A long while ago, inspired by Nick Berry‘s analysis of optimal Hangman strategy, I worked it backwards to find the hardest words to guess when playing Hangman. This week, I showed these to my colleague Grace – who turns out to be a fan of word puzzles – and our conversation inspired me to go a little deeper. Is it possible, I thought, for me to make a Hangman game that cheats by changing the word it’s thinking of based on the guesses you make in order to make it as difficult as possible for you to win?
The principle is this: every time the player picks a letter, but before declaring whether or not it’s found in the word –
Make a list of all possible words that would fit into the boxes from the current game state.
If there are lots of them, still, that’s fine: let the player’s guess go ahead.
But if the player’s managing to narrow down the possibilities, attempt to change the word that they’re trying to guess! The new word must be:
Legitimate: it must still be the same length, have correctly-guessed letters in the same places, and contain no letters that have been declared to be incorrect guesses.
Harder: after resolving the player’s current guess, the number of possible words must be larger than the number of possible words that would have resulted otherwise.
You might think that this strategy would just involve changing the target word so that you can say “nope” to the player’s current guess. That happens a lot, but it’s not always the case: sometimes, it’ll mean changing to a different word in which the guessed letter also appears. Occasionally, it can even involve changing from a word in which the guessed letter didn’t appear to one in which it does: that is, giving the player a “freebie”. This may seem counterintuitive as a strategy, but it sometimes makes sense: if saying “yeah, there’s an E at the end” increases the number of possible words that it might be compared to saying “no, there are no Es” then this is the right move for a cheating hangman.
Playing against a cheating hangman also lends itself to devising new strategies as a player, too, although I haven’t yet looked deeply into this. But logically, it seems that the optimal strategy against a cheating hangman might involve making guesses that force the hangman to bisect the search space: knowing that they’re always going to adapt towards the largest set of candidate words, a perfect player might be able to make guesses to narrow down the possibilities as fast as possible, early on, only making guesses that they actually expect to be in the word later (before their guess limit runs out!).
I also find myself wondering how easily I could adapt this into a “helpful hangman”: a game which would always change the word that you’re trying to guess in order to try to make you win. This raises the possibility of a whole new game, “suicide hangman”, in which the player is trying to get themselves killed and so is trying to pick letters that can’t possibly be in the word and the hangman is trying to pick words in which those letters can be found, except where doing so makes it obvious which letters the player must avoid next. Maybe another day.
In the meantime, you’re welcome to go play the game (and let me know what you think, below!) and, if you’re of such an inclination, read the source code. I’ve used some seriously ugly techniques to make this work, including regular expression metaprogramming (using regular expressions to write regular expressions), but the code should broadly make sense if you want to adapt it. Have fun!
You may recall that on Halloween I mentioned that the Bodleian had released a mini choose-your-own-adventure-like adventure game book, available freely online. I decided that this didn’t go quite far enough and I’ve adapted it into a hypertext game, below. (This was also an excuse for me to play with Chapbook, Chris Klimas‘s new under-development story format for Twine.
If the thing you were waiting for before you experienced Shadows Out of Time was it to be playable in your browser, wait no longer: click here to play the game…
Notes from #musetech18 presentations (with a strong “collaboration” theme). Note that these are “live notes” first-and-foremost for my own use and so are probably full of typos. Sorry.
Matt Locke (StoryThings, @matlocke):
Over the last 100 years, proportional total advertising revenue has been stolen from newspapers by radio, then television: scheduled media that is experienced simultaneously. But we see a recent drift in “patterns of attention” towards the Internet. (Schedulers, not producers, hold the power in radio/television.)
The new attention “spectrum” includes things that aren’t “20-60 minutes” (which has historically been dominated by TV) nor “1-3 hours” (which has been film), but now there are shorter and longer forms of popular medium, from tweets and blog posts (very short) to livestreams and binging (very long). To gather the full spectrum of attention, we need to span these spectra.
Rhythm is the traditions and patterns of how work is done in your industry, sector, platforms and supply chains. You need to understand this to be most-effective (but this is hard to see from the inside: newcomers are helpful). In broadcast television as a medium, the schedules dictate the rhythms… in traditional print publishing, the major book festivals and “blockbuster release” cycles dominate the rhythm.
Then how do we collaborate with organisations not in our sector (i.e. with different rhythms)? There are several approaches, but think about the rhythmic impact.
Partnered with Google Arts & Heritage; Google’s first single-partner project and also their first project with a multi-site organisation.
This kind of tech can be used to increase access (e.g. street view of closed sites) and also support curatorial/research aims (e.g. ultra-high-resolution photography).
Aside from the tech access, working with a big company like Google provides basically “free” PR. In combination, these benefits boost reach.
Learnings: prepare to work hard and fast, multi-site projects are a logistical nightmare, you will need help, stay organised and get recordkeeping/planning in place early, be aware that there’ll be things you can’t control (e.g. off-brand PR produced by the partner), don’t be afraid to stand your ground where you know your content better.
Decide what successw looks like at the outset and with all relevant stakeholders involved, so that you can stay on course. Make sure the project is integrated into contributors’ work streams.
Daria Cybulska (Wikimedia UK, @DCybulska):
Collaborative work via Wikimedians-in-residence not only provides a boost to open content but involves engagement with staff and opens further partnership opportunities.
Your audience is already using Wikipedia: reaching out via Wikipedia provides new ways to engage with them – see it as a medium as well as a platform.
Wikimedians-in-residence, being “external”, are great motivators to agitate processes and promote healthy change in your organisation.
