About this Journal
Current Month
 12345
6789101112
13141516171819
20212223242526
2728293031
Jul. 22nd, 2008 @ 03:31 pm Uncountable infinities in Magic
Tags: , ,
Update, someone else raised a very similar question on a message board. Indeed, using much the same technique I suggested, and I had found that link once before, but forgotten about it.

Page 1
Page 2

On page 1, someone asks a rules question that's a particularly apposite example of uncountable rules:

* The defender has generated an infinite number of small blocking creatures
* (Using a combo which involves mana burning down to a negative infinite amount of life!)
* The attacker has a spell which will win the game if any creature is unblocked
* The attacker uses two Nacatl War Pride, which when it attacks copies itself for each defending creature
* And turns both Nacatl War Pride into creatures that also are doubling season ("whenever a counter is put into play, instead put twice that many into play", although I think only the first one is relevant). Thus the second one puts an infinite number of creatures into play, to which an infinite number of doubling effects apply
* And asks "Will there be any unblocked attacking creatures?"

It's a particularly good example, because the cardinality is exactly relevant: the defender is exactly trying to make a bijection between blocking creatures and attacking creatures, and the attacker wants to know if there will always be an excess attacking creature.

On the second page someone proposes an explicit bijection (or rather, absence of a bijection).
I think this is functionally equivalent to my example.
About this Entry
Jul. 20th, 2008 @ 02:48 pm Sample Format: Infinite Magic II
Tags: , ,
In Magic:TG, you have a deck of 60+ cards, containing at most four of any card (except basic lands, which produce mana). This is sort of an historical aberration. When Richard Garfield first invented Magic:TG he was working out what it should be from scratch, and he imagined people trading one-on-one for cards they wanted, thus part of the game is acquiring the cards you need, and part of the game is building a deck out of them, and part of the game is playing a game with those decks.

However, it turned out that the internet came along and made it very easy to trade cards with people all over the world. Thus a casual player might be limited by the cards they had to hand, but someone willing to pay, or a professional player who had to pay to get the best deck, could buy the best cards. So, instead a rule was instituted you could only have 4 of any card, and magic cards are designed with this assumption.

Read more... )

I'd be interested to see the metagame (which decks are good, and which beat which other ones, like rock-paper-scissors), but it doesn't look like it'll be very different to playing finite decks with no four card limit.

Next time

What if you play with the four card limit on infinite decks? (Or maybe ban cards which are very broken in this format?)
About this Entry
Jul. 18th, 2008 @ 05:59 pm Sample format: Infinite magic 1 [1]
Tags: , ,
Is there a simple example which would make use of the rules? How about infinite magic: each player starts with infinite life?

It would be a place where people who like making infinite combos could play, because those would always be the best way to win, and never beaten to the punch by someone attacking for 20 or 30 points of damage :) I doubt that would be a fun format forever, but it would be very nice to try :)

The normal methods of kills would be:

* doing infinite damage
* special cases, like "you win the game" cards, and giving ten poison counters
* running out of cards (that's a loss)
* doing damage each turn for an infinite number of turns[2]

Of course, there'd be some other differences: Read more... )
About this Entry
Jul. 18th, 2008 @ 04:38 pm An infinite amount of pain
Tags: , ,
Back to the example of Magic:TG. People have often pondered the most appropriate infinity rules. There's a few things it would be nice to do:

* If you gain an infinite amount of life, you can't be killed by any finite amount of damage
* If you gain an infinite amount of life, you can be killed by an infinite amount of damage
* If you gain nought life an infinite number of times, it doesn't make any difference

In jargon, "gain an infinite amount of life" refers to a cycle of moves which gains life and you could repeat without stopping. (Eg. "When X happens, gain 1 life", "When you gain life, do Y" and "When Y happens, do X".)

Read more... )
About this Entry
Jul. 17th, 2008 @ 06:49 pm To infinity and beyond and beyond
Infinity rules in go

Any go rule is generally either universal, or divides rulesets into three groups[1] which play the same in practice: one which ignores it; one which uses a big ban-hammer to make it deterministic, but proponents of the third interpretation think is anaesthetic; and one which defines it terms you can only understand if you already have a good go player's intuition about the game.

1. The "ko" rule This says that you cannot immediately repeat a board position. If black places a stone at a, capturing a white stone at b, white cannot immediately place a stone at b, if this captures the black stone right back again.

This is a venerable part of the game of go, and any alternative interpretation has to be equivalent to it.

