beware however; it is possible to hopelessly bog down the search when trying to highlight commonly found text. Verbose reports using the Large vocabulary can be 400,000 text lines. Verbose report text can be copy-pasted into text editors.

• The Cond. checkbox results in the verbose output to be a condensed format that lists the guess words in order of highest information entropy first. Here is an example:

• The Keyed checkbox results in each of the verbose data output lines keyed to the guess word to which that data applies. This format can be useful for copying and pasting the data to another application for further processing while maintaining to which guess word the data applies.

• The concept of Wordle Groups is explained in an allegory here: Groups Allegory

Groups Driller

• Groups Driller is a side utility that performs a groups analysis using the Words Entered. Classic, Classic+ and Large vocabulary against any group of Words Entered into its input field. It is intended for investigating a word group's effective size, in other words how easily a word's group resolves to a single word.
• The Entropy option filters the summarized optimal words to those that contain the highest gained entropy information.
• Copy a word group from any Verbose Report (or a spreadsheet row) and paste it into the Groups Driller entry field. Text that includes rank numbers copied from the Helper words list may also be pasted. Pasted text will be properly formatted into a list and analyzed when pressing the Process button. Pressing and releasing the Return keyboard key will instead clean and format the entry without starting the analysis process.
• The word entry field appears limited in the number of words it can take, but you can actually paste the entire Large vocabulary, rankings included, into the entry. The rankings will be automatically stripped away.
• Clear 'N Paste clears the current list entries and pastes the current Clipboard to be the entry. The entry is then cleaned up. Whatever words you have copied last get pasted. The Clipboard will then be empty. Clear 'N Paste will not clear the current entry if the Clipboard happens to be empty.
• With Groups Driller running, one leaves the Helper's Verbose Report open using its Find feature to show a guess's groups. Copy and Paste a group to be further analyzed into the Groups Driller entry field. Then press the Process button.
• Groups Driller can, given the time, process essentially an unlimited number of words in context with The Wordle Helper. The entire Large vocabulary may be copied and pasted from The Wordle Helper.
• Groups Driller summarizes the results and also opens a Verbose Report identical to the type shown by the Helper. The workflow allows one to leave the Helper's verbose groups window open to navigate to different guess word results that can be then investigated further by pastes into the Group Driller.

• The Group Driller verbose report window is not being shown in this README. It is identical in function and appearance to the Helper's verbose report window when not using the Condensed option.
• The Keyed option includes the guess word for each group pattern. This option is useful for maintaining the guess word associations when exporting the groups data (copy and paste) for all guesses.
• The Condensed option verbose report omits showing the guess word groups. Instead, only the guess word's group stats are output in a format intended for copy and pasting into a spreadsheet application for further investigation.

Wordle Play Strategies

• Discover Wordle play strategies yourself with the Helper's assistance. That was the reason for creating this Helper.
• One initial goal was to find a strategy that tends to result in an under-three-pick Wordle game. This Helper appears to show that is impossible.

Information Window Content

The Wordle helper shows five-letter words from which you can select for playing the Wordle game.

Word Ranking Method

• The five-letter words are assigned a rank according to how common the letters are in the Wordle possible solution words. The 'Occurrence' method does not consider where letters occur in the word. The 'Position' method considers the letter's position. The 'Both' method adds the other two rank values. This helper presents the ranked words from the lowest rank to the highest rank. The word list always shows scrolled to the highest ranking words at its bottom. Scroll the list upwards to see the lower ranking words.

• Checking the Classic Ranking option ranks according to the Classic 2309 Wordle solutions letter frequency. When Classic Ranking is not checked ranks are assigned according to the Classic+ solutions letter frequency.

• Word rank represents relative occurrence probability; however, any word matching the filter could be the Wordle word regardless of its rank.

Word Filtering

• The Allow Duplicate Letters option includes words having duplicate letters. After your first or second Wordle choice you should start to consider words with duplicate letters. Depending on your known letters status, duplicate letters ought to be shown before making the third selection.

• Checking Letters To Be Excluded letter check boxes results in words not containing those letters.

• Checking Letters To Be Required letter check boxes results in words containing those letters. No words will show when six or more letters are required for the word.

• The checkboxed Exclude and Required letters are arranged in order of use frequency based on the Classic Ranking. The checkboxed letters do not rearrange to Classis+ Ranking when that ranking is in use. Classis+ Ranking is the default ranking. The actual ranking order currently in use is seen when freshly selecting the Letter Ranking button in the Information window.

• The Clear All button in the checkbox lineups clears all the checkboxes in that lineup. The letter check boxes are ordered according to letter use frequency. The vertical lines indicate a jump in letter use frequency and are useful to describe letter rank group types. The group descriptions in turn provide a language useful for discussing game strategy and game results.