Creative Collaborations ( Kate Noble @kateinoble, Ina Pruegel @3today,  Joanna Salter,  Michal Cudrnak, Johnathan Prior):
Digital making (learning about technology through making with it) can link museums with “maker culture”. Cambridge museums (Zoology, Fitzwilliam) used a “Maker in Residence” programme and promoted “family workshops” and worked with primary schools. Staff learned-as-they-went and delivered training that they’d just done themselves (which fits maker culture thinking). Unexpected outcomes included interest from staff and discovery of “hidden” resources around the museums, and the provision of valuable role models to participants. Tips: find allies, be ambitious and playful, and take risks.
National Maritime Museum Greenwich/National Maritime Museum – “re.think” aimed to engage public with emotive topics and physically-interactive exhibits. Digital wing allowed leaving of connections/memories, voting on hot issues, etc. This leads to a model in which visitors are actively engaged in shaping the future display (and interpretation) of exhibitions. Stefanie Posavec appointed as a data artist in residence.
SoundWalk Strazky at Slovak National Gallery: audio-geography soundwalks as an immersive experiential exhibition; can be done relatively cheaply, at the basic end. Telling fictional stories (based on reality) can help engage visitors with content (in this case, recreating scenes from artists’ lives). Interlingual challenges. Delivery via Phonegap app which provides map and audio at “spots”; with a simple design that discourages staring-at-the-screen (only use digital to improve access to content!).
Maritime Museum Greenwich: wanted to find out how people engage with objects – we added both a museum interpretation and a community message to each object. Highly-observational testing helped see how hundreds of people engage with content. Lesson: curators are not good judges of how their stuff will be received; audience ownership is amazing. Be reactive. Visitors don’t mind being testers of super-rough paper-based designs.
Nordic Museum / Swedish National Heritage Board explored Generous Interfaces: show first, don’t ask, rich overviews, interobject relationships, encourage exploration etc. (Whitelaw, 2012). Open data + open source + design sprints (with coding in between) + lots of testing = a collaborative process. Use testing to decide between sorting OR filtering; not both! As a bonus, generous interfaces encourage finding of data errors. bit.ly/2CNsNna
IWM on the centenary of WWI: thinking about continuing the crowdsourcing begun by the IWM’s original mission. Millions of assets have been created by users. Highly-collaborative mechanism to explore, contribute to, and share a data space.
Lauren Bassam (@lswbassam) on LGBT History and co-opting of Instagram as an archival space: Instagram is an unconventional archival source, but provides a few benefits in collaboration and engagement management, and serves as a viable platform for stories that are hard to tell using the collections in conventional archives. A suitably-engaged community can take pride in their accuracy and their research cred, whether or not you strictly approve of their use of the term “archivist”. With closed stacks, we sometimes forget how important engagement, touch, exploration and play can be.
Owen Gower (@owentg) from Dr. Jenner’s House Museum and Garden: they received EU REVEAL funding to look at VR as an engagement tool. Their game is for PSVR and has a commercial release. The objects that interested the game designers the most weren’t necessarily those which the curators might have chosen. Don’t let your designers get carried away and fill the game with e.g. zombies. But work with them, and your designers can help you find not only new ways to tell stories, but new stories you didn’t know you could tell. Don’t be afraid to use cheap/student developers!
Rebecca Kahm @rebamex from Pelagios Commons (@Pelagiosproject): the problem with linked data is that it’s hard to show its value to end users (or even show museums “what you can do” with it). Coins have great linked data, in collections. Peripleo was used to implement a sort-of “reverse Indiana Jones”: players try to recover information to find where an artefact belongs.
Jon Pratty: There are lots of useful services (Flickr, Storify etc.) and many are free (which is great)… but this produces problems for us in terms of the long-term life of our online content, not to mention the ethical issues with using services whose business model is built on trading personal data of our users. [Editor’s note: everything being talked about here is the stuff that the Indieweb movement have been working on for some time!] We need to de-siloise and de-centralise our content and services. redecentralize.org? responsibledata.io?
In-House Collaboration and the State of the Sector:
Rosie Cardiff @RosieCardiff, Serpentine Galleries on Mobile Tours. Delivered as web application via captive WiFi hotspot. Technical challenges were significant for a relatively small digital team, and there was some apprehension among frontline staff. As a result of these and other problems, the mobile tours were underused. Ideas to overcome barriers: report successes and feedback, reuse content cross-channel, fix bugs ASAP, invite dialogue. Interesting that they’ve gained a print guides off the back of the the digital. Learn lessons and relaunch.
Sarah Younaf @sarahyounas, Tyne & Wear Museums. Digital’s job is to ask the questions the museum wouldn’t normally ask, i.e. experimentation (with a human-centric bias). Digital is quietly, by its nature, “given permission” to take risks. Consider establishing relationships with (and inviting-in) people who will/want to do “mashups” or find alternative uses for your content; get those conversations going about collections access. Experimental Try-New-Things afternoons had value but this didn’t directly translate into ideas-from-the-bottom, perhaps as a result of a lack of confidence, a requirement for fully-formed ideas, or a heavy form in the application process for investment in new initiatives. Remember you can’t change everyone, but find champions and encourage participation!