Although it would be interesting to see if any of the alternatives would make sense. How would go change if the "ko" rule said that the first player could not repeat the ko position? That would favour a defender rather than an attacker. Or the chess rule allowing a player to claim a draw (or equivalently, letting the ko repeat forever). That would mean the player in the stronger position would be unable to play in the ko.

Superko rule )
About this Entry
Jul. 17th, 2008 @ 05:49 pm To infinity and beyond
I've spent all day thinking about this now, and not got that far, because go is a game of unsurpassed depth and subtlety, and my head hurts :) In any game where each player acts in turn, and it's possible for a sequence of moves to repeat, the rules have to face the question of what to do if the players get stuck in a loop.

In Magic:TG there are complicated but well-defined set of rules which invite you to compare them to either conceptualised rules "what would happen if you could repeat the sequence infinitely many times" or "what happens if it went on and on, but one player had to break out of the loop eventually". (These are often discussed, eg. on toothywiki.)

In magic the situation is complicated by it sometimes mattering how many times you went round the loop (eg. if you can repeatedly put a new creature into play, can you end up with infinite creatures? Or an arbitrarily large amount?) But it occurred to me, the rules are essentially doing the same job as the ko rule in go or the three-repeats-or-fifty-reversible-moves-is-a-draw rules in chess.

In chess or go, going round the loop multiple times is the same as going round it once, so if you ever break out of the loop, it's the same as doing so at once.

How do the actual rules in place compare to what would happen if you could endlessly repeat?

Chess )
About this Entry
May. 19th, 2008 @ 04:20 pm Illuminati
On Saturday, I joined sonic, mobbsy, martin and pseudomonas for board games, and Mobbsy introduced us to Illuminati. This was something I'd heard about, and always felt I should play at some point, and it turns out it is pretty fun.

I've got a feeling there wasn't quite the full experience; we took a little while to get used to the mechanics, and so there wasn't as much cut-throat action as is possibly normal, but it's funny, and fairly easy to get into: the rules are somewhat complicated, but less so than many games and quite intuitive. And it took quite a while to get through a game.

But it didn't feel like a long time, it never dragged, and was definitely fun.

Thanks to Mobbsy for explaining the rules to us all, that's always a little uphill (especially if you feel constrained in your ability to play evilly and make backstabbing deals by having to compromise with the need to explain to people what's going on and what might be fair and what might not.)

Description )
About this Entry
Apr. 25th, 2008 @ 11:03 am (no subject)
Tags: , ,
Portal ✓
About this Entry
Dec. 10th, 2007 @ 02:31 pm Balderdash
Tags: ,
I assume it goes without saying that I'm not very good at Balderdash :) However, I was wondering about the rules.

The basic idea (varied slightly in different incarnations) is that one player picks a random word (or film title, or acronym[1]), either by drawing the next card in the pile from the published game, or by flopping a dictionary open in the freestyle version.

She announces it, and then each other player invents a definition, handed to her on a bit of paper. Then she reads them all out, and each player guesses which is correct. You get one point for guessing the correct definition, and one point for each person who guesses yours.

This has the implicit assumption that no-one will know the definition already. Typically, if you know the right definition beforehand, you get N points (where N is 1 or larger), but don't participate in the rest of the round. (One set of rules says the rest of the round is cancelled if several players do.)[2]

The question is, what's the fairest way of doing it? Should players be rewarded for knowing? It's actually barely related to the real point of the game. Giving them a bonus and moving on seems most sensible.

Another option would be that you don't get anything extra; you make up a definition anyway, and just get one extra point for voting for the right one.

Another would be that your definition is entered, and everyone who votes for an equivalent answer to the real one gets a point, but you get a point for anyone who votes for yours instead of the real one.

The things to avoid are: it being an advantage to *not* know the answer, which really seems unfair, and putting too much judgement on the caller. After all, if she doesn't know wha

[1] You know what I mean.

[2] Did someone in fact get it right?

Words are ok, you generally know or not.

Complete the silly law is ok for the opposite reason. They're all made up, so (unless by an immense stroke of luck, you actually really know the answer), you don't get any points for saying something else it's illegal to do on Tuesdays in Cardiff -- after all, there's lots of things -- you have to guess what's on the card.

But we had difficulty with people. Do you have to guess whatever's on the card, however weird? The correct answer for "John Dee" was "invented the crystal ball" and for "Christian Huygens" was "invented the pendulum clock"[3]. Do you get points for saying "British court magician/philosopher" and "Dutch physicist and astronomer"[4]?

