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Automating Boggle

Last week, I had a conversation with a good friend in the spirit of the “Cult of Done” (valuing action over perfection, boldly experimenting and learning through doing) and sharing our work. Based on this conversation, I decided to get my hands dirty and attempt to create a quick and fun project, constraining myself to a couple hours of work on a Saturday morning. Key here is not worrying about perfection, but getting something out there quickly1.

Thrifted Boggle

My girlfriend and I enjoy playing board and card games. Recently, we’ve picked up a copy of Boggle in a thrift shop. Boggle is a word game where you try to find as many words as you can from 16 dice, each with a different letter, that are shaken in a covered tray and then set in a $4\times4$ grid. Players get three minutes to find words that are at least three letters long, and each letter in the word has to touch the letter before it in any direction. Players are not allowed to use the same letter dice more than once in a word. Once time’s up, players compare their lists and any word that appears on more than one list gets cancelled out, with players scoring points based on the length of their unique words.

Boggle board

Our second-hand copy of Boggle has a couple of problems, however (excluding the fact that one of the dice was replaced by a Scrabble block by the previous owner). Our main problem is that the hourglass provided with our copy is broken, so we have to set up a smartphone timer. Other problems include:

  • Counting the points afterwards takes up a lot of time, especially if we want to confirm that our words are actually on the board
  • Confirming if a found word is an actual word takes time as well (as I love making up some plausible sounding Dutch words, looking them up in the dictionary, and claiming that I was certain that it exists if it’s not there.)

Project Goals

As I want to create something that both helps solve the problems above, but I also want to get something done quickly, the goal for this project is threefold:

  1. First, create a Telegram bot that can:
    • Receive a picture of the shaken tray of dice
    • Start a built-in timer to know when the round starts and ends
    • Count our points by confirming that our words are on the board and that the words themselves exist based on a (Dutch) dictionary
  2. Next, I want to share my work using this blog post (in the spirit of the Cult of Done)
  3. Do all this in a couple of hours on a Saturday morning (instead of enjoying the nice Spring weather like a normal person)

Implementation

I started with a planning, trying to come up with the necessary sub-tasks:

  1. Recognising labelled dice from a picture, which we need to reconstruct the grid
  2. Create a data structure that contains the allowed list of words
  3. Algorithm that traverses the grid, finding all valid words
  4. Create a Telegram bot that uses the above to act as a “referee”
  5. Write the text (that you’re currently reading) whilst doing all of the above

Recognising labelled dice

As I am not that familiar with computer vision techniques, and I wanted to move quickly, my first attempt was to use GPT-4V, or gpt-4-vision-preview, to take a picture of the Boggle grid as input and retrieve the letters from that picture as a continuous string. If this would work out, I could quickly move to the other steps of the project. I used the following prompt:

Given the image of a 4x4 grid of Boggle dice, 
convert the letters visible on the dice into a 
continuous 16-character string by reading from left to right,
top to bottom. 
 
For example, if the top row contains the letters 'A', 'B', 'C', 'D', 
and the second row contains letters 'E', 'F', 'G', and 'H', etc., 
your output should be 'ABCDEFGH...etc', up to the 16th letter.
 
Keep in mind that letters could be rotated!

This failed miserably, however. The received output based on the image above (cropped to only display the grid of dice) was:

The continuous 16-character string from the Boggle dice 
is "INRAWMNBUDOVSOLO".

Afterwards, I lost an hour trying out different things with OpenCV and tesseract, but this did not seem to work out. As I still wanted to move quickly, I skipped this step and will rely on user input for the grid.

Recognising valid words

The trie is an efficient data structure for storing large word lists. The data structure itself can be seen as a finite state machine that only accepts words used for its creation. Each node of the trie represents a prefix, with the root as the empty string. Transitions between nodes adds characters to the prefixes. This offers quick search capabilities, therefore making it suitable for our project.