Kati Price @katiprice on Structuring for Digital Success in GLAM. Study showed that technical leadership and digital management/analysis is rated as vital, yet they’re also underrepresented. Ambitions routinely outstrip budgets. Assumptions about what digital teams “look” like from an org-chart perspective don’t cover the full diversity: digital teams look very different from one another! Forrester Research model of Digital Maturity seems to be the closest measure of digital maturity in GLAM institutions, but has flaws (mostly relating to its focus in the commercial sector): what’s interesting is that digital maturity seems to correlate to structure – decentralised less mature than centralised less mature than hub-and-spoke less mature than holistic.
Jennifer Wexler, Daniel Pett, Chiara Bonacchi on Diversifying Museum Audiences through Participation and stuff. Crowdsourcing boring data entry tasks is sometimes easier than asking staff to do it, amazingly. For success, make sure you get institutional buy-in and get press on board. Also: make sure that the resulting data is open so everybody can explore it. Crowdsourcing is not implicitly democratisating, but it leads to the production of data that can be. 3D prints (made from 3D cutouts generated by crowdsourcing) are a useful accessibility feature for bringing a collection to blind or partially-sighted visitors, for example. Think about your audiences: kids might love your hip VR, but if their parents hate it then you still need a way to engage with them!
I see a lot of ideas online for things to do with your child, but most of them are a lot of work. Many of them involve an unnerving amount of craftiness and/or require going out to buy things. Almost all of them involve moving around which, many days, is fine, but some days can be pretty rough. N…
I see a lot of ideas online for things to do with your child, but most of them are a lot of work. Many of them involve an unnerving amount of craftiness and/or require going out to buy things. Almost all of them involve moving around which, many days, is fine, but some days can be pretty rough. Not that I don’t love getting down on the floor and playing with my kid (I love it a great deal) but I’m an adult in my mid-thirties. I can pretend to be a dinosaur for about 90 minutes (something I happily list on my professional resume) but after an hour and a half, all bets are off. And given that many days I’m home with my son for over eight hours, things can get a bit dicey.
I’ve taken the liberty of brainstorming some fun child/parent activities in which your child can be adventurous and creative and you can lie on the sofa reading a book. Here’s my list so far.
The year was 1995, and CompuServe’s online service cost $4.95 per hour. Yet thousands of people logged into this virtual world daily.
WorldsAway was born 20 years ago, when Fujitsu Cultural Technologies, a subsidiary of Japanese electronics giant Fujitsu, released this online experiment in multiplayer communities. It debuted as part of the CompuServe online service in September, 1995. Users needed a special client to connect; once online, they could chat with others while represented onscreen as a graphical avatar.
I was already a veteran of BBSes (I even started my own), Prodigy, CompuServe, and the Internet when I saw an advertisement for WorldsAway in CompuServe magazine (one of my favorite magazines at the time). It promised a technicolor online world where you could be anything you wanted, and share a virtual city with people all over the globe. I signed up to receive the client software CD. Right after its launch in September, I was up and running in the new world. It blew my young mind.
For the last few months, I’ve been GMing a GURPS campaign (that was originally a Warhammer Fantasy Roleplay 1st-edition campaign, in turn built upon a mixture of commercially published and homegrown modules, including, in turn, an AD&D module…) for a few friends.
But mostly I wanted to make this post so that I had a point of context in case I ever get around to open-sourcing some of the digital tools I’ve been developing to help streamline our play sessions. For example, most of our battle maps and exploration are presented on a ‘board’ comprised of a flat screen monitor stripped of its stand and laid on its back, connected via the web to a tool that allows me to show, hide, or adapt parts of it from my laptop or mobile phone. Player stats, health, and cash, as well as the date, time, position of the sun as well as the phases of the moons are similarly tracked and are available via any player’s mobile phone at any time.
These kinds of tools have been popular for ‘long-distance’/Internet roleplaying for years, but I think there’s a lot of potential in locally-linked, tabletop-enhancing (rather than replacing) tools that deliver some of the same benefit to the (superior, in my opinion) experience of ‘proper’ face-to-face adventure gaming. Now, at least, when I tell you for example about some software I wrote to help calculate the position of the sun in the sky of a fictional world, you’ll have a clue why I would do such a thing in the first place.
As you may know, I’ve lately found an excuse to play with some new web technologies, and I’ve also taken the opportunity to try to gain a deeper understanding of some less bleeding-edge technologies that I think have some interesting potential. And so it was that, while I was staffing the Three Rings stall at last week’s NCVO conference, I made use of the time that the conference delegates were all off listening to a presentation to throw together a tech demo I call Steer!
As you can see from the GIF above, Steer! is a driving game. The track and your car are displayed in a web browser on a large screen, for example a desktop or laptop computer, television, or tablet, and your mobile phone is used to steer the car by tilting it to swerve around a gradually-narrowing weaving road. It’s pretty fun, but what really makes it interesting to me is the combination of moderately-new technologies I’ve woven together to make it possible, specifically:
The Device Orientation API, which enables a web application to detect the angle at which you’re holding your mobile phone
Websockets as a mechanism to send that data in near-real-time from the phone to the browser, via a web server: for the fastest, laziest possible development, I used Firebase for this, but I’m aware that I could probably get better performance by running a local server on the LAN shared by both devices
The desktop browser does all of the real work: it takes the orientation of the device and uses that, and the car’s current speed, to determine how it’s position changes over the time that’s elapsed since the screen was last refreshed: we’re aiming for 60 frames a second, of course, but we don’t want the car to travel slower when the game is played on a slower computer, so we use requestAnimationFrame to get the fastest rate possible and calculate the time between renderings to work out how much of a change has occurred this ‘tick’. We leave the car’s sprite close to the bottom of the screen at all times but change how much it rotates from side to side, and we use it’s rotated to decide how much of its motion is lateral versus the amount that’s “along the track”. The latter value determines how much track we move down the screen “behind” it.
