Made a little progress on the game idea I’d been experimenting with. The idea is to do find a series of orthogonal (like a rook in chess!)
moves that land on every square exactly once each before returning to the start, dodging walls and jumping pits.
But the squares have arrows (limiting the direction you can move out of them) or numbers (specifying the distance you must travel from them).
Every board is solvable, starting from any square. There’ll be a playable version to use on your device (with helpful features like “undo”) sometime soon, but for now you can give them
a go by hand, if you like this kind of puzzle!
In light of Trump’s attempts to axe Voice of America, because it is, he claims,
“anti-Trump” (and because he’s so insecure that he can’t stand the thought that taxpayer dollars might go to anybody who disagrees with him in any way, for any reason), I’ve produced a
suggested update to the rules of Twilight Struggle for the inevitable 9th
printing:
I guess the Russian player gets to stretch their influence unchecked, anywhere they want, from 2025 onwards.
In the game, I mean.
Yet another blow to US soft power in order to appease the ego of convicted felon Donald Trump. Sigh.
I didn’t know how to solve the puzzle, but I did know how to write a computer program to solve it for me. That would probably be even more fun, and I could argue that it didn’t
actually count as cheating. I didn’t want the solution to reveal itself to me before I’d had a chance to systematically hunt it down, so I dived across the room to turn off the
console.
I wanted to have a shower but I was worried that if I did then inspiration might strike and I might figure out the answer myself. So I ran upstairs to my office, hit my Pomodoro
timer, scrolled Twitter to warm up my brain, took a break, made a JIRA board, Slacked my wife a status update, no reply, she must be out of signal. Finally I fired up my preferred
assistive professional tool. Time to have a real vacation.
…
Obviously, I’d be a fan of playing your single-player video game any damn way you like. But beyond that, I see Robert’s point: there are some
puzzles that are just as much (or more) fun to write a program to solve than to solve as a human. Digital jigsaws would be an obvious
and ongoing example, for me, but I’ve also enjoyed “solving” Hangman (not strictly a single-player game, but
my “solution” isn’t really applicable to human opponents anyway), Mastermind (this is single-player, in my personal
opinion – fight me! – the codemaster doesn’t technically have anything “real” to do; their only purpose is to hold secret information), and I never got into Sudoku principally because I
found implementing a solver much more fun that being a solver.
Anyway: Robert’s post shows that he’s got too much time on his hands when his wife and kids are away, and it’s pretty fun.
Being on your phone all the time and while also not being on your phone all the time has never been more important.
“It is as if you were on your phone” is a phone-based experience for pretending to be on your phone without needing to be on your phone. All from the comfort of your phone.
Relax and blend in with familiar gestures and realistic human behaviour.
When I tried this fun and experimental game, I was struck by a feeling of deja vu. Was this really new? It felt ever so familiar.
Turns out, it draws a lot of inspiration from its 2016 prequel, It is as if you were playing
chess. Which I’d completely forgotten about until just now.
It really is almost as if I were on my phone.
Anyway, It is as if you were on your phone is… well, it’s certainly a faithful simulation of what it would be like to be on my phone. If you saw me, you’d genuinely think that
I was on my phone, even though in reality I was just playing It is as if you were on your phone on my phone. That’s how accurate it is.
I’ve been playing Sean O’Connor’s Slay for around 30 years (!), but somehow it took until today, on the Android version,
before I tried my hand at “rewilding” the game world.
The rules of the game make trees… a bad thing: you earn no income from hexes with them. But by the time I was winning this map anyway, I figured that encouraging growback would be a
pleasant way to finish the round.
Play your videogames any damn way you want. Don’t let anybody tell you there’s a right or wrong way to enjoy a single-player game. Today I took a strategy wargame and grew a forest. How
will you play?
Except to children, I don’t really give Christmas presents to (or expect to receive them from) others any more.
But that didn’t stop my buying myself a gift of a particularly fun Lego set to build over the festive period (with a little help from the eldest child!).
Today, while I cooked dinner, I introduced my two children (aged 10 and 8) to Goat Simulator.
Within half an hour, they’d added an imaginative twist and a role-playing element. My eldest had decreed themselves Angel of Goats and the younger Goat Devil and the two were locked in
an endless battle to control the holy land at the top of a rollercoaster.
The shrieks of joy and surprise from the living room could be heard throughout the entire house. Perhaps our whole village.
My past self, receiving a copy of Transport Tycoon for his 14th birthday, would have his mind blown if he could see the kind of insanely-complex super-stations that are
possible in (the open-source successor to) the game 30 years on.
