Hanamikoji by Kota Nakayama

At least ten years ago I played a round of Street Fighter IV with my best friend Nat (Yep, the same Nat that is now the other half of Curious Lynx) and I still think about that round more often than is probably reasonable.

There was a small break in the action and Nat threw an attack that was visibly mistimed - too far away from me and too slow to land, and I saw it. I knew how I could punish it.

But I didn't bite.

Something about Nat's mistake was too obvious. Nat is not a player who throws moves away at that range. If I were playing against my son or anyone else in the room that I’d identified as a button-masher, I would have gone in ‘guns’ blazing. Instead I started up a counter that I could cancel out of, just in case the whole thing was a trap.¹

He cancelled out of his attack and jumped in on a counter-punish. I cancelled out of my counterattack and dashed to safety, and we both backed off.²

To anyone watching, a whole lot of nothing had happened. Two characters kinda wiggled at each other and stepped apart. The real game - the bluff, the counter-bluff, the counter-counter-bluff… it had taken place entirely in our heads.

The only outwardly visible evidence that anything had happened at all was that we both immediately burst out laughing, much to the bafflement of the friends watching. I don’t think that usually happens in a professional fight.

That fighting moment is what came back to me when I was deep into my first game of Hanamikoji.

The Japanese word Hanamikoji (花見小路, literally "flower-viewing lane") is the name of a real street running through the Gion district of Kyoto, the historic heart of geisha and maiko culture. So the framing of the game is appropriately delicate: two patrons of the arts compete for the favour of seven geisha by gifting each of them their preferred items.

Mechanically, it's a set-collection card game that you can teach in two minutes and play in fifteen, and every minute of those fifteen is spicy.

You and your opponent are fighting over the loyalty of seven geisha, each represented by a card with a number on it. That number is two things at once: how many copies of her preferred item are in the deck, and the number of charm points she's worth at the end of the round.

That's 5 + 4 + 3 + 3 + 2 + 2 + 2 = 21 item cards in the deck, vying to win over 7 geisha. You win the game by gaining the favour of four of them at the end of a round OR by having 11 charm points, which is only possible if you have the 5, the 4, and another, or the 5 and both 3s.

Before either of you make a move, during round setup, one item card is dealt face-down off to the side and never seen by either player - akin to Love Letter. This means you never quite have a perfect view of the information available. Every probability you might want to compute already has a small but inescapable margin of "it might just be the one we set aside."

You start each round with a hand of six cards. On each of your four turns ⁸, you draw one more card and then perform one of these four actions - the catch being that you must perform each action exactly once, across four turns.

1. Reserve. Take one card from your hand and place it face-down. It scores at the end of the round, but your opponent doesn't get to see what it is until then.

2. Discard. Take two cards from your hand and remove them face-down from the round. Your opponent doesn't get to see those either.

3. Three for them to choose from. Take three cards from your hand and reveal them. Your opponent picks one to play to their side. You play the other two to yours.

4. Two and two. Take four cards from your hand and split them into two face-up piles of two cards each. Your opponent picks one pile to play to their side. You play the other to yours.

If action 4 sounds familiar, then you might have played Magic: The Gathering? It's Fact or Fiction, one of the most beloved blue instants of all time⁴, lifted out of the trading card game and dropped into a setting where it pretty much drives the whole game. I love designs that take a beautiful mechanic from one game and build a whole experience around it, and Hanamikoji is certainly a example of that.

The reserve and the discard are about hiding information. Actions 3 and 4 are about exposing it - but in a way where what looks balanced might be wildly imbalanced, and only one of you knows how.

At the end of the round the geishas are scored - for each one if you have more of her favourite items than the other player you gain control, but draw and instead control remains where it is. In the first round that leaves the geisha neutral, but in later rounds you won’t lose control of a geisha unless your opponent beats you - a draw is not enough.

Here's the thing about Hanamikoji - when your opponent splits four cards into two piles and asks you to choose, the obvious thought - "well, that pile gives me three points and that one gives me four" - is probably not the calculation that matters.

What matters is what's not on the table.

Imagine you've already taken your reserve action. You haven't shown anyone what you reserved, but you know it's a "2" - one of only two copies of that item in the deck. That single hidden card warps the value of every like item still available. The other copy of that same item, wherever it is, has just become almost meaningless to your opponent: even if they get to play it, they can't win that Geisha, because you've already quietly made sure they can't.

So when you split your own four cards for them to choose from, do you make a pile that looks balanced, knowing it's actually skewed your way thanks to your reserve? Or do you make piles that look skewed, but the skew is illusory, and the apparently weaker pile is - to anyone who doesn't know what's in your reserve - actually the stronger one?