The track is generated very simply by the addition of three sine waves of different offset and frequency – a form of very basic procedural generation. Despite the predictability of mathematical curves, this results in a moderately organic-feeling road because the player only sees a fraction of the resulting curve at any given time: the illustration below shows how these three curves combine to make the resulting road. The difficulty is ramped up the further the player has travelled by increasing the amplitude of the resulting wave (i.e. making the curves gradually more-agressive) and by making the road itself gradually narrower. The same mathematics are used to determine whether the car is mostly on the tarmac or mostly on the grass and adjust its maximum speed accordingly.
In order to help provide a visual sense of the player’s speed, I added dashed lines down the road (dividing it into three lanes to begin with and two later on) which zip past the car and provide a sense of acceleration, deceleration, overall speed, and the impact of turning ‘sideways’ (which of course reduces the forward momentum to nothing).
This isn’t meant to be a finished game: it’s an experimental prototype to help explore some technologies that I’d not had time to look seriously at before now. However, you’re welcome to take a copy – it’s all open source – and adapt or expand it. Particular ways in which it’d be fun to improve it might include:
Allowing the player more control, e.g. over their accelerator and brakes
Adding hazards (trees, lamp posts, and others cars) which must be avoided
Adding bonuses like speed boosts
Making it challenging, e.g. giving time limits to get through checkpoints
Day and night cycles (with headlights!)
Multiplayer capability, like a real race?
Smarter handling of multiple simultaneous users: right now they’d share control of the car (which is the major reason I haven’t given you a live online version to play with and you have to download it yourself!), but it’d be better if they could “queue” until it was their turn, or else each play in their own split-screen view or something
Improving the graphics with textures
Increasing the entropy of the curves used to generate the road, and perhaps adding pre-scripted scenery or points of interest on a mathematically-different procedural generation algorithm
Switching to a local LAN websocket server, allowing better performance than the dog-leg via Firebase
Greater compatibility: I haven’t tried it on an iPhone, but I gather than iOS devices report their orientation differently from Android ones… and I’ve done nothing to try to make Steer! handle more-unusual screen sizes and shapes
Anything else? (Don’t expect me to have time to enhance it, though: but if you do so, I’d love to hear about it!)
There’s a wonderful tool for making web-based “choose your own adventure”-type games, called Twine. One of the best things about it is that it’s so accessible: if you wanted to, you could be underway writing your first ever story with it in about 5 minutes from now, without installing anything at all, and when it was done you could publish it on the web and it would just work.
But the problem with Twine is that, in its latest and best versions, you’re trapped into using the Twine IDE. The Twine IDE is an easy-to-use, highly visual, ‘drag-and-drop’ interface for making interactive stories. Which is probably great if you’re into IDEs or if you don’t “know better”… but for those of us who prefer to do our writing in a nice clean, empty text editor like Sublime or TextMate or to script/automate our builds, it’s just frustrating to lose access to the tools we love. Plus, highly-visual IDEs make it notoriously hard to collaborate with other authors on the same work without simply passing it back and forwards between you: unless they’ve been built with this goal in mind, you generally can’t have two people working in the same file at the same time.
Earlier versions of Twine had a command-line tool called Twee that perfectly filled this gap. But the shiny new versions don’t. That’s where I came in.
In that way that people who know me are probably used to by now, I was very-slightly unsatisfied with one aspect of an otherwise fantastic product and decided that the correct course of action was to reimplement it myself. So that’s how, a few weeks ago, I came to release Twee2.
If you’re interested in writing your own “Choose Your Own Adventure”-type interactive fiction, whether for the world or just for friends, but you find user-friendly IDEs like Twine limiting (or you just prefer a good old-fashioned text editor), then give Twee2 a go. I’ve written a simple 2-minute tutorial to get you started, it works on Windows, MacOS, Linux, and just-about everything else, and it’s completely open-source if you’d like to expand or change it yourself.
(there are further discussions about the concept and my tool on Reddit here, here, here and here, and on the Twinery forums here, here and here)
My geek-crush Ben Foxall posted on Twitter on Monday morning to share that he’d had a moment of fun nostalgia when he’d come into the office to discover that somebody in his team had covered his monitor with two layers of Post-It notes. The bottom layer contained numbers – and bombs! – to represent the result of a Minesweeper board, and the upper layer ‘covered’ them so that individual Post-Its could be removed to reveal what lay beneath. Awesome.
Not to be outdone, I hunted around my office and found some mini-Post-Its. Being smaller meant that I could fit more of them onto a monitor and thus make a more-sophisticated (and more-challenging!) play space. But how to generate the board? Sure: I could do it by hand, but that doesn’t seem very elegant at all – plus, humans make really bad random number generators! I didn’t need quantum-tunnelling-seeded Minesweeper (yes, that’s a thing) levels of entropy, sure, but it’d still be nice to outsource the heavy lifting to a computer, right?
So naturally, I wrote a program to do it for me. Want to see? It’s at danq.me/minesweeper. Just line up some Post-Its on a co-worker’s monitor to work out how many you can fit across it in each dimension (I found that I could get 6 × 4 standard-sized Post-Its but 7 × 5 or even 8 × 5 mini-sized Post-Its very comfortably onto one of the typical widescreen monitors in my office), decide how many mines you want, and click Generate. Don’t like the board you get? Click it again!