Of course, this kind of thing – multiple simultaneously shared in-and-out routes on a bidirectional station – wasn’t (sensibly) possible before the introduction of path-based signalling in OpenTTD 0.7.0. And modern path-based signals in the game are even smarter.
But still, 14-year-old me had a dream. And nowadays that dream is real.
Playing simultaneous games against both children might have been less challenging if they hadn’t both kept trying to start fights with one another at the same time! 😂
Dungeons & Dragons players spend a lot of time rolling 20-sided polyhedral dice, known as D20s.
In general, they’re looking to roll as high as possible to successfully stab a wyvern, jump a chasm, pick a lock, charm a Duke1,
or whatever.
Submerging your dice set in the blood of a halfling is a sure-fire way to get luckier rolls.
Roll with advantage
Sometimes, a player gets to roll with advantage. In this case, the player rolls two dice, and takes the higher roll. This really boosts their chances of not-getting a
low roll. Do you know by how much?
I dreamed about this very question last night. And then, still in my dream, I came up with the answer2.
I woke up thinking about it3
and checked my working.
1
2
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20
1
1
2
3
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5
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7
8
9
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18
19
20
2
2
2
3
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9
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20
3
3
3
3
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9
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20
4
4
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4
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5
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9
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20
5
5
5
5
5
5
6
7
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9
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11
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13
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15
16
17
18
19
20
6
6
6
6
6
6
6
7
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9
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17
18
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20
7
7
7
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7
7
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7
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11
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20
8
8
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18
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20
9
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10
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11
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20
12
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20
Table illustrating the different permutations of two D20 rolls and the “advantage” result (i.e. the higher of the two).
The chance of getting a “natural 1” result on a D20 is 1 in 20… but when you roll with advantage, that goes down to 1 in 400: a huge improvement! The chance of rolling a 10 or 11 (2 in
20 chance of one or the other) remains the same. And the chance of a “crit” – 20 – goes up from 1 in 20 when rolling a single D20 to 39 in 400 – almost 10% – when rolling with
advantage.
You can see that in the table above: the headers along the top and left are the natural rolls, the intersections are the resulting values – the higher of the two.
The nice thing about the table above (which again: was how I visualised the question in my dream!) is it really helps to visualise why these numbers are what they are. The
general formula for calculating the chance of a given number when rolling D20 with advantage is ( n2 – (n-1)2 ) / 400. That is, the square of the number
you’re looking for, minus the square of the number one less than that, over 400 (the total number of permutations)4.
Why roll two dice when one massive one will do?
Knowing the probability matrix, it’s theoretically possible to construct a “D20 with Advantage” die5. Such a tool would
have 400 sides (one 1, three 2s, five 3s… and thirty-nine 20s). Rolling-with-advantage would be a single roll.
I don’t think anybody’s ever built a real 400-sided die, but Numberwang! claimed to have one.
This is probably a totally academic exercise. The only conceivable reason I can think of would be if you were implementing a computer system on which generating random numbers
was computationally-expensive, but memory was cheap: under this circumstance, you could pre-generate a 400-item array of possible results and randomly select from it.
But if anybody’s got a 3D printer capable of making a large tetrahectogon (yes, that’s what you call a 400-sided polygon – you learned something today!), I’d love to see an “Advantage
D20” in the flesh. Or if you’d just like to implement a 3D model for Dice Box that’d be fine too!
Footnotes
1 Or throw a fireball, recall an anecdote, navigate a rainforest, survive a poisoning,
sneak past a troll, swim through a magical swamp, hold on to a speeding aurochs, disarm a tripwire, fire a crossbow, mix a potion, appeal to one among a pantheon of gods, beat the
inn’s landlord at an arm-wrestling match, seduce a duergar guard, persuade a talking squirrel to spy on some bandits, hold open a heavy door, determine the nature of a curse, follow a
trail of blood, find a long-lost tome, win a drinking competition, pickpocket a sleeping ogre, bury a magic sword so deep that nobody will ever find it, pilot a spacefaring rowboat,
interpret a forgotten language, notice an imminent ambush, telepathically commune with a distant friend, accurately copy-out an ancient manuscript, perform a religious ritual, find
the secret button under the wizard’s desk, survive the blistering cold, entertain a gang of street urchins, push through a force field, resist mind control, and then compose a ballad
celebrating your adventure.
2 I don’t know what it says about me as a human being that sometimes I dream in
mathematics, but it perhaps shouldn’t be surprising given I’m nerdy enough to have previously recorded instances of dreaming in (a) Perl, and (b) Nethack (terminal mode).
