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POAlgorithm to choose random letters for word search game that allows many words to be spelled
 

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  1. POAlgorithm to choose random letters for word search game that allows many words to be spelled
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    <p>I'm making a <a href="http://en.wikipedia.org/wiki/Boggle" rel="nofollow noreferrer">boggle</a>-like word game. The user is given a grid of letters like this:</p> <pre><code>O V Z W X S T A C K Y R F L Q </code></pre> <p>The user picks out a word using any adjacent chains of letters, like the word "STACK" across the middle line. The letters used are then replaced by the machine e.g. (new letters in lowercase):</p> <pre><code>O V Z W X z e x o p Y R F L Q </code></pre> <p>Notice you can now spell "OVeRFLoW" by using the new letters. My problem is: What algorithm can I use to pick new letters that maximizes the number of long words the user can spell? I want the game to be fun and involve spelling e.g. 6 letter words sometimes but, if you pick bad letters, games involve the user just spelling 3 letter words and not getting a chance to find larger words.</p> <p>For example:</p> <ul> <li><p>You could just randomly pick new letters from the alphabet. This does not work well.</p></li> <li><p>Likewise, I found picking randomly but using the letter frequencies from Scrabble didn't work well. This works better in Scrabble I think as you are less constrained about the order you use the letters in.</p></li> <li><p>I tried having a set of lists, each representing one of the dies from the Boggle game, and each letter would be picked from a random die side (I also wonder whether I can legally use this data in a product). I didn't notice this working well. I imagine the Boggle dice sides were chosen in some sensible manner, but I cannot find how this was done.</p></li> </ul> <p>Some ideas I've considered:</p> <ul> <li><p>Make a table of how often letter pairs occur together in the dictionary. For the sake of argument, say E is seen next to A 30% of the time. When picking a new letter, I would randomly pick a letter based on the frequency of this letter occurring next to a randomly chosen adjacent letter on the grid. For example, if the neighboring letter was E, the new letter would be "A" 30% of the time. The should mean there are lots of decent pairs to use scattered around the map. I could maybe improve this by making probability tables of a letter occurring between two other letters.</p></li> <li><p>Somehow do a search for what words can be spelt on the current grid, taking the new letters to be wildcards. I would then replace the wildcards with letters that allowed the biggest words to be spelt. I'm not sure how you would do this efficiently however.</p></li> </ul> <p>Any other ideas are appreciated. I wonder if there is a common way to solve this problem and what other word games use. </p> <p>Edit: Thanks for the great answers so far! I forgot to mention, I'm really aiming for low memory/cpu requirements if possible, I'm probably going to use the SOWPODS dictionary (about 250,000) and my grid will be able 6 x 6. </p>
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    1. COI like your idea of using letter juxtaposition probabilities. You could expand it further: for any given letter location, figure out the probability of each letter being adjacent to its immediately surrounding letters and average these probabilities into a single one, then pick a random letter using the averaged probabilities as weights.
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      1. USCameron
 

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