And because I was looking for a fresh excuse to play with Periscope, I broadcast the first game I set up live to the Internet. In the end, 66 people ended up watching some or all of a paper-based game of Minesweeper played by my colleague Liz, including moments of cheering her on and, in one weird moment, dispair at the revelation that she was married. The internet’s strange, yo.
Anyway: in case you missed the Periscope broadcast, I’ve put it on YouTube. Sorry about the portrait-orientation filming: I think it’s awful, too, but it’s a Periscope thing and I haven’t installed the new update that fixes it yet.
Now go set up a game of Post-It Minesweeper for a friend or co-worker.
Rust, a 2013 indie survival game from Facepunch Studios, plays like a cross between Minecraft and Grand Theft Auto. Players find themselves “born” into a mysterious wilderness, naked and alone, forced to forage for resources and to craft clothing, supplies and shelter for themselves. They must contend with starvation, hypothermia and animal attacks, but by far the most dangerous threat comes from other players who roam the island.
When the game was first opened up, all players were given the same default avatar: a bald white man. With the most recent update, Rust’s lead developer, Garry Newman, introduced different avatars of different racial origins into the mix. However, they did so with a twist — unlike typical massively multiplayer online role-playing games, Rustdoes not allow players to choose the race of their avatar. Instead, they are assigned one at random. Newman explained the change in a blog post…
What’s the hardest word to guess, when playing hangman? I’ll come back to that.
Last year, Nick Berry wrote a fantastic blog post about the optimal strategy for Hangman. He showed that the best guesses to make to get your first “hit” in a game of hangman are not the most-commonly occurring letters in written English, because these aren’t the most commonly-occurring letters in individual words. He also showed that the first guesses should be adjusted based on the length of the word (the most common letter in 5-letter words is ‘S’, but the most common letter in 6-letter words is ‘E’). In short: hangman’s a more-complex game than you probably thought it was! I’d like to take his work a step further, and work out which word is the hardest word: that is – assuming you’re playing an optimal strategy, what word takes the most-guesses?
First, though, we need to understand how hangman is perfectly played. Based on the assumption that the “executioner” player is choosing words randomly, and that no clue is given as to the nature of the word, we can determine the best possible move for all possible states of the game by using a data structure known as a tree. Suppose our opponent has chosen a three-letter word, and has drawn three dashes to indicate this. We know from Nick’s article that the best letter to guess is A. And then, if our guess is wrong, the next best letter to guess is E. But what if our first guess is right? Well, then we’ve got an “A” in one or more positions on the board, and we need to work out the next best move: it’s unlikely to be “E” – very few three-letter words have both an “A” and an “E” – and of course what letter we should guess next depends entirely on what positions the letters are in.
What we’re actually doing here is a filtering exercise: of all of the possible letters we could choose, we’re considering what possible results that could have. Then for each of those results, we’re considering what guesses we could make next, and so on. At each stage, we compare all of the possible moves to a dictionary of all possible words, and filter out all of the words it can’t be: after our first guess in the diagram above, if we guess “A” and the board now shows “_ A _”, then we know that of the 600+ three-letter words in the English language, we’re dealing with one of only about 134. We further refine our guess by playing the odds: of those words, more of them have a “C” in than any other letter, so that’s our second guess. If it has a C in, that limits the options further, and we can plan the next guess accordingly. If it doesn’t have a C in, that still provides us with valuable information: we’re now looking for a three-letter word with an A in the second position and no letter C: that cuts it down to 124 words (and our next guess should be ‘T’). This tree-based mechanism for working out the best moves is comparable to that used by other game-playing computers. Hangman is simple enough that it can be “solved” by contemporary computers (like draughts – solved in 2007 – but unlike chess: while modern chess-playing computers can beat humans, it’s still theoretically possible to build future computers that will beat today’s computers).
Now that we can simulate the way that a perfect player would play against a truly-random executioner, we can use this to simulate games of hangman for every possible word (I’m using version 0.7 of this British-English dictionary). In other words, we set up two computer players: the first chooses a word from the dictionary, the second plays “perfectly” to try to guess the word, and we record how many guesses it took. So that’s what I did. Here’s the Ruby code I used. It’s heavily-commented and probably pretty understandable/good learning material, if you’re into that kind of thing. Or if you fancy optimising it, there’s plenty of scope for that too (I knocked it out on a lunch break; don’t expect too much!). Or you could use it as the basis to make a playable hangman game. Go wild.
Running the program, we can see that the hardest three-letter word is “xxv”, which would take 22 guesses (20 of them wrong!) to get. But aside from the roman numeral for 25, I don’t think that “xxv” is actually a word. Perhaps my dictionary’s not very good. “Oak”, though, is definitely a word, and at 20 guesses (17 wrong), it’s easily enough to hang your opponent no matter how many strokes it takes to complete the gallows.
There are more tougher words in the four-letter set, like the devious “quiz”, “jazz”, “zinc”, and “faux”. Pick one of those and your opponent – unless they’ve seen this blog post! – is incredibly unlikely to guess it before they’re swinging from a rope.
As we get into the 5, 6, and 7-letter words you’ll begin to notice a pattern: that the hardest words with any given number of letters get easier the longer they are. That’s kind of what you’d expect, I suppose: if there were a hypothetical word that contained every letter in the alphabet, then nobody would ever fail to (eventually) get it.