3 When I woke up I also found that I had One Jump from Disney’s Aladdin stuck in my head, but I’m not sure
that’s relevant to the discussion of probability; however, it might still be a reasonable indicator of my mental state in general.
4 An alternative formula which is easier to read but harder to explain would be ( 2(n
– 1) + 1 ) / 400.
5 Or a “D20 with Disadvantage”: the table’s basically the inverse of the advantage one –
i.e. 1 in 400 chance of a 20 through to 39 in 400 chance of a 1.
My life affords me less time for videogames than it used to, and so my tastes have changed accordingly:
I appreciate games that I can drop at a moment’s notice and pick up again some other time, without losing lots of progress1.
And if the game can remind me what it was I was trying to achieve when I come back… perhaps weeks or months later… that’s a bonus!
I’ve a reduced tolerance for dynamically-generated content (oh, you want me to fetch you another five nirnroot do you? – hard pass2):
if I might only get to throw 20 hours total at a game, I’d much prefer to spend that time exploring content deliberately and thoughtfully authored by a human.
And, y’know, it has to be fun. I rarely buy games on impulse anymore, and usually wait weeks or months after release dates even for titles I’ve been anticipating, to see
what the reviewers make of it.
That said, I’ve played three excellent videogames this year that I’d like to recommend to you (no spoilers):
Horizon: Forbidden West
I loved Horizon: Zero Dawn. Even if this review persuades you that you should play its sequel, Forbidden
West, you really oughta play Zero Dawn first3.
There’s a direct continuation of plot going on there that you’ll appreciate better that way. Also: Zero Dawn stands alone as a great game in its own right.
Horizon gives a lot to love, from a rich world and story, immersive environments, near-seamless loading, excellent voice acting, and a rewarding difficulty curve. But perhaps
all are second-place to what a kickass character the protagonist is.
The Horizon series tells the story of Aloy from her childhood onwards, growing up an outcast in a tribal society on a future Earth inhabited by robotic reimaginings of
creatures familiar to us today (albeit some of them extinct). Once relatively docile, a mysterious event known as the derangement, shortly before Aloy’s birth, made these
machines aggressive and dangerous, leading to a hostile world in which Aloy seeks to prove herself a worthy hunter to the tribe that cast her out.
All of which leads to a series of adventures that gradually explain the nature of the world and how it became that way, and provide a path by which Aloy can perhaps provide a brighter
future for humankind. It’s well-written and clever and you’ll fight and die over and over as you learn your way around the countless permutations of weapons, tools, traps, and
strategies that you’ll employ. But it’s the kind of learning curve that’s more rewarding than frustrating, and there are so many paths to victory that when I watch Ruth play she uses tactics that I’d never even conceived of.
Horizon: Forbidden West is like Zero Dawn but… more. More quests, more exploration, more machines, more characters, and more of the same story, answering questions
you might have found yourself thinking during the prequel. But it’s not just more-of-the-same.
Forbidden West is in some ways more-of-the-same, but it outgrows the mould of its predecessor, too. Faced with bigger challenges than she can take on by herself, Aloy comes to
assemble a team of trusted party members, and when you’re not out fighting giant robots or spelunking underwater caves or exploring the ruins of ancient San Francisco you’re working
alongside them, and that’s one of the places the game really shines. Your associates chatter to each other, grow and change, and each brings something special to the story that invites
you to care for each of them as individuals.
The musical score – cinematic in its scope – has been revamped too, and shows off its ability to adapt dynamically to different situations. Face off against one of the terrifying new
aquatic enemies and you’ll be treated to a nautical theme, for example. And the formulaic quests of the predecessor (get to the place, climb the thing…), which were already
fine, are riddled with new quirks and complexities to keep you thinking.
And finally: I love the game’s commitment to demonstrating the diversity of humanity: both speaking and background characters express a rarely-seen mixture of races, genders, and
sexualities, and the story sensitively and compassionately touches on issues of disability, neurodiversity, and transgender identity. It’s more presence than
representation (“Hey look, it’s Sappho and her friend!”), but it’s still much better than I’m used to seeing in major video game releases.
Thank Goodness You’re Here!
If ever I need to explain to an American colleague why that one time they visited London does not give them an understanding of what life is like in the North of England… this is the
videogame I’ll point them at.
Among the many language options available for the game are “English”, as you’d probably expect, and “Dialect”, which imposes a South Yorkshire accent to everything, as illustrated
here by the main menu.
