“Do you have something to say to me?” says Erika Hanhal, hands on her hips.

I sigh at my luck. The magic demonstrations went smoothly and consisted of me going into a room with a panel of examiners and showing them my spells and divinations. Very simple, almost boring. The latter was a bit extensive since I had to set up my full array, but it was satisfying to display my efforts. But now it’s the next day at the first competitive divination test which I’m much more anxious about. Naturally my first opponent is the sister who I wanted to avoid of the brother who I found so annoying.

“Your brother is annoying,” I say, deciding on bluntness.

“I know. Why do you?”

“We were in the same archery test. He mentioned you. You’re shorter than I expected.” She’s only a head taller than me.

“Thanks for reminding me. Why was a mage taking a squire’s test?”

“It’s not exclusive, and I have a spell for it.”

“Sounds brutish.”

“Very.” I roll my eyes dryly. “Do you not know any combat spells?”

“None. Why would I want any? Leave the barbarity to the knights. Mages should be above such things.”

“…The Empress is known for having powerful combat magic. Are you criticizing her?”

She doesn’t even flinch at the suggestion that her words could be construed as treasonous, rolling her eyes as if saying it was a clumsy move. “She may know combat spells, but she hasn’t used them in battle in thirty years. Her magic’s main contribution to her empire comes from her other spells, and divinations. Besides, you haven’t proven that she wanted to learn combat spells instead of being forced to by the constant threat of assassination. A burden we her loyal subjects do not share.”

“How clumsy of me to forget her burdens.”

“Indeed, one might almost suspect your loyalty.”

“I’m afraid it’s my provincialism at fault. We don’t hear much of our beloved sovereign’s troubles so far west.”

“West? You aren’t from Caethlon are you? There was a distasteful noble integrating from there in one of my tests. Well, I say integrating, what I mean is hiding from the rebels while pretending to be here for the exam. You have a similar accent, and I’m beginning to think a similar personality.”

“Near Caethlon, on the border. We kept guard against the barbarians for a hundred years, but I’m afraid the empire’s success means we’re no longer relevant.”

“You sound bitter of our success. Be wary, suspicions linger.”

I’d be more worried she’s serious if it weren’t for the slight upturning of her lips hinting at the smile she’s trying to hide. No doubt she’s not used to being around people with as heightened senses as me or she would hide her teasing better.

“Oh, you shouldn’t linger your thoughts on me. I’m just a poor noble from the outskirts. But no worries. I’m sure our irrelevance will be remedied shortly. After all, I'm confident in becoming very relevant soon.”

“How boringly confident.”

“Oh, aren’t you too? Shouldn’t I at least match my opponent in that regard?”

“No. It’s annoying for a provincial to think he understands things on the same level as me.”

“Well,” I give a toothy smile, “let’s see how long I can keep the annoyance up then.”

The starting whistle blows before she can respond causing us both to stiffen and focus on the game.

“Four.” She rolls on the die.

“Five.”

“Tsk, you go first. What occulter?”

“Cards.” I say, going with the simplest, most recommended choice for the first round.