When we make a graph of each word length, showing which proportion of the words require a given number of “wrong” guesses (by an optimised player), we discover a “sweet spot” window in which we’ll find all of the words that an optimised player will always fail to guess (assuming that we permit up to 10 incorrect guesses before they’re disqualified). The window seems small for the number of times I remember seeing people actually lose at hangman, which implies to me that human players consistently play sub-optimally, and do not adequately counteract that failing by applying an equal level of “smart”, intuitive play (knowing one’s opponent and their vocabulary, looking for hints in the way the game is presented, etc.).
In case you’re interested, then, here are the theoretically-hardest words to throw at your hangman opponent. While many of the words there feel like they would quite-rightly be difficult, others feel like they’d be easier than their ranking would imply: this is probably because they contain unusual numbers of vowels or vowels in unusual-but-telling positions, which humans (with their habit, inefficient under normal circumstances, of guessing an extended series of vowels to begin with) might be faster to guess than a computer.
I’ve got a new favourite game, this week: Movie Title Mash-Ups (with thanks to Cougar Town). Ruth and I sat up far too late last night, playing it. Here’s how you do it:
Movie Title Mash-Ups
Take two movie titles which share a word (or several words, or just a syllable) at the end of one and at the beginning of the other. Shmoosh them together into a combined movie title, then describe the plot of that movie in a single sentence by borrowing elements from both component movies. See if anybody can guess what your mash-up movies were.
Here are some examples. The answers are ROT13-encoded, but if you’re reading this post directly on my blog, you can click on each of them to decode them (once you’ve given up!).
Zombies claw their way out of a graveyard, and Batman spends most of the film hiding in the attic. Gur Qnex Xavtug bs gur Yvivat Qrnq
While trapped in an elevator at the end of October, a superficial man is hypnotised into murdering a bunch of high-school students with knife. Funyybj Unyybjrra
A crazy professor and a kid travel back in time in a souped-up car, where local bully Biff cuts off the kid’s hand and tells him he’s his father. Gur Rzcver Fgevxrf Onpx gb gur Shgher
Bill Murray has to live the same day over and over, until he can survive the zombie apocalypse by escaping to an island. Tebhaqubt Qnl bs gur Qrnq
A pair of alcoholic, out-of-work actors stay at the countryside house of a Monty, dangerous robot who has learned to override his programming. Jvguanvy naq V, Ebobg
An evil genie who maliciously manipulates words and misinterprets wishes opens a portal between Eternia and Earth, which He-Man and Skeletor come through. Jvfuznfgref bs gur Havirefr
A bunch of outlawed vigilante superheroes fight shapeshifters and werewolves as they investigate a mystical curse which threatens to shatter the fragile cease-fire between Dark and Light forces in Russia. Avtug Jngpuzra
Harrison Ford and Michelle Pfeiffer hold a seance to communicate with subterranean humans who worship a giant bomb. Jung Yvrf Orarngu gur Cynarg bs gur Ncrf
A lion cub born to a royal family grows up, climbs the Empire State Building, and fights aeroplanes. Gur Yvba Xvat Xbat
James Bond is sent to investigate the murder of three British MI6 agents, who turn out to have been killed using a military satellite that concentrates the sun’s rays into a powerful laser. (hint: both films are James Bond films) Yvir naq Yrg Qvr Nabgure Qnl
Monopoly – the world’s best-selling board game – sucks. I’ve said it before, but it bears saying again. I’ve never made any secret of my distaste for the game, but it’s probably worth spelling out the reasons, in case you’ve somehow missed them.
Broadly-speaking, there are four things wrong with Monopoly: the rules, the theme, the history, and the players.
The following issues have plagued Monopoly for at least the last 75 years:
It takes a disproportionately long time to play, relative to the amount of fun it provides or skill it tests. A longer game is not intrinsically more-exciting: would a 1000-square Snakes & Ladders be ten times as good as a 100-square one? Monopoly involves a commitment of three to four hours, most of it spent watching other people take their turns.
It’s an elimination game: players are knocked out (made bankrupt) one at a time, until only one remains. This invariably leads to a dull time for those players first removed from the game (compounded by the game length). In real-world play, it’s usually the case that a clear winner is obvious long before the game ends, leading to a protracted, painful, and frankly dull slow death for the other players. Compare this to strategic games like Power Grid, where it can be hard to call the winner between closely matched players right up until the final turns, in which everybody has a part.
It depends hugely on luck, which fails to reward good strategic play. Even the implementation of those strategies which do exist remain heavily dependent on the roll of the dice. Contrast the superficially-simpler (and far faster) property game For Sale, which rewards strategic play with just a smidgen of luck.
It’s too quick to master: you can learn and apply the optimal strategies after only a handful of games. Coupled with the amount of luck involved, there’s little to distinguish an expert player from a casual one: only first-time players are left out. Some have argued that this makes it easier for new players to feel like part of the game, but there are other ways to achieve this, such as handicaps, or – better – variable starting conditions that make the game different each time, like Dominion.
There’s little opportunity for choice: most turns are simply a matter of rolling the dice, counting some spaces, and then either paying (or not paying) some rent. There’s a little more excitement earlier in the game, when properties remain unpurchased, but not much. The Speed Die add-on goes a small way to fixing this, as well as shortening the duration of the game, but doesn’t really go far enough.
The rules themselves are ambiguously-written. If they fail to roll doubles on their third turn in jail, the rules state, the player much pay the fine to be released. But does that mean that they must pay, then roll (as per the usual mechanic), in which case must it be next turn? Or should it be this turn, and if so, should the already-made (known, non-double) roll be used? Similarly, the rules state that the amount paid when landing on a utility is the number showing on the dice: is this to be a fresh roll, or is the last roll of the current player the correct one? There are clarifications available for those who want to look, but it’s harder than it needs to be: it’s no wonder that people seem to make it up as they go along (see “The Players”, below, for my thoughts on this).