As I’ve recently had to create an implementation of tries for other work, I simply reused this for this project. The idea behind the construction algorithm is very simple: starting from the initial state, we check every symbol in each word. We follow transitions to states if they already exist, and create new states and transitions if they don’t. At the end of each word, we mark the last state as the final state.

def trie(sequences):  
    """Constructs a trie from given collection of sequences."""  
    fsm = Automaton()  
    for sequence in sequences:  
        current = fsm.initial  
        for symbol in sequence:  
            if symbol not in fsm.alphabet:  
                fsm.add_symbol(symbol)  
            if (next_state := fsm.follow(current, symbol)) is None:  
                next_state = fsm.add_state()  
                fsm.set_transition(current, next_state, symbol)  
            current = next_state  
        fsm.accepting.add(current)  
    return fsm
words = {"tree", "three", "trie", "tried"}
automaton = trie(words)
 
automaton.accept("tree")  # True
automaton.accept("tried")  # True
automton.accept("thr")  # False
 
show(automaton)

Example of the trie for set (tree, trie, three, tried)

For the dictionary of valid words, I relied on the OpenTaal wordlist, containing over 400k Dutch words. We can shorten this list significantly by filtering out the ones that are impossible to find in Boggle:

  • Words that contain something other than the letters from a to z
  • Words shorter than 3 letters or longer than 10 letters (as we’re usually never finding any words longer than 6, 10 is very generous)

In the end, we end up with a large trie that accepts all words from our Dutch wordlist.

Searching for words in a grid

If we have a string representing the grid as input (e.g., "NTAWIRIRNBDAOASO"), we can find all possible words by converting our grid into a graph, allowing us to utilize graph traversal algorithms to systematically search for potential word formations. This graph representation simplifies the problem into a more navigable structure where each dice is a vertex, denoted by its character. Edges between vertices are formed based on a dice’s spatial relation to its neighbours, indicating possible transitions or movements in our word formation process.

To find all words in the grid, we can perform a depth-first traversal starting from each dice, exploring as far as possible along each branch before backtracking. It is an ideal choice for our case here since we are interested in finding all potential paths that form words. Starting from each dice (or vertex), our DFT traces all unique paths devoid of cycles, while continuously inspecting the trie to confirm whether the traced path is leading to a valid word. We stop traversing further in a given path if the prefix is not present in the trie. This way, we retrieve all acyclic paths in the graph that have a path in the trie, and we don’t go deeper than necessary into the current path.

Telegram bot

Using the above, we can create a Telegram bot that uses the above to confirm our words and to keep track of our scores:

Screenshot of the Telegram chat with <code>bogglebot</code>

Users input their Boggle game board as a grid by invoking the /new command in a chat with the bot, and the bot generates a list of all possible words by simulating all possible paths in the grid. The bot will then confirm the start and the counter of the game. During the game, the users type in the words they find, and the bot checks if the word is valid (i.e., is in the list of possible words). If the word is valid, the user’s score is incremented according to the length of the word. The score and game updates are sent back to the user in the chat. The bot is built using the python-telegram-bot library, which allows easy interaction with the Telegram Bot API.

Possible Extensions

Given the flexibility of the implementation, there are various ways we could extend this project in the future:

  • Wordlist Variants: Depending on our mood or the challenge we desire, we could spice up our games by introducing different wordlists for specific themes. For example, a game could be based solely on palindromes, or we could introduce a Flemish dialect-based wordlist. The possibilities and variations are endless, making each game a fresh and exciting challenge.
  • Custom Time Counter: A part of the thrill of Boggle comes from the time pressure. We could experiment with this element by introducing a varying time or perhaps even a countdown whereby the time decreases each round, raising the stakes progressively.
  • Automatic Scoring: One of the main appeals of this project is that it removes the cumbersome task of manual point counting. This could be further extended to automatically keep track of our scores across multiple games or even different days. Thus, we could concentrate on the game at hand, while the bot takes care of the statistics and progress tracking.
  • Speed Chess Inspired Mode: Perhaps one of the most exciting possibilities would be to create a ‘speed chess’ inspired mode. Each player could have an individual clock, and you’d need to quickly spot and share a unique word to pause your countdown and switch turns. The game would then continue until someone’s time reaches zero. This offers the perfect blend of frantic quick-thinking, strategy, and suspense — a true test of one’s Boggle skills!

In the spirit of the “Cult of Done”, I have focused on quickly getting this project up and running first in a short amount of allotted time, before worrying about enhancements or delivering the perfect project.

  1. As the goal of this experiment was to move fast, this writing is assisted using GPT-4 through the OpenAI API. Everything in italics was first written with the help of an LLM using my instructions and provided information, and rewritten and tweaked afterwards to fit my writing style. ↩︎

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