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!
I’m increasingly convinced that Friedemann Friese‘s 2009 board game Power Grid: Factory Manager (BoardGameGeek) presents gamers with a highly-digestible model of the energy economy in a capitalist society. In Factory Manager, players aim to financially-optimise a factory over time, growing production and delivery capacity through upgrades in workflow, space, energy, and staff efficiency. An essential driving factor in the game is that energy costs will rise sharply throughout. Although it’s not always clear in advance when or by how much, this increase in the cost of energy is always at the forefront of the savvy player’s mind as it’s one of the biggest factors that will ultimately impact their profit.
Given that players aim to optimise for turnover towards the end of the game (and as a secondary goal, for the tie-breaker: at a specific point five rounds after the game begins) and not for business sustainability, the game perhaps-accidentally reasonably-well represents the idea of “flipping” a business for a profit. Like many business-themed games, it favours capitalism… which makes sense – money is an obvious and quantifiable way to keep score in a board game! – but it still bears repeating.
There’s one further mechanic in Factory Manager that needs to be understood: a player’s ability to control the order in which they take their turn and their capacity to participate in the equipment auctions that take place at the start of each round is determined by their manpower-efficiency in the previous round. That is: a player who operates a highly-automated factory running on a skeleton staff benefits from being in the strongest position for determining turn order and auctions in their next turn.
The combination of these rules leads to an interesting twist: in the final turn – when energy costs are at their highest and there’s no benefit to holding-back staff to monopolise the auction phase in the nonexistent subsequent turn – it often makes most sense strategically to play what I call the “sweatshop strategy”. The player switches off the automated production lines to save on the electricity bill, drags in all the seasonal workers they can muster, dusts off the old manpower-inefficient machines mouldering in the basement, and gets their army of workers cranking out widgets!
With indefinitely-increasing energy prices and functionally-flat staff costs, the rules of the game would always eventually reach the point at which it is most cost-effective to switch to slave cheap labour rather than robots. but Factory Manager‘s fixed-duration means that this point often comes for all players in many games at the same predictable point: a tipping point at which the free market backslides from automation to human labour to keep itself alive.
The demise of the automated car wash may seem trivial next to these former triumphs of homo technologicus but it sits on the same continuum. It is just one of a gathering list of technologies that we used to be able to use, but can no longer express (through market or state spending) a purpose for. More worrying, however, is the direction in which we are willingly going in our collective decision to move from complexity to simplicity. The demise of the automated car wash has not followed a return to the practice of people washing their own cars (or paying the neighbours’ kid to do it). Instead we have more or less happily accepted serfdom (the use of debt and blackmail to force people to work) and slavery (the use of physical harm) as a reasonable means of keeping the cost of cleaning cars to a minimum (similar practices are also keeping the cost of food down in the UK). This, too, is precisely what is expected when the surplus energy available to us declines.
I love Factory Manager, but after reading Watkins’ article, it’ll probably feel a little different to play it, now. It’s like that moment when, while reading the rules, I first poured out the pieces of Puerto Rico. Looking through them, I thought for a moment about what the “colonist” pieces – little brown wooden circles brought to players’ plantations on ships in a volume commensurate with the commercial demand for manpower – represented. And that realisation adds an extra message to the game.
Beneath its (fabulous) gameplay, Factory Manager carries a deeper meaning encouraging the possibility of a discussion about capitalism, environmentalism, energy, and sustainability. And as our society falters in its ability to fulfil the techno-utopian dream, that’s perhaps a discussion we need to be having.
But for now, go watch Sorry to Bother You, where you’ll find further parallels… and at least you’ll get to laugh as you do so.
VICTORIA, BC – After data collection from thousands of parties across the country, reports are coming in that the annoying person who brings an acoustic guitar to a party is now officially less hated than the person who expects everyone to sit down and play Cards Against Humanity.
“At least when some asshole starts playing the tune to Wonderwall you can get up and go to a different room,” says Michelle Kalleta, 22, avid partygoer. “Jerks who show up with any sort of card game expect everyone to play, and the last thing I want to do at a party is sit in a circle with a bunch of people who think they’re hilariously edgy.”