But that’s not what Monopoly‘s about, is it? Its purpose is to instill entrepreneurial, capitalist values, and the idea that if you work hard enough, and you’re lucky enough, that you can become rich and famous! Well, that’s certainly not its original purpose (see “The History”, below), but even if it were, Monopoly‘s theme is still pretty-much broken:
It presents a false financial model as if it were a reassuring truth. “The Bank can never go bankrupt,” state the rules, instructing us to keep track of our cash with a pen and paper if there isn’t enough in the box (although heaven help you if your game has gone on long enough to require this)! Maybe Parker Brothers’ could have simply given this direction to those financial institutions that collapsed during the recent banking crisis, and saved us all from a lot of bother. During a marathon four-day game at a University of Pittsburgh fraternity, Parker Brothers couriered more money to the gamers to “prop up” their struggling bank: at least we can all approve of a bailout that the taxpayer doesn’t have to fund, I suppose! Compare this to Puerto Rico, a game which also requires a little thematic suspension of disbelief, but which utilises the depletion of resources as an important game mechanic, forcing players to change strategies in order to remain profitable.
Curiously, this same rule does not apply to the supply of houses and hotels, which are deliberately limited: the Monopoly world is one in which money is infinite but in which bricks are not. This makes it more valuable to build houses when there are few resources (in order to deprive your opponents). In actual economies, however, the opposite is true: houses are always needed, but the resources to built them change in value as they become more or less scarce. Watch the relative perceived values of the huts available to build in Stone Age to see how a scarcity economy can really be modelled.
Also, it has a completely-backwards approach to market forces. In the real world, assuming (as Monopoly does) a free market, then it is consumer demand that makes it possible to raise capital. In the real world, the building of three more hotels on this side of the city makes it less-likely that anybody will stay at mine, but this is not represented at all. Compare to the excellent 7 Wonders, where I can devalue my neighbour-but-one’s goods supply by producing my own, of the same type.
It only superficially teaches that “American dream” that you can get ahead in the world with a lot of work and a little luck: this model collapses outside of frontier lands. If you want to see what the real world is like, then wait until you’ve got a winner in a game of Monopoly, and then allow everybody else to re-start the game, from the beginning. It’s almost impossible to get a foothold in a market when there’s already a monopoly in existence. This alternative way of playing might be a better model for real-world monopolies (this truth is captured by the game Anti-Monopoly in a way that’s somehow even less-fun than the original).
You might shoot down any or all of these arguments by pointing out that “it’s just a game.” But on the other hand, we’ve already discovered that it’s not a very good game. I’m just showing how it manages to lack redeeming educational features, too. With the exception of helping children to learn to count and handle money (and even that is lost in the many computer editions and semi-computerised board game versions), there’s no academic value in Monopoly.
You’ve seen now why Monopoly isn’t a very good game both (a) because it’s not fun, and (b) it’s not really educational either – the two biggest reasons that anybody might want to play it. But you might also be surprised to find that its entire history is pretty unpleasant, too, full of about as much backstabbing as a typical game of Monopoly, and primarily for the same reason: profit!
If you look inside the rulebook of almost any modern Monopoly set, or even in Maxine Brady’s well-known strategy guide, you’ll read an abbreviated version of the story of Charles Darrow, who – we’re told – invented the game and then published it through Parker Brothers. But a little detective work into the history of the game shows that in actual fact he simply made a copy of the game board shown to him by his friend Charles Todd. Todd, in turn, had played it in New Jersey, to which it had traveled from Pennsylvania, where it had originally been invented – and patented – by a woman called Elizabeth Magie.
Magie’s design differed from modern interpretations in only one major way: its educational aspect. Magie was a believer in Georgian economic philosophy, a libertarian/socialist ideology that posits that while the things we create can be owned, the land belongs equally to everybody. As a result, Georgists claim, the “ownership” of land should be taxed according to its relative worth, and that this should be the principal – or only, say purists – tax levied by a state. Magie pushed her ideas in the game, by trying to show that allowing people to own land (and then to let out the right of others to live on it) serves only to empower landlords… and disenfranchise tenants. The purpose of the game, then, was to show people the unfairness of the prevailing economic system.
Magie herself approached Parker Brothers several times, but they didn’t like her game. Instead, then, she produced sets herself (and an even greater number were home-made), which proved popular – for obvious reasons, considering their philosophical viewpoints – among Georgists, Quakers, and students. She patented a revised version in 1924, which added now-familiar features like cards to mark the owned properties, as well as no-longer-used ideas that could actually go a long way to improving the game, such as a cash-in-hand “goal” for the winner, rather than an elimination rule.
Interestingly, when Parker Brothers first rejected Charles Darrow, they said that the game was “too complicated, too technical, took too long to play”: at least they and I agree on one thing, then! Regardless, once they eventually saw how popular Lizzie Magie’s version had become across Philadelphia, they changed their tune and accepted Darrow’s proposal. Then, they began the process of hoovering up as many patents as they could manage, in order to secure their very own monopoly on a game that was by that point already 30 years old.
