Magic: the Gathering and the axiom of choice

After yesterday’s exertions on the golf course, I took it a bit easier today. Mostly I worked on Darths & Droids story planning, but I took a lunch break to walk up to the local shops and get a chicken burger for lunch.

I also had some interesting discussions with friends in our online chat. Some of it was Darths & Droids story planning, so I won’t go into that further. But somehow we segued into a discussion of the phasing rules in Magic: the Gathering – I think prompted by Mark Rosewater’s latest design article, in which he says:

We’re experimenting with making phasing deciduous.

Okay, this probably makes no sense if you don’t know the early history of Magic: the Gathering, but bear with me. Phasing is a rule that first appeared in the game in 1996, but which was considered too confusing and cumbersome to use again. But now they’re playing with bringing it back, at least in a limited way. (“Deciduous” in the above quote means a rule mechanic that they always consider available to include in new card sets if it makes sense for that set.)

Phasing, in essence, is an effect that makes cards in play behave as though they are not in play – they “phase out” for a turn and then reappear. While phased out, nothing can affect them, nor can the phased out card affect anything else. It’s as if they are briefly shunted to another reality.

In the ensuing discussion, I said they shouldn’t merely have one “alternate reality” – things should be able to phase into specific other realities, of which there could be several… or even infinitely many. Then if you have two infinite sets of alternate realities orthogonal to one another, and you reference them by real numbers (i.e. all the integers, rationals, algebraic irrationals, and transcendental numbers), you could phase all of your creatures in such a way that you could duplicate them using the Banach-Tarski theorem. (For a reminder on why that premise leads to that conclusion, refer to my Irregular Webcomic! annotation on the Banach-Tarski theorem.)

Someone of course immediately pointed out that you can only use the Banach-Tarski theorem if you assume the axiom of choice to be true. (For a simple primer on the axiom of choice, see my annotation on that.)

Then someone else said that rule 722.2a of the Comprehensive Rules of Magic: the Gathering (June 1, 2020 edition) might actually imply the axiom of choice. Rules 722.2a says:

722.2a At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. This sequence may be a non-repetitive series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns. It can’t include conditional actions, where the outcome of a game event determines the next action a player takes. The ending point of this sequence must be a place where a player has priority, though it need not be the player proposing the shortcut.

Example: A player controls a creature enchanted by Presence of Gond, which grants the creature the ability “{T}: Create a 1/1 green Elf Warrior creature token,” and another player controls Intruder Alarm, which reads, in part, “Whenever a creature enters the battlefield, untap all creatures.” When the player has priority, they may suggest “I’ll create a million tokens,” indicating the sequence of activating the creature’s ability, all players passing priority, letting the creature’s ability resolve and create a token (which causes Intruder Alarm’s ability to trigger), Intruder Alarm’s controller putting that triggered ability on the stack, all players passing priority, Intruder Alarm’s triggered ability resolving, all players passing priority until the player proposing the shortcut has priority, and repeating that sequence 999,999 more times, ending just after the last token-creating ability resolves.

The argument is that it is not only possible within the rules of MtG to produce a loop of actions, but nested loops of actions, and at each loop this rule says you can specify how many times the loop is executed. If the nest of loops is infinitely deep, this means that you are effectively choosing an element from each of an infinite number of sets, where each set contains an infinite number of elements. The rules of the game say you can do this. Therefore the rules of the game say that you can apply the axiom of choice.

This is, in mathematical terms, a rather simplistic case and doesn’t (I believe) in fact rely on the axiom of choice to be doable in an actual game (although I may be wrong), but that didn’t stop us having a fun discussion about it. It was topped off by the original proposer of the example of rule 722.2a saying:

I’m not sure what it says about us that I can say “the Magic: the Gathering comprehensive rules imply the axiom of choice” as a throwaway joke, and the responses are “your rule numbering is out of date”, “no they don’t” and “actually maybe they do” (and not, for example, “ha”, “what the fuck”, or “you nerd”).

This is nowhere near the nerdiest argument we’ve ever had, by the way…

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Goldfish updates

This morning I took Scully for a walk and along the way passed a banksia tree which had a couple of rainbow lorikeets feeding on the flowers. I was pretty close, and wondered if I could get close enough to take a decent photo with my phone (which like all phones doesn’t have much telephoto capability). I was within a step or two of the tree and aiming the phone, but I scared the birds away. But I was reasonably quick on the shutter button, and managed to get this.

Taking flight

Not too bad for an opportunistic shot.

I spent some time updating the Magic: the Gathering Goldfish Draft website that I maintain, adding/updating results from tournaments and adding a bunch of the card lists we used. You can now see the evolution of the card list as we gained experience with various combinations and the potential for ludicrous scores. The recent tournament we did (mentioned here when I was actively playing it out) now has the scores in.