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.
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.
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.
If you liked this, you might also be interested in:
Have you ever come across non-transitive dice? The classic set, that you can get in most magic shops, consists of three different-coloured six-sided dice:
There are several variants, but a common one, as discussed by James Grime, involves one die with five “3” sides and one “6” side (described as red below), a second die with three “2” sides and three “5” sides (described as green below), and a third die with one “1” side and five “four” sides (described as blue below).
They’re all fair dice, and – like a normal six-sided dice – they all have an average score of 3.5. But they’ve got an interesting property, which you can use for all kinds of magic tricks and gambling games. Typically: the red die will beat the green die, the green die will beat the blue die, and the blue die will beat the red die! (think Rock, Paper, Scissors…)
If you want to beat your opponent, have them pick a die first. If they pick green, you take red. If they take red, you take blue. If they take blue, you take green. You now have about a 60% chance of getting the highest roll (normally you’d have about a 33% chance of winning, and a 17% chance of a draw, so a 60% chance is significantly better). To make sure that you’ve got the best odds, play “best of 10” or similar: the more times you play, the less-likely you are to be caught out by an unfortunate unlucky streak.
But if that doesn’t bake your noodle enough, try grabbing two sets of nontransitive dice and try again. Now you’ll see that the pattern reverses: the green pair tends to beat the red pair, the red pair tends to beat the blue pair, and the blue pair tends to beat the green pair! (this makes for a great second act to your efforts to fleece somebody of their money in a gambling game: once they’ve worked out how you keep winning, give them the chance to go “double or nothing”, using two dice, and you’ll even offer to choose first!)
The properties of these dice – and of the more-exotic forms, like Oskar van Deventer’s seven-dice set (suitable for playing a game with three players and beating both of your opponents) and like the polyhedral varieties discussed on Wikipedia – intrigue the game theorist and board games designer in me. Could there be the potential for this mechanic to exist in a board game? I’m thinking something with Risk-like combat (dice ‘knock out’ one another from highest to lowest) but with a “dice acquisition” mechanic (so players perform actions, perhaps in an auction format, to acquire dice of particular colours – each with their own strengths and weaknesses among other dice – to support their “hand” of dice). There’s a discussion going on in /r/tabletopgamedesign…
I’ve even written a program (which you’re welcome to download, adapt, and use) to calulate the odds of any combination of any variety of non-transitive dice against one another, or even to help you develop your own non-transitive dice sets.
Here’s another non-transitive game for you, but this time: I’ve made it into a real, playable game that you can try out right now. In this game, you and I will each, in turn, predict three consecutive flips of a fair coin – so you might predict “tails, heads, heads”. Then we’ll start flipping a coin, again and again, until one of our sequences comes up. And more often than not, I’ll win.
[button link=”https://danq.me/penney/” align=”center” size=”large” caption=”Click here to play a non-transitive coin game.”]Play “Penney’s Game”[/button]
If you win 10 times (or you lose 20 times, which is more likely!), then I’ll explain how the game works, so you know how I “cheated”. I’ll remind you: the coin flips are fair, and it’s nothing to do with a computer – if we played this game face-to-face, with a real coin, I’d still win. Now go play!
For our fourth day at the Edinburgh Fringe, Ruth, JTA and I decided to take a little break from the rushing-around-to-comedy-shows game and get out and see the sights. Ruth had somehow acquired a somewhat romantic idea of nearby Leith: that it would be full of quays and boats and suchlike, and not – as we would come to discover instead – full of rain and a foul-smelling burst sewer pipe.
We started with breakfast from Snax Cafe, under Matt‘s recommendation, which turned out to be a good one, as this tiny greasy spoon/takeaway turns out to serve a fantastic selection of fried foods ready-to-eat at great prices. I opted for a fried egg sandwich, with which I quickly made a mess of my t-shirt and shorts when I accidentally spilt the yolk all over myself.