• Letter Positioning is where letters may be excluded or required for one of the five possible Wordle word letter positions. For each requirement, select the letter and position. The plus (+) and minus (-) buttons add or remove the respective position requirement. The Z buttons clear the entire position list.

• In the puzzle game context a letter indicated not at its correct position is a letter known to be present in the word, so it will also be required. For such letters, its checkbox will not appear checked in Letters To Be Required, but its filter requirement will be applied. If perhaps you want to follow a strict letter elimination strategy, and you want the helper word list to not include unknown position letters, then use the letter's Letters To Be Excluded check box and do not apply an Exclude From Position for that letter. Otherwise, the word list will be empty because no word can have the letter and also not have the letter.

• Special Patterns and Multiple Same Letters are two features: Special Patterns and Multiple Same Letters.

Special Pattern allows one to quickly introduce a custom require or exclude filter pattern that can operate on letter position. Pattern was initially intended for adjacent letter patterns such as TT, ITE, GHT or SS. One might use this to compare the number of words having a SS pattern versus S.S or S..S patterns where the period character, ".", means 'any letter'. The pattern S..S shows words having any two letters between S letters like the words SMUSH and TSARS.

Pattern turns out to be especially useful for spotting words groups in part because its setting is independent of the Exclude and Require Position controls. Thus, you can very quickly set and then clear Pattern without affecting one's thought train.

Multiples allows one to specify "there must be two E letters" or "there cannot be two E letters, nor three E letters". The entry format is 'number''letter' , 'number''letter' and so on. For example: 2A,3E. A space character also puts in the comma for you.

Multiples is a concept that may be difficult to understand at first. If your guess word has multiple same letters and one of those letters is yellow or green then all words with two or more of those letters must be excluded via Multiples because one of those letters being gray means the solution has just one of those letters. You can ignore the idea when all of those guess same letters are grey. If your guess word has multiple same letters and both of those letters is yellow or green in any combination then all words with two or more of those letters must be included via Multiples. You might need to think about needing three of those letters being included. Multiples operates as either include or exclude. More complicated requirements can be achieved by combining Multiples inclusions with Exclude From Position exclusions or Special Pattern. The Helper does not do any thinking for you in this regard.

• Special Pattern allows one to quickly introduce a custom require or exclude filter pattern that can operate on letter position. One might use this to compare the number of words having a SS pattern versus S.S or S..S patterns where the period character, ".", means 'any letter'. The pattern S..S shows words having any two letters between S letters like the words SMUSH and TSARS.

• Special Pattern turns out to be especially useful for spotting words groups in part because its setting is independent of the Exclude and Require Position controls. Thus, you can very quickly set and then clear Special Pattern without affecting one's thought train.

• Show Genetic highlights the highest genetic ranking word in the current showing word list. The highest genetic ranking word is a word from the list that is most in common with the word list in regard to letters. The highest genetic ranking word, or words sometimes, could either rule out the most number of words or rule in the highest number of discovered letters. For example for the word GLIDE, its genetic rank is the sum of all the times its own letters, G, L, I, D, E show up once in each word in the given list plus an adjustment equal to the number of times a letter in the subject word (GLIDE) repeats within the subject word. High genetic ranking words perform well as Wordle plays. It is quickly determined and is often what some people like to figure from the words they think remain. That is why the method is a pywordletool feature. Genetic ranking is a valid strategy, but it does not perform as quite as well as groups analysis.

• Pick Random highlights a random word in the current showing word list. There can be a point where there is no single better selection amongst the remaining words list. Any one of the words shown could be the Wordle word or might have equal results as any other word in the list. This feature is intended for use when the list has become small where you can surmise the correct word would be a random selection.

• Optimals highlights the word or words that result in the lowest average remaining words when that word is used as a guess. The analysis is performed on the current words Showing or the entire Classic, Classic+ or Large vocabularies using groups analysis. The process identifies the guess word that makes a groups set having the highest entropy. The group finding process is lengthy and may take an extended time to finish. The group optimal guess word is likely to result in smaller remaining word groups, thus increasing chances to find the solution in fewer guesses. Optimal group analysis should be performed on the total selection list that contains multiple letters because the analysis is for selecting the solution versus guessing for letter discovery. A separate window opens to report all the group pattern information during the analysis when the Verbose checkbox is checked. Group optimal words identified from guess word sources other than the showing words cannot be highlighted if the word is not in the shown list.

