If you haven’t muttered this under your breath a few times, you likely haven’t played Scrabble very much.But are you muttering this because of a mental block or truly bad tiles? Within the vast universe of possible Scrabble racks, what does “good” look like?

The serious Scrabble player would state that the effective value of a hand depends on where you are in the game. The early game favors scrabble racks that “play well with others”, giving you relatively large words with common letters that can easily be patched onto an open board. The end game favors prefixes, suffixes, and small words you can sneak into an open space. Bonus squares and the opportunity to build on large (5 – 7 letter) existing words also boost your score. All of this is true.

But here is a simpler way to approach the question: what if we look at the highest scoring word you can create using just the letters in your rack?

Mathematically, this question became: for a standard Scrabble rack, how many points of words (aka. the expected value) should the average Scrabble rack contain?

Fortunately, this question is easily answered with a little computer modeling (described at the end of this article). We simulated drawing tiles from the standard scrabble distribution and fed them into a word solver program. This program identifies the word with the highest score which could be constructed from each set of tiles. When we tallied up the results after 10,000 iterations, here is how the points were distributed:

Key points from this analysis:

• The median points value per scrabble hand came out between 9 – 10 points.
• Almost everybody had something….hands with less than six points were rare…
• Bingo’s were fairly common: about 12% of scrabble hands could be sorted into words which would consume all seven letters if placed on the board “standalone”.

So the next time you’re stuck looking at a rack of letters you can’t seem to reassemble into a reasonable word, take hope! Statistically, there’s at least one word hiding in there and in many case…a rather nice one!

Or as us math nerds like to say: A Solution Exists

Details of the Analysis:

This analysis treats scrabble in a manner similar to a game of seven card “stud” poker; select seven tiles (cards) and see what you can make with them. Instead of poker’s set of possible hands, we’re looking for English words. To implement this idea, we used Python to build a simulation model: we randomly selected seven tiles from the scrabble letter distribution. These seven tiles were fed them into a dictionary search program that identifies the words that can be built from those tiles. We scored the words and selected the highest word. If the word used all seven tiles, we gave credit for a scrabble bingo (+50 points). Since computer time is cheap, we repeated the process 10,000 times.

The post What Good Looks Like: The Expected Value of a Scrabble Rack appeared first on Hanging Hyena.

We opted for a minimalist approach – enter your letters and we give you a list of possible words. The player is free to play them how they wish – keeping them involved in the strategy of how to put down their tiles while we help out with crunching through the dictionary of potential words. This gives a nice balance of help without making the game too easy…

Naturally, we did a version of the scrabble solver which was customized into a words with friends helper. Same basic design, just optimized some features for that game. Interestingly enough – while I suspect most of our audience is actually playing words with friends, the bulk of our scrabble traffic is on the regular scrabble solver. We actually saw a similar effect on the hangman offering – people tend to use the relatively generic hangman solver rather than our customized hanging with friends cheat.

We did look at a couple of alternatives – the algorithm behind the scrabble helper is actually fairly flexible. One of our early designs actually envisioned a full board solver. From a technical perspective, this would have been fairly straighforward. We would have basically written some loops to generate the additional cells (full board vs. row) and then extended our solver to iterate across the different rows/columns. The biggest challenge, from a usage perspective, is the chore of entering / maintaining every more. We suspected that would turn off about 99% of the audience (based on analysis of a couple of similar sites)…. and thus our simpler approach (which gets a bit more love).

The key is balance – give people just enough assistance that they can win a little more often, while giving them just enough skin in the game that they want to keep playing..

Incidently, we’re open to feedback – if there’s a feature you like / hate / love / need, drop us a line and we’ll take a look at it…

Head Hyena.

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Give it a try and let us know what you think. It has the same basic look and feel as our regular Hangman Solver, which you are (hopefully) already using!

The post New Improved Solver For Hanging With Friends appeared first on Hanging Hyena.

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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