Those are possibly less specific, but a whole lot more accurate. They (when we went over to the internet) basically the first sentences of the wikipedia entries.

But if so, how is the caller supposed to know if they're accurate or not? I guessed that John Dee supposedly invented the crystal ball, but I wouldn't done if I didn't know who he was.

[3] Leaving aside the inaccuracy of that.

[4] I wasn't *sure* of either. I knew the scientists I was thinking of existed and had similar names, but I could equally well have been confused with "Jack Dee" and "Hayden Christensen"
About this Entry
Nov. 15th, 2007 @ 01:55 pm (no subject)
I was flicking through, on top of the pile of books to give away, a Gor book. Amongst many other peccadillos it describes a chess variant. My original thought had been that it was so stupid, obviously chess with a few ill-thought out extra rules tacked on that are totally incompatible. Okay, that's still what I think, but having experimented with penultima, I'm going to admit it's *possible*.

The key characteristics described:

* A slightly larger board and slightly larger number of pieces

Perfectly reasonable. Unnecessary, in my opinion, to make it more impressive, more complicated interactions would sound better, it's not like chess is "solved", but perfectly reasonable.

* The king-equivalent piece, and some others, are placed on the board within the first n moves.

* Weaker opponents playing experts often claim advantages, eg. handicapping the expert by several pieces.

Yes, that works. It's a lot harder to calibrate than in go, where it works well: missing a queen is a decisive disadvantage. On the other hand, good players can certainly beat me starting from behind. I suspect most of the time one or other would still have a notable advantage in the game. But it's possible.

* In the game described, the expert appears to be losing, makes three random moves, which ultimately reveal a "check", allowing a minor piece to take the king-equivalent piece on the last move, one move before the other player would have won.

That's a reasonable description of an expert winning against a weaker player in an apparently strong position. It didn't ring true to me, though. At first, I missed what they were describing. But even after, I know how easy it is to fall into fool's mate or similar, but with more of the pieces clear of the board, and examining the meaning of an apparently bizarre move, you think you could easily examine every piece.

My current rationale is that the pieces interact in some way, so that the minor piece was unusually strong (a vague description along these lines was made, but not clear if it meant only used in conjunction with, or it actually altered how the piece can move), eg. its move depends on the configuration of others, so the weaker player forgot that it might be able to move like that.

I don't think that was in the mind of the author, but it's consistent.

* A weaker player is often given an advantage, to move thrice in succession once in the game.

This just sounded mad. The king-equivalent piece was described as "captured", not "check-mated", so in most positions, this would be an instant win! How is that not completely unbalanced?

I really don't think this was thought through. On the other hand, it's not impossible. In go, for instance, it would be similar to starting with several pieces on the board, or the expert player conceding several areas of the board at once, both of which are negatives, but completely recoverable.

My rationale is that something like check-mate applies even if it's described, eg. pieces prevent other pieces from moving near them, or similar, so protection applies even when it's not your turn, or that check-mate applies to the king. Then, it might just be possible to guard even intermediate points, so the weaker player can't bring in the pieces necessary for even a fool's mate. But I still don't think it was a good idea.

* A naturally gifted player can beat a good player on their second ever game.

I just don't believe it. However gifted, whatever you've heard, it surely takes longer than that to learn the moves of the pieces?
About this Entry
Aug. 28th, 2007 @ 02:38 pm (no subject)
A while back I was considering porting my flash game to run standalone and efficiently, or possibly designing a sequel so, but wasn't sure what language (a) suited me (b) was conveniently cross-platform and (c) could handle reasonably efficient and clear code, but also put graphics on the screen with no fuss. It seemed possible the answer was java, which worried me.

Then I considered various cross-platform graphic libraries, SDL (popular cross-platform simple 2-d graphics library), Allegro (based on SDL, also provides sprites, etc,) and wondered if there was anything that actually handled tiles, etc I could borrow.

Recently it occurred to me possibly the code I should have been using was http://en.wikipedia.org/wiki/Gnash (cross-platform GPL flash player, though possibly not up-to-date on windows) :)
About this Entry
Jul. 18th, 2007 @ 11:29 pm Narbacular Drop
Narbacular Drop is ingenious.

It's a free computer game. It's based in a simplistic 3D world, made out of orthogonal surfaces in one of two or three textures (so far) with a few objects.