My score was 10148.9 points, or 7.775×10148 in standard scientific notation. You might think this is a pretty high score, but that only managed to place me sixth out of eight players. The winning score was about 10↑↑↑4 (using Knuth’s up-arrow notation for large numbers). Suffice to say this number is so large that it’s impossible to write it down in the form 10101010… because the number of 10s you’d need to add to that continued exponentiation itself is too large to write down.

Yeah, this is pretty nerdy stuff.

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Cauliflower Bomb!

This morning I went to play a round of golf at the local course. I enjoyed the time outside and getting some exercise, but my round was poor, scoring my equal worst total for the 9 holes. So let’s forget that and move on.

Speaking of high scores, I spent some time calculating my score in the Goldfish Draft Magic: the Gathering tournament that I mentioned yesterday. I needed a spreadsheet to keep track, and ended up with a score of 7.8×10144, as best I can estimate. That’s nowhere near the winning score, alas, as at least three of the other players have been mentioning that their scores require Knuth’s up-arrow notation to write down succinctly.

Tonight for dinner I cooked a thing taken from a TV recipe that my wife saw the other day. It’s a roast miso-seasoned cauliflower, with a bunch of toppings an garnishes. The recipe is here (although it doesn’t list the ingredients for the cashew cream, which is 2/3 cup cashews, 1 tbsp maple syrup, and 1 tsp apple cider vinegar).

Miso Cauliflower Bomb

It wasn’t hard to make, and it was delicious! I’ll definitely be cooking this again.

New content today:

Goldfishing

I’ve been busy today participating in a Goldfish Draft Magic: the Gathering tournament with my friends. This is a tournament format invented by one of my friends, in which we draft cards (a bit like a normal Magic draft), then build a deck and calculate our score based on how much damage we can do to an unresponsive opponent in 7 turns. That is each player’s score – we don’t actually play any games of Magic against one another.

We’ve done this style of tournament several times in the past and it’s always a blast. But it’s truly mind-bending. My score in the last game was 3.75×1040, and I’m pretty sure that was a losing score.

Yes… in fact after checking with my friends, we have records that the winning score in that tournament was approximately 10↑↑↑7, where the arrows are Knuth’s up-arrow notation. Calculating one’s score usually involves a spreadsheet. Yes, we do this for fun. Yes, we’re nerds.

I also wrote some new comic scripts for Darths & Droids. And did various cooking and housework stuff.

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Late Friday: Magic event

Writing Friday night’s post on Saturday morning, because last night was the huge Magic: the Gathering games night event that I’ve been organising for weeks. So, now that my friends have been surprised, I can finally reveal some details!

I put together a cube draft tournament, selecting 360 Magic cards from various different sets, and randomly distributing them to produce 24 faux boosters, for the booster draft format. I even printed cover pictures for the faux boosters and sealed the cards inside. Here’s a picture of the 24 faux boosters – There’s a theme, which you might be able to recognise. Be quick, I’m going to spoil it in the next paragraph:

The theme is that all these things were released in 1993-1995. Not coincidentally, Magic: the Gathering was released in 1993. The gimmick with this cube draft was that many of the cards I selected were from some of the very early released sets of Magic. Now, some of those cards were very powerful and have never been reprinted, so they are scarce, and thus have become insanely valuable over time. The best known are the so-called “Power Nine” cards, which now change hands for prices of the order of several thousand US dollars each. I started playing Magic after these cards had stopped being printed, so I don’t own any of them. But I have a friend who started playing Magic before me, and he has a full set of all these early sets, including not only the Power Nine, but also dozens of other rare and very valuable cards. (If you know Magic, he has complete sets of Unlimited, Antiquities, Legends, The Dark, and an almost complete set of Arabian Nights.)

He hasn’t played with those cards for some time, and wondered if I would like to use them in games with my Magic playing group. Needless to say I leapt at the opportunity to borrow them! I selected 360 of the most powerful cards I could get my hands on, including some cards from more recent sets from my own collection (I kept track of ownership in a spreadsheet). I double-sleeved the cards to protect them, then created the faux boosters ready for playing.

My friends had no idea what I had prepared; I’d only told them that I was organising a draft tournament and would provide all the cards. To get into the spirit of “old timey” stuff, I suggested we get dressed up in jackets and ties, and I brought several bottles over to make cocktails. While we waited for the last players to arrive, they speculated on what was in store. Someone suggested I had made an entire self-designed Magic set based on a James Bond theme.

Old Timey Magic draft

When everyone had arrived, I handed out the first booster packs. Everyone was intrigued by the cover design but nobody picked up on the theme. Then when they opened the packs and saw the cards within… It was great. Many expressions of shock and disbelief as most of them saw for the first time with their own eyes renowned cards they’d only ever heard about in hushed tones before, and realised they were going to get to play games with them.

We went through the rounds of drafting, with many expressions of incredulity at the cards they were seeing. And then built our decks and played the games, which led to several epic and hilarious plays throughout the evening.