A combination of the weather quickly turning against us, Leith being significantly further away than it first appeared on a map, and the three of us still being remarkably tired since the previous day turned this expedition into a far more arduous affair than we had initially expected. By the time we’d reached the pretty little boats and bars of the waterfront, we were damp (admittedly, we’d all but JTA underdressed for the excursion: his overcoat helped protect him, but it had the side-effect of making him look like a flasher, his bare legs poking out from under it).
We escaped from the weather just as it began to get sunnier again, into a pub called the Teuchter’s Landing, which Ruth had discovered earlier during her research into the area. There, we drank beer and played some of the boardgames made available by the pub: Scrabble™ (at which I scored abysmally low, for which I partially blame rotten luck on draw after draw: my final hand – representative of my fortunes – was R-R-R-L-L-U-O; my starting hand contained only one consonant), the Who Wants To Be A Millionare boardgame (which took a significant amount of sorting to put it back into a working order, and in which we had to work around some missing pieces), and a few hands of Knockout Whist (with the most static-electricity-inducing deck of cards I’ve ever encountered: almost impossible to deal without giving each player four or five cards at the same time).
The food was good, though: we lunched upon freshly-made haggis stovies, served in mugs, with chunky chips (in further mugs) and oatcakes. And when we were done, and set out into the world again to explore the waterfront… that’s when it began raining again, even harder than before. Fucking marvellous.
By the time we’d worked our way around the docks, we were damp and tired, so we found a bus to take us back to Princes’ Street, cut across to a cheesemonger in Grassmarket to stock up on delicious cheeses, and then returned to the flat for a quick nap, because we were all pretty pooped.
Later, we went out for another helping of Peter Buckley Hill and Some Comedians. Being Tuesday – the day before Buckers’ day off – and close to the end of the Fringe, he was clearly exhausted, and kept digressing from the usual (awesome) shite to random stream-of-consciousness new shite. Still all funny, and some enjoyable guests.
I’ve had a few weekends fully of party. It’s no wonder I’m knackered.
First, there was Andy‘s 30th birthday. Ruth, JTA and I slogged our way over to Cardiff to celebrate in style with pizza, booze, and dancing.
Siân‘s got more to say on the subject, but suffice it to say this: it’s been a long, long time since I’ve found myself dancing in a nightclub until half past two in the morning, then grabbing a thoroughly disgusting-looking (but remarkably good-tasting) portion of fried food as an after-club snack. Oh, and Alec drooled all over himself long before he ended up sharing a bed with me.
Honestly, I didn’t think I had it in me to party like that any more: I’m such an old man (having myself turned thirty a good year and a bit prior). Didn’t stop me from getting up before anybody else the following morning for a quick geocaching expedition, though…
Summer Party On Earth
The following weekend was the Summer Party On Earth: an event that started out with Ruth saying “Let’s have a summer party!” and finished as a nostalgia-themed marathon of epic proportions.
This… was a party with everything. It had kids’ toys like Brio wooden railway, Lego bricks, and a marble run; it had soup and buffets and a barbeque and cakes; it had board games and party games and drinking games; it had beer and wine and cocktails; it had the world’s tiniest and most-nettley geocaching expedition… and from the time that we first started entertaining guests to the moment that the last of them left, it lasted for an exhausting 36 hours.
It was particularly interesting to get together with people from all of our varied social circles: workmates, former workmates, local friends, distant friends, partners of friends… all kinds of random folks coming to one place and – for example – pointing foam guns at one another.
In order to help us identify, classify, and dispose of some of the vast collection of booze that Ruth has recently inherited, JTA invented a drinking game. What can I say about it? Well: it certainly brought us all a lot closer together to suffer through some of the drinks we were served…
As usual for any party at which Ruth caters, everybody was required to consume their own weight in (delicious, delicious) desserts, and we only just finished eating the very last of the party food, almost two weeks later.
Matthew & Katherine’s Wedding
Finally, then, just the weekend after that, was the wedding of two folks I know via the Oxford Quakers: Matthew and Katherine.
I turned down the curious “What to expect at a Quaker wedding” leaflet as I entered: after all, I felt like an old-hand now, after helping make Ruth & JTA’s wedding into one of the most spectacular events ever. Well, maybe I shouldn’t have, because every wedding is as different as every bride and groom, and Matthew and Katherine’s was no exception. They’d clearly put so much thought into exactly what it is they wanted to do to celebrate their special day, and – with their help of their friends and family – had pulled everything together into a beautiful and remarkable occasion.