The twist is that you can cause a portal to be connected between any two points -- aim at a wall, and open one end, and aim at another wall and open another end. That *sounds* like it would make getting anywhere trivial, but it's rather hard.

The portals are elegant. It doesn't feel like teleporting from A to B, but rather causing A and B to become topologically joined. You can see through, you can move in either direction, other things can come through. The portals can be anywhere, wall, floor ceiling, and gravity switches when you come through; there can be a moment where you see yourself running in your original orientation relative to the portal before reorienting and falling.

(It wouldn't quite work in real life because walls aren't impervious and objects aren't atomic. And actual wormholes raise questions about continuity of gravity, etc. But it fits here perfectly.)

(I always wanted to achieve that effect with penultima rules, warping the board rather than the pieces, but couldn't quite manage it.)
About this Entry
Jul. 9th, 2007 @ 02:19 pm Deadly Rooms of Death -- Journey to Rooted Hold
This is the sequel to DROD (caravelgames.com), that along with Chip's Challenge and Puzzle Pits inspired the Winnie-the-Pooh flash game.

It was very good. It felt easier than DROD, actually. I don't know if that's just because I'd got more used to the style, or was playing more intently. There were few rooms where I got really stuck, though many I had to take a break from.

I liked the story. Non-invasive, but funny and slightly creepy. Introducing story into a puzzle game is hard but they did it well.

I'm afraid I wimped out for hints three times -- once about half way when I wished I hadn't but was tired, once when I'd completed a room but wanted to know if I could retrace my steps without replaying it, and once on a too-tedious level on the penultimate level.

Spoilers )
About this Entry
Mar. 19th, 2007 @ 04:20 pm CUSFS games
Tags: ,
Friday night was CUSFS games evening. This was almost entirely new CUSFS, but full and fun.

Poohsoc people came too (hi!) stressing the forming giant geek collective :)

There was zendo, which was pleasant. Rules were guessed which were simple and elegant, and had pretty koans. I'm trying to articulate the sort of rule I want to make, but can't manage better than "one that makes everyone laugh when they work it out"...

There was a game I can't remember the name of. Have a grid of indented hexagons with lots of balls resting on, and take it in turns to drop a ball on other balls. The aim is place all your balls: balls which end up on hexagons of the same colour are deleted.

Any game that uses real physics is really fun. You could do something similar with dice somehow or other. But watching a ball skitter chaotically (literally) from hexagon to hexagon once they're jarred loose is really cool. You have an intuitive understanding of how the rules work, despite not having seen the game before, because much of them rely on your already-understood notions of dynamics.

And there was a massive 15-player game of roborally. The quote sums it up, "For the first two and a half hours, it was pretty fun." I'm glad I did it, though probably it's something to be done only once, as it is insane.

Variants making robots race past each other are 100% more fun. Demolition derby may be over the top, but configurations designed to produce interactions are good. Watching six robots skitter back and forth on a conveyor-belt as half tried to move one way and half the other was worth the price of admission. A long solitary dash to the last checkpoint was not very fun.

I did eventually win though, though Ed was close behind at the end as I stalled for about four turns due to having three damage and no good cards. In your face, people good at roboralley! :)

The most satisfying moment was breaking from back end of the pack with two judiciously-timed-dealt move-three cards to dash across the maelstrom board, and due to a robotic arm tag the checkpoint on the conveyor past as everyone ahead fought to disembark. Followed about two turns of me scooting round the conveyor to the next checkpoint while everyone argued about who was in the lead, until I made a break onto the next board and everyone languishing in a big pileup said "Wait, did you touch the checkpoint already? Maybe I'm not in the lead after all" :)

Then I came home and got six hours of sleep.
About this Entry
Feb. 26th, 2007 @ 06:29 pm Invitation: Dinner and Games (Munchkin) on Saturday
Tags: ,
Again, on Saturday a couple of friends are coming round for dinner

* hopefully Chinese takeaway

and conversation and games

* hopefully SPAAAACE MUNCHKIN
* or Killer Bunnies, or Carcassonne, or Zendo, depending who turns up.

And it would be good if you would join us. Does anyone want to? Come at about 7.30 and we'll order food, or if you want let me know what you want beforehand and I'll add it to the order.
About this Entry
Feb. 14th, 2007 @ 03:14 pm Wake and Afmaelisdagr
Reeve: You're polychromatic and overly large!
Companions: You couldn't light up a face, let alone a world.
Reeve: Yah, boo, you blow!
Companions: Yeah, s'right! So's your mother!
Companions: Sun! Sun! Sun! Shun! Shun! Shun!
Spectator: What are you doing?
Reeve: We're winding the sun up. Didn't you read website?