A short, somewhat minigame-driven, absurd to the point of Monty Python-ism, wildly British comedy game, Thank Goodness You’re
Here! is a gem. It’s not challenging by any stretch of the imagination, but that only serves to turn focus even more on the weird and wonderful game world of Barnsworth (itself
clearly inspired by real-world Barnsley).
Playing a salesman sent to the town to meet the lord mayor, the player ends up stuck with nothing to do4,
and takes on a couple of dozen odd-jobs for the inhabitants of the town, meeting a mixed bag of stereotypes and tropes as they go along.
Ahm gowin t’shop to gi’ sumof Big Ron’s Big Pies! Y’wanout, buggerlugs? Players without a grounding in Yorkshire English, and especially non-Brits, might benefit from turning
the subtitles on.
Presented in a hand-drawn style that’s as distinctive and bizarre as it is an expression of the effort that must’ve gone into it, this game’s clearly a project of passion for
Yorkshire-based developers Coal Supper (yes, that’s really what they call themselves). I particularly enjoyed a recurring joke in which the
player is performing some chore (mowing grass for the park keeper, chopping spuds at the chippy) when the scene cuts to some typically-inanimate objects having a conversation (flowers,
potatoes) while the player’s actions bring them closer and closer in the background. But it’s hard to pick out a very favourite part from this wonderful, crazy, self-aware slice of
Northern life in game form.
Tactical Breach Wizards
Finally, I’ve got to sing the praises of Tactical Breach Wizards by Suspicious
Developments (who for some reason don’t bother to list it on their website; the closest thing to an official page for the project other than its Steam entry might be this launch announcement!)5, the
team behind Gunpoint and Heat Signature.
The game feels like a cross between XCOM/Xenonauts‘ turn-based tactical combat and Rainbow Six‘s special ops theme. Except instead of a squad of gun-toting
body-armoured military/police types, your squad is a team of wizards in a world in which magical combat specialists work alongside conventionally-equipped soldiers on missions where
their powers make all the difference.
Jen the Storm Witch primarily uses large static shocks to fling targets around: relatively harmless, unless she and her teammates have arranged for/tricked enemies to be standing next
to something they can be thrown into… or near a window they can be flung out of!
By itself, that could be enough: there’s certainly sufficient differences between all of the powers that the magic users exploit that you’ll find all kinds of ways to combine them. How
about having your teleport-capable medic blink themselves to a corner so your witch’s multi-step lightning bolt can use them as a channel to get around a corner and zap a target there?
Or what about using the time-manipulation powers of your Navy Seer (yes, really) to give your siege cleric enough actions that they can shield-push your opponent within range of the
turret you hacked? And so on.
But Tactical Breach Wizards, which stands somewhere between a tactical squad-based shooter and a deterministic positional puzzle game, goes beyond that by virtue of its
storytelling. Despite the limitations of the format, the game manages to pack in a lot of background and personality for every one of your team and even many of the NPCs too (Steve Clark, Traffic Warlock is a riot). Oh, and much of the dialogue is laugh-out-loud funny, to boot.
The dialogue between your teammates – most of it right as they’re about to breach a door – reads like lighthearted banter but exposes the underpinning backstory of the setting.
The writing’s great, to the extent that when I got to the epilogue – interactive segments during the credits where you can influence “what happens next” to each of the characters you’ve
come to know – I genuinely flip-flopped on a few of them to give some of them a greater opportunity to continue to feature in one another’s lives. Even though the game was clearly over.
It’s that compelling.
And puzzling out some of the tougher levels, especially if you’re going for the advanced (“Confidence”) challenges, too, is really fun. But with autosaves every turn, the opportunity to
skip and return to levels that are too challenging, and a within-turn “undo” feature that lets you explore different strategies before you commit to one, this is a great game for
someone who, like me, doesn’t have much time to dedicate to play.
![A notebook is held in front of terminal output. The terminal begins with 'Start position: [0,4]' and then shows a series of 5×5 grids containing numbers: one, labelled 'Route:', shows random grid of the numbers 0 through 24; the second, labelled 'Puzzle:', contains 1s, 2s, and 3s, corresponding perhaps to the orthagonal distances between consecutive numbers from the first grid; the third, whose title is obscured by the notebook, shows the same thing again but with 'walls' drawn in ASCII art between some of the numbers. The notebook in front contains hand-drawn sketches of similar grids with arrows "jumping" around between them.](/_q23u/2025/03/20250313_100059-640x487.jpg)
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