The first set of games involves pattern searching and word completion: given a partial set of the letters in a word, fill in the missing letters and guess the word. Solving these problems involves executing a fast pattern search against a list with enough words. This is the basic mechanism behind the hangman solver which we built. As an example of cosmetic differences between games, we were able to easily adapt this into a hanging with friend solver by adding a new scoring system and tweaking the seach logic.

The second set of games revolves around identifying which possible permutations of a set of letters are proper words. This is the basis for Scrabble (solver here) and it’s Zynga clone, Words With Friends (solver here). The same logic also works for a word unscrambler. Most scrabble variants involve some form of placing tiles on a board, modifying the universe of potential solutions through requiring a player to build off an existing word (more letters) and adding constraints around where tiles can be placed (empty spaces, adjacent tiles must form a word). Solving these challenges efficiently requires the player to transpose the letters in their hand into words. This is also where you generally need to start doing serious algorithm work around a solver: there are usually enough permutations of a seven letter rack that many naive approaches are computationally impractical.

The third broad class of word games in general use is a grid search, such as Boggle or larger n x n word searches. We built a version of this using Python as part of our Boggle solver. Computationally, this is a mix of a permutation search and pattern matching – you need to iterate through all the possible paths in a grid and spot situations where the word fragement matches the pattern of a known word.

I’ve seen a fourth model proposed but the gaming market hasn’t really embraced it: a blend of Scrabble and Poker. This involves building words from letters in your hand (a basic scrabble style permuation search) but incorporating mechanics to allow a player to control the relative “payoff” of hand via betting and bluffing. I suspect this game can really only be played pleasurably between players at a similar vocabulary level: adding betting mechanics allows players with a large vocabulary to both build better words and have better insight into the relative value of their hand. Eg. score more points and do a better job of identifying situations where they should increase their bet (or fold).

These three patterns dominate the commercial word game space, for both board games and mobile gaming.

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It has recently come to our attention that there are a large number of people in the world who cheat at online hangman. They use technology to crack good hangman words. Who knew? I swear, we built our hangman solver strictly as an academic exercise! To quote Captain Renault in Casablanca:

I’m shocked, shocked to find gambling going on here!

We at Hanging Hyena, as loyal guardians of the public morals, have launched a historic research project. Yup, we’ve already booked our tickets to Stockholm.

Our question: Are certain words for hangman harder to guess than others?

This specific question isn’t exactly unexplored. However, most of the available studies presume an unassisted human player will be using their findings. That’s just so 1995! We’re moving this analysis into the 21st century, and providing our participants with access to the finest hangman solver on the Internet! Our new question:

What words should you play in hangman if you suspect your opponent is cheating?

In other words, we want very HARD hangman words….

To understand the impact of cheating on game outcome, we dissected how a hangman cheat program gives the cheating player an advantage. First, your effective vocabulary is massively expanded – with about 70K eligible words at your disposal, you’re the uber word-nerd! But wait, there’s more! The cheat tool eliminates most of your word recall bias – eg. since you probably don’t actually walk around thinking about midevil warfare or flesh eating warts! But the really big edge – which trumps all the others – is that a good hangman cheat program lets you use what statisticians call “conditional probability” to eliminate words faster. This lets you step around the worst of the good hangman words.

Most of us know that vowels are the most common letters of the alphabet and logically should be your first guess in game of hangman. A and E are generally good guesses. However, there’s a limit to just how much of this stuff you can keep in your noggin…

For example, the distribution of letters does vary by word length. E is best for longer words, A is best for shorter words, S is usually a very good second guess. Static decision making tactics like this lose their value several moves into the game. If several guesses have already been made, the universe of possible words may be reduced to under a hundred – with a radically different letter distribution. A cheat program gives a player the ability to refine their next guess using the remaining words after each guess. This will create a significant advantage (-2 handicap for Spock, – 8 handicap for Homer Simpson).

During the past several days, we have played about 240,000 games of hangman, using a simulator. For the computer scientists in the audience, we ran this as a map-reduce job. We took the solver program behind this site and applied it to every word in the Enable dictionary (same one used by Zynga for Hanging With Friends). The computer used the suggest letters feature of our solver to pick the most effective letter to guess for each round. We kept track of how many strikes each word racked up and tallied the answers. And we created rules to find good hangman words.

Since every player has the choice of guessing a letter or guessing a word, our simulator looked at how many potential words remained at the end of each guess. Once the list of possible words got small enough, it would switch to guessing words (vs. iterating through the remaining letters). This mimics how a human guesser usually acts (filters down to a list of possible words, picks a target word to focus their final guesses around).

We gave extra credit if the universe of possible words stayed “huge” for most of the round. For example, words where a rational guesser never got below 20 words until the last few guesses ranked higher than words where the guesser quickly reduced the list of possible words down to 3 – 4 candidates. This reduces the odds of the player successfully ignoring “rational guidance” and making a lucky guess…

So what did we learn:

• As most of you are well aware, Hanging With Friends (the usual field of battle for this stuff) gives you a handful of strikes until your cute little character takes a tumble. Fortunately for you, our solver gets the word in under five strikes almost 80% of the time. Yippie!!!

• There are a bunch of “skunk words” – words where there is a good chance a rational opponent can guess the word without a single strike. Some of these were actually relatively intelligent sounding words – they were just part of a fairly small set of words you could find at with safe guesses (A, E, etc.). Easy prey for a highly literate player.
• Many words are hard to solve – even with a hangman solver. These are likely to work against a normal player. This was the starting point for finding unbeatable words.
• Surprisingly- most of these hard words are not weird words. No 15th century art. No pagan rites. No suspicion? Weird words are not good hangman words.
• Many of these are common and simple words. They look so similar to other words that the other player can’t tell them apart…

Picking The Good Hangman Words

So what do you send your frenemy? What are the Unbeatable Words?

Funny, Lucky, Ducky, Faux, Bomb, Mock, Muck

In a word…4 or 5 letter words. No. Not THAT four letter word. Although it is also hard to guess. The safest words inflict strikes before they get most of the word on the board.

JAZZ is an interesting case. While it is technically hard to guess, we’re not sure if you can actually get the double Z in Hanging With Friends (rare tile). It is also fairly famous as a hard hangman word, so an experienced player will likely be on the lookout for JAZZ.

Many four letter words are unbeatable words because they overwhelm your opponent with possible options. Several five letter words also had good results. Here are some examples:

• 4 letter words ending in “uff”. Nine to choose from, most you know (cuff, buff, puff, etc.). Plus you will inflict a bunch of strikes before they figure out you played an “f”.
• The simulator has a sense of humor – here are some of the more ironic choices that did well: Faux, Bomb, Tomb, Dump, Mock, Baby, Void, Muck (most “uck” words did well)…
• “Funny” – absolutely awesome word. Generally dished out eight strikes BEFORE the universe of possible words got below 50, plus another four before the computer got within legitimate distance of a guess (<10 possible words). Best of all – this one looks totally innocent…
• Some “Ky” words – Lucky, Ducky…delivered similar beatings to what “Funny” dished out, with a similarly low level of suspicion…
• My personal favorite – “capo” (mob boss). Knows how to whack ’em when they come looking for him…

We approached this project as an analysis of traditional Hangman. However, for those of you interested in Hanging with Friends, you should be aware that Zynga tweaked their version which reduce the number of guesses. The most significant tweak is their policy of giving you a free letter – usually the last vowel of a word. This reduces the average # of guesses required (for a hanging with friends cheat) by 20% (about 1/2 guess per word).

So there you have it. Some of these words are not like the others. So get off your duff (another excellent choice) and go prank a cheetah with one of the impossible words!

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