OK, for the record that was completely fictional. But CUSFS and Jomsborg the New did successfully raise the sun for the next year. Dan invoked a fearsome vaguely germanic speech exhorting the sun to rise, we circled, we libated mead, we shouted, and the sun came up.

It had the shape and aspect of like a death circus, with lasers and stuff, which is the best shape it's had for ages :)

And the wake was fun. We played Penultima, and Zendo, and a long bridge session, and a few rounds of Concrete, Abstract or Squoingy, kept the reeve awake, and got to Castle Mound in plenty of time.
About this Entry
Jan. 9th, 2007 @ 05:19 pm This Saturday, MAO AND GAMES all afternoon and BLACK TIE BIRTHDAY all evening
Happy New Year, all!

I will shortly be 25 years old, and in honour of the occasion I would like to invite you to two parties on saturday.

ALL AFTERNOON (2pm->) there will be MAO AND GAMES.
ALL EVENING (8pm->) there will be BLACK TIE PREFERRED PARTY.


It would be wonderful if as many of you as possible could come. Especially if people who don't normally play Mao any more would like to give it a go, and if everyone would come in the evening.

If you want to come from outside Cambridge, I may be able to arrange crash-space -- let me know. (And apologies to people who would like to come but are missing out, or who haven't met me.)

Please bring a bottle and other half, and not a present unless you must :) We will order takeaway food inbetween, feel free to come at 7ish if you want to eat. You don't have to RSVP but it would be good to know if you want to come, particularly if you want to play mao so I know how many people will be there.

Directions and contact: http://semichrome.net/~jack/social/directions.html

Thank you,

Jack (aka CartesianDaemon)
About this Entry
Oct. 24th, 2006 @ 01:34 am Pizza
Tags: , , ,
They changed the menu at Pizza Express. They had a wide variety of intense mushroom consisting dishes, which we all ordered piles of and surrounded senji mwahahaing.

We visited Fivemack (thank you!) to taste eastern european wines of interesting quality.

We played bridge again. I enjoyed it, though would let the other players say whether they did or not :) I wouldn't say I played well, per se, but I think reasonably confidently, and with some idea of what was where. Of course, we played four hands and no-one scored any positive points at all (hey, the four-nil trump split wasn't my idea. Bidding the other hand up, I'll take the blame for), so it was fun, and I will try again again.
About this Entry
Oct. 17th, 2006 @ 12:26 pm Bridge
Tags: , ,
At the end of post pizza we played Bridge, for me the first time in many many years. It was pretty fun, the play style is about as casual as I like it, and the play level close enough to mine that I can reasonably follow about what's going on.

I think the problem when I first learnt bridge was I was taught very large amounts of things at about the same time, and couldn't tell the defference between a rule and a convention, or maxims applicable 90% of the time and maxims applicable 10% of the time. And too swamped by information to concentrate on common sense ways to play

Tangent on other things learnt this way )

But playing with very simple, natural conventions, and some common sense during play, I find it feels like I do have some intuition for what's right afterall. Now practice and learning might actually help :)

To put it another way

I've been on both sides, in Bridge, and other varied incidents in games, maths, life. Someone quite naturally offers good advice like "At the end, when you played the SX, you should have played the Sy because [explanation]."

But often, the advice you *should* give is "At the start of the game, you should see if you're likely to make any tricks in S and if so how it might be possible."

In fact, the beginner had lost track in S before that point, so the advice is useless, because they didn't understand it so won't remember it.

In fact

At home I drew out a random hand and studied how each I'd play it. It somehow made much more sense than it did eight years ago :) And having an idea of how the hand is going to play out as a whole makes bidding entirely more intuitive :)
About this Entry
Sep. 13th, 2006 @ 11:07 pm ...their twitchy little noses...
Tags: , ,
And in Tuesday's update, thanks to sonic for croquet and killer bunnies! It was a fun evening. Though I think I'm not cut out for world domination, I drew nearly all of the bunnies, and nearly all of the macguffins, and felt awfully guilty sitting there with six bunnies to everyone else's none, mowing them down as they appeared. Martin killed them all with a giantic black hole, but it was too late. It did come down to a 50/50 chance in the end, as the winning card was the last one drawn, and the penultimate drawer had a choice of two.
About this Entry