• Verbose output displays either all the groups data resulting from guesses or a sorted condensed groups data list. The Cond. checkbox sets which mode is displayed. In the standard verbose display the verbose summary lists those words that generate the most number of groups and also the guess word having the highest entropy. That highest entropy word might generate less word groups. This display is sorted by entropy. Because the list only shows the highest entropy word it omits less group generating guesses that have higher entropy than those maximum group generating guesses. In short, the standard verbose summary shows the top guess, but does not necessarily show the top x guesses. The condensed verbose display lists the guesses sorted by entropy. That display shows the top x entropy guesses.

• Entropy filters the optimal guess words to those that contain the highest gained entropy information bits (base 2). Many guess words can result in the same number of possible solution word groups, but the number of words in those groups can vary. There can be a technical information difference due to the word group sizes. The information is quantified as entropy.

• Cond. The verbose output will be a condensed format that lists the guess words in order of highest information entropy first. Besides showing the best entropy based guess choice, the condensed verbose output is particularly useful to copy and paste into another application to more quickly find the hard mode compliant guesses.

• Keyed Results in each of the verbose data output lines keyed to the guess word to which that data applies. This format can be useful for copying and pasting the data to another application for further processing while maintaining to which guess word the data applies.

Word Vocabulary

• The Large vocabulary is the 14,855 word list. Wordle accepts only words that are in the Large vocabulary. A fraction of the Large vocabulary words are words that will be the day's Wordle solution. Originally, forNew York Times (NYT) Wordle, that faction was 2,309 words. The Classic vocabulary is those 2,309 words. The balance of the Large vocabulary with the Classic vocabulary removed are words that would never be solution words. The NYT acquired Wordle and in coordination with its WordleBot implementation is making changes to the vocabularies. One change transfers words from Large vocabulary to add to the Classic vocabulary. Furthermore, the NYT has removed some words considered politically incorrect. Supposedly, not all NYT transferred words may not be are actual solution candidates. The Classic plus the transferred words and less the censored words is the Classic+ vocabulary.

• Using the Classic+ vocabulary yields results essentially identical to what the NYT WordleBot shows. The transferred words are not published, but they can be inferred from WordleBot remaining words outputs.

• Another change the NYT has made is to censure some Classic words. Thus, some Classic words that were originally solution candidates have been removed from the possible solutions list. These words are still acceptable play words but will never be a solution and will never show up in a WordleBot remaining solutions list. These words will show up in The Wordle Helper. When using the Classic+ word vocabulary for possible solution candidates, (Make sure Allow Duplicate Letters is checked.), the remaining words should equal what the WordleBot indicates.

• If The Wordle Helper shows more words than WordleBot by a word or so, then there is a censured word or there is an issue with multiple same letters.

• If The Wordle Helper shows fewer words than WordleBot, then The Wordle Helper is missing some transferred words or there is an issue with multiple same letters.

Tips

• When adding a new exclusion position for a letter that already has an excluded position, first select that letter's exclusion in the list. That selection puts the letter in the combobox so that you need only to indicate the letter position before pressing the plus (+) button.

• Seeing an empty list can seem to be an error at times. No, it is not an error. The criteria you entered resulted in the empty list. A simple example is Excluding a letter and then also Requiring that same letter. The filtering happens in discrete stages. In the simple example, the resulting list of words that exclude a letter is then asked to list words having that same letter. There would be none.

• Exclude From Position in the Letter Positioning options applies letter requirements for letters you indicate for position exclusion. This is actually two separate filter commands. The letter is required in the word, but not at the position indicated. Wordle uses Yellow color blocks for such letters. In subsequent guesses, Wordle marks that same previously marked Yellow color letter as Grey color when that letter is not in the correct position and when the guess has erroneous multiple instances of that same letter. Exclude From Position such letters. Do not apply the broad brush Excluding for such letters. An empty list results if you do as just previously explained.

• Beware in general of any guess that contains multiple same letters. You are in the clear when all of those letters are gray. Otherwise, you have to stop and think. If only one is either a green or yellow clue then then you should take all possible measures to exclude extraneous words. If both letters are a clue, particularly two yellow clues or a green and yellow clue, then filtering for the multiple same letter is required. The Special Patterns and Multiple Same Letters control will help you with these situations.

Word Vocabularies

• The Classic and Large word vocabularies are current as of May 3, 2023. In the past year the vocabularies were seen to change once.
• The Classic+ word vocabulary is the Classic word vocabulary plus additional words that the NYT WordleBot adds to the Classic words for reasons not explicitly explained by the NYT but that clearly serve both as an intentional fuzziness to the vocabulary the WordleBot uses to solve the Wordle and to serve as a means to add additional solutions that the WordleBot would be able to solve. The groups method used by the WordleBot and this Wordle Helper requires the solution to be within the possible solutions' vocabulary.