For me, particular highlights included:
One of the most adorable couples ever.
Not just a “vegetarian-friendly” meal, but one where vegetarianism was the norm (and guests were required to state if this wasn’t okay for them).
Catching up with folks who I don’t see as much of these days as I might like (and meeting new people, too).
A céilidh! More weddings should have these (although it’s the first time I’ve ever seen a “first dance” where the bride and groom were given instructions on what steps to do right before the music started).
I hadn’t really talked about it yet, because I’ve been too busy… I don’t know… blogging about Marmite and beds and computers or something… but I had the most fabulous time at a New Year’s party hosted by Liz and Simon at their house in Macclesfield. There was drinking, and board games, and truly awful Troma films, and then at midnight we all counted down from 7, or 12, or something, and spontaneously broke out into a chorus of Auld Lang Syne. See: there’s a video and everything –
It seems that my mnemonic (as used in the title of this post) is broken, unless we reinstate Pluto as a planet and rename the fourth and eighth planets in the solar system to Lars and Septune, respectively. Which I think are better names, anyway.
It was a fantastic opportunity to catch up with folks I don’t see enough of, to talk about what had gone right (and wrong) about the year gone by, and what we were looking forward to in the year to come. Liz suggested that perhaps this should become a regular thing, a little like “fake Christmas” has begun to, and that seems like a good idea (and I’m pretty sure I heard Bryn volunteer to host it next year…).
By the way: do you remember how last year Paul, Ruth, JTA and I invented Argh! It Burns Night? We’re doing it again this year, and because so many of you expressed an interest in joining us, we’d like you to come too. It’ll be on the evening of Saturday 4th February (yes, we know this is a little late for a Burns Night, but the second part of Ruth & JTA’s honeymoon is going to get in the way otherwise): drop me an email if you want to come along for a night of haggis, whisky, and fanfiction.
Family Picnic: Joining Ruth and JTA at Ruth’s annual family picnic, among her billions of second-cousins and third-aunts.
New Earthwarming: Having a mini housewarming on New Earth, where I live with Ruth, JTA, and Paul. A surprising number of people came from surprisingly far away, and it was fascinating to see some really interesting networking being done by a mixture of local people (from our various different “circles” down here) and distant guests.
Bodleian Staff Summer Party: Yet another reason to love my new employer! The drinks and the hog roast (well, roast vegetable sandwiches and falafel wraps for me, but still delicious) would have won me over by themselves. The band was just a bonus. The ice cream van that turned up and started dispensing free 99s: that was all just icing on the already-fabulous cake.
New Earth Games Night: Like Geek Night, but with folks local to us, here, some of whom might have been put off by being called “Geeks”, in that strange way that people sometimes do. Also, hanging out with the Oxford On Board folks, who do similar things on Monday nights in the pub nearest my office.
Meeting Oxford Nightline: Oxford University’s Nightline is just about the only Nightline in the British Isles to not be using Three Rings, and they’re right on my doorstep, so I’ve been meeting up with some of their folks in order to try to work out why. Maybe, some day, I’ll actually understand the answer to that question.
Alton Towers & Camping: Ruth and I decided to celebrate the 4th anniversary of us getting together with a trip to Alton Towers, where their new ride, Thirteen, is really quite good (but don’t read up on it: it’s best enjoyed spoiler-free!), and a camping trip in the Lake District, with an exhausting but fulfilling trek to the summit of Glaramara.
That’s quite a lot of stuff, even aside from the usual work/volunteering/etc. stuff that goes on in my life, so it’s little wonder that I’ve neglected to blog about it all. Of course, there’s a guilt-inspired downside to this approach, and that’s that one feels compelled to not blog about anything else until finishing writing about the first neglected thing, and so the problem snowballs.
So this quick summary, above? That’s sort-of a declaration of blogger-bankruptcy on these topics, so I can finally stop thinking “Hmm, can’t blog about X until I’ve written about Code Week!”