And the moment you're sitting on the receiving end of that split - what are you actually basing your choice on?

You can ‘do the maths’. There are some number of cards you can't see. You can’t see your opponent's remaining hand, their reserve if they’ve used it, their two discards if they’ve used them, the face-down setup card but you can divide the unseen population by the available slots and assign probabilities. That's a perfectly defensible way to play.

Or you can play the player. You've played a few games with this person. You know they always reserve a 3 on action 1 if they can. You know they get a bit nervous about action 4 and tend to leave it for last. You know they overvalue the geisha worth 5 because she looks the shiniest.

Or you can try to do both, tie yourself in knots⁶, and end up choosing badly because what you "know" about your opponent is exactly what they want you to think you know.

Rock-paper-scissors is the cleanest possible model of the knot Hanamikoji ties you in. The game theory of it is settled: against an optimal opponent in a one-off match, the best you can do is throw each symbol exactly one third of the time, completely at random. No tells, no patterns, no exploit. You'll break even in expectation, and you can't do any better.

This is a deeply unsatisfying conclusion, because humans are not optimal random number generators⁷. We have habits, biases, comfort throws. So in practice, an experienced player can absolutely beat a beginner as the beginner has tells the expert can read and exploit.

But what happens when two experts play each other? The first expert spots the second expert's tell and adjusts. The second expert spots the first expert spotting their tell and un-adjusts. The first expert spots the un-adjustment and re-adjusts. The chain of "yes, but he knows that I know that he knows…" doesn't terminate anywhere useful, and the equilibrium they're forced into is the equilibrium where they both stop trying to read each other and just throw uniformly at random.

Which is to say: at the highest level, two expert RPS players are observably indistinguishable from absolute beginners. Both are throwing at near-random. Neither has a tell to exploit, because exploiting a tell would create one of their own.

Nat and I have demonstrably not reached this plateau. We once played Rock Lobster, Paper Tiger, Scissors Lizard to determine who got to play first in a game of Magic, and it took 7 draws before that could even be decided. I don’t remember a thing about the actual game of Magic that we played, only the way we chose who was on the play!

This raises a slightly distressing question. If the way to play correctly at the very top is to be indistinguishable from a player who has no idea what they're doing, what was the point of getting good again? I wish to revisit this in a whole article dedicated to skill - if you have any stories to tell about how a game made you feel skilful I would love to here it, in the comments of this article, or by e-mail to [email protected].

The rock-paper-scissors structure of fighting games is interesting. The basic close-range rhythm of Street Fighter (and most of its cousins) is a triangle:

The third side of that triangle isn't quite symmetric with the other two. When you "win" the rock-paper-scissors of throwing the right symbol, you score. When you "win" a Hanamikoji geisha, you take her card. When you "win" a fighting-game block, though, you don't actually deal any damage. You just get to spend another second alive, slightly closer to your opponent, with a very slightly better read on what they're doing. Blocking is a rock-paper-scissors win that pays out in scouting reports.

Which puts blocking in an uncomfortable position. Is it too defensive to be worth it (no damage!), or actually too good to pass up (free reads!)? The answer, of course, is the same answer Hanamikoji gives you: it depends on who you're playing.

Back to the actual game I’m reviewing: One interesting thing about Hanamikoji's design is that each of your four actions feels kinda horrible to play last, but for a different reason.

The first time I noticed this I had a small crisis at the table. Every action looks terrible! Then it dawned on me as I noticed the lovely symmetry: my opponent has exactly the same problem. They're sitting in a mirror-image chair with a mirror-image hand with the same dread of what to leave for last.

The last time I really felt like that was when I played Twilight Struggle - a game about the Cold War in which you’re forced to play cards that are good events from your opponent, all you get to choose is the timing of when they happen. Again, the game can torture you with a hand of terrible options but you simply must realise that your opponent is being equally tortured. I’m very happy to see that feeling in a much shorter game though! (Twilight Struggle can take a very long time to play.)

So the actual game isn't maybe isn’t so much "find the killer move," it's more "leave yourself in the least horrible position." Assume your opponent will value something incorrectly at some point, and keep grinding out rounds until they do.

If you've never played it Hanamikoji I cannot recommend it enough. It's quick, it's gorgeous, it's two-player only, it teaches in five minutes, it’s available on BGA, and the second game is always better than the first - because the second game is precisely when the mind games start.

Eventually, when you and your favourite opponent get good enough at it that your matches start ending in carefully balanced ties on most of the geisha, with a single deliberate tip that decides the round - when, in other words, your games start to look from the outside like absolutely nothing is happening - that's the point at which you know you've made it.

You'll know. They'll know you know. And, like Nat and me, you'll laugh, and the people watching won't have the faintest idea why.

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