They weren’t entirely successful, of course, and there have been a variety of controversies around the legality and enforcability of the Monopoly trademark. Parker Brothers (and nowadays, Hasbro) have famously taken to court the makers of board games with even-remotely similar names: most-famously, the Anti-Monopoly game in the 1970s, which they alternately won, then lost, then won, then lost again on a series of appeals in the early 1980s: there’s a really enjoyable book about the topic, and about the history of Monopoly in general. It’s a minefield of court cases and counter-cases, but the short of it is that trade-marking “Monopoly” ought to be pretty-much impossible. Yet somehow, that’s what’s being done.
What’s clear, though, is that innovation on the game basically stopped once Parker’s monopoly was in place. Nowadays, Hasbro expect us to be excited when they replace the iron with a cat or bring out yet another localised edition of the board. On those rare occasions when something genuinely new has come out of the franchise – such as 1936’s underwhelming Stock Exchange expansion, it’s done nothing to correct the fundamental faults in the game and generally just makes it even longer and yet more dull than it was to begin with.
The fourth thing that I hate about Monopoly is the people who play Monopoly. With apologies for those of you I’m about to offend, but here’s why:
Firstly, they don’t play it like they mean it. Maybe it’s because they’ve come to the conclusion that the only value in the game is to waste time for as long as possible (and let’s face it, that’s a reasonable thing to conclude if you’ve ever played the game), but a significant number of players will deliberately make the game last longer than it needs to. I remember a game once, as a child, when my remaining opponent – given the opportunity to bankrupt me and thus win the game – instead offered me a deal whereby I would give him some of my few remaining properties in exchange for my continued survival. Why would I take that deal? The odds of my making a comeback with a total of six houses on the board and £200 in my pocket (against his monopoly of virtually all the other properties) are virtually nil, so he wasn’t doing me any favours by offering me the chance to prolong my suffering. Yet I’ve also seen players accept deals like like, masochistically making their dull pick-up-and-roll experience last even longer than it absolutely must.
Or maybe it’s just that Monopoly brings out the cruel side of people: it makes them enjoy sitting on their huge piles of money, while the other players grovel around them. If they put the other players out of their misery, it would end their fun. If so, perhaps Lizzie Magie’s dream lives on, and Monopoly really does teach us about the evils of capitalism: that the richest are willing to do anything to trample down the poorest and keep them poor, so that the divide is kept as wide as possible? Maybe Monopoly’s a smarter game than I think: though just because it makes a clever point doesn’t necessarily make a board game enjoyable.
It’s not that I’m against losing. Losing a game like Pandemic is endless fun because you feel like you have a chance, right until the end, and the mechanics of games like Tigris & Euphrates mean that you can never be certain that you’re winning, so you have to keep pushing all the way through: both are great games. No: I just object to games in which winning and losing are fundamentally attached to a requirement to grind another person down, slowly, until you’re both sick and tired of the whole thing.
The second thing that people do, that really gets on my nerves, is make up the damn rules as they go along. I know that I spent a while further up this page complaining that Monopoly’s rules are pretty awful, but I can still have a rant about the fact that nobody seems to play by them anyway. This is a problem, because it means that if you ever play Monopoly with someone for the first time, you just know that you’re setting yourself up for an argument when it turns out that their crazy house rules and your crazy house rules aren’t compatible.
House rules for board games are fine, but make them clear. Before you start the game, say, “So, here’s the crazy rule we play by.” That’s fine. But there’s something about Monopoly players that seems to make them think that they don’t need to. Maybe they assume that everybody plays by the same house rules, or maybe they don’t even realise that they’re not playing by the “real” rules, but it seems to me that about 90% of the games of Monopoly I’ve been witness to have been punctuated at some point by somebody saying “wait, is that allowed?”
Because I’m a bit of a rules lawyer, I pay attention to house rules. Free Parking Jackpot, in which a starting pile of money – plus everybody’s taxes – go in to the centre of the board and are claimed by anybody who lands on Free Parking, is probably the moth loathsome house rule. Why do people feel the need to take a game that’s already burdened with too much luck and add more luck to it. My family used to play with the less-painful but still silly house rule that landing exactly on “Go!” netted you a double-paycheque, which makes about as much sense, and it wasn’t until I took the time to read the rulebook for myself (in an attempt, perhaps, to work out where the fun was supposed to be stored) that I realised that this wasn’t standard practice.
Playing without auctions is another common house rule, which dramatically decreases the opportunity for skillful players to bluff, and generally lengthens the game (interestingly, it was a house rule favoured by the early Quaker players of the game). Allowing the trading of “immunity” is another house rule than lengthens the game. Requiring that players travel around the board once before they’re allowed to buy any properties is yet another house rule that adds a dependence on luck and – yet again – lengthens the game. Disallowing trading until all the properties are owned dramatically lengthens the game, and for no benefit (why not just shuffle the property deck and deal it out to everybody to begin with: it’s faster and achieves almost the same thing?).
I once met a family who didn’t play with the rule that you have to spend 10% extra to un-mortgage a property, allowing them to mortgage and un-mortgage with impunity (apparently, they found the arithmetic too hard)! And don’t get me started on players who permit “cheating” (so long as you don’t get caught) as a house rule…
Spot something in common with these house rules? Most of them serve to make a game that’s already too long into something even longer. Players who implement these kinds of house rules are working to make Monopoly – an already really bad game – into something truly abysmal. I tell myself, optimistically, that they probably just don’t know better, and point them in the direction of Ticket to Ride, The Settlers of Catan, or Factory Manager.
But inside, I know that there must be people out there who genuinely enjoy playing Monopoly: people who finish a game and say “fancy another?”, rather than the more-rational activity of, say, the clawing out of their own eyes. And those people scare me.
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