For those savvy with the game, one memorable incident from a game I played: I mana-accelerated into Eureka, thinking my hand stacked with huge creatures would prevail over whatever my opponent had. He put out Nicol Bolas, which bemused me because he didn’t have the necessary lands to pay for the upkeep. But then he put out Tawnos’s Coffin, which I thought would neutralise one of my big creatures, but then he activated it to exile his own Nicol Bolas, and I realised his cunning plan. On his next turn he played the last land he needed to pay Bolas’s upkeep, and unleashed him from the Coffin…. and it was all over red rover for me, as Nicol Bolas proceeded to pound me for huge damage until I was dead.

By the end of the night, much fun had been had by all, and everyone agreed it had been one of our most memorable Magic tournaments ever!

(The other thing I did on Friday before going to games night was finish a new entry for 100 Proofs that the Earth is a Globe…)

New content today:

Die Bahn

Two things today: I put the finishing touches on the preparation for Friday night’s Magic: the Gathering event. Phew. It was a lot of work, but it’s good to have it completed. Now I just have to wait with eager anticipation for Friday night, when my friends and I get to play this tournament!

And secondly I did some preparation for my upcoming trip to Germany for ISO photography standards meetings. My wife is travelling with me. Unfortunately because of the way the dates work out and the time zone shift, we have to fly back home from Frankfurt on the evening of the day before our wedding anniversary, and we don’t get home until the morning of the day after our anniversary. Basically, we’re going to lose our anniversary this year. We end up spending a couple of hours waiting for a connecting flight at 3am in Dubai Airport, but that’s not exactly conducive to a romantic meal or anything. So I’ve booked a fancy restaurant in Cologne for the evening before we leave, two days early. It’s a place we’ve eaten at before, so we know it’ll be good.

I also booked our connecting train tickets today. Die Bahn is a great service, but gosh the tickets are expensive. We’re travelling from Frankfurt Airport to Essen, where we’re going to attend a day of the Spiel board gaming fair, and then we travel back to Cologne for my ISO meetings, before heading home. It’ll be a short trip, but should be fun!

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Comic batching

I still had three or four strips to write in the latest batch of Irregular Webcomic!, so I started on those first thing this morning. I powered through writing them in about an hour or so, and it was still early enough to get to work on photographing, so I did. I had to run down to the garage to retrieve my Lego Jabba the Hutt for one new comic. It would have been ideal to have the Lego Boushh figure as well, but I don’t have that so I had to improvise:

... holding a thermal detonator!

Now that I look at it, I realise this scene shouldn’t have Leia in the slave outfit next to Jabba… but, oh well. Anyway, building sets and taking photos for the comics took several hours, and I didn’t finish until a late lunch time.

After lunch I took Scully for a walk and dropped in at the small nearby supermarket to pick up some fruit. And this afternoon I starting putting the finishing touches on the Magic: the Gathering thing I’m preparing for Friday night. It’s nearly finished – hopefully I’ll be able to finish it off tomorrow so I can work on some other things later in the week.

New content today:

Lazy Sunday

The title pretty much sums it up. Slept in, took Scully for a couple of walks and plays in the park, and otherwise bummed around the house.

What I did was mostly sorting through old Magic: the Gathering cards. Over the years my friends and I have played dozens of booster draft tournaments as new sets were released, and I had dozens of old decks from these tournaments lying around. I decided to sort all the cards and put them into some proper storage. I haven’t completed the task… at the moment the dining table is covered in piles of cards. I’ll try and finish it tomorrow.

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One quarter of the way

Today I wrote another one of the 100 Proofs that the Earth is a Globe, number 25 out of the planned 100. A nice milestone! In fact, I have more than 100 planned… but it’s a quarter of the way to the nominal target.

In the afternoon I did more preparation for the Magic: the Gathering event I’m planning for my friends. I still have several hours worth of work to do, but I should have plenty of time before the date, which is still over 2 weeks away.

That’s kind of all I’ve done today – those two things together took up over 12 hours of work. Well, I also took Scully for a walk and cooked dinner (curried vegetables in pastry parcels) and other normal daily stuff. I’m a bit tired now…

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Magical Sunday

Most of today I spent doing more preparation for the Magic: the Gathering game night I’m organising for my friends. Not much more I can say about it at this stage, I’m afraid.

Apart from that, my wife and I went out for a late lunch at Balmoral Beach, which is a pleasant harbour beach about 15 minutes drive away. We had a pleasant lunch of beetroot and roast pumpkin salads on the promenade looking across at the beach and the water. The weather was still a little windy, but there were several people enjoying the sunshine and swimming in the water, though most of the people there were on the grass, having picnics, walking dogs, etc. Unfortunately I forgot to take my phone, so I couldn’t capture any photos of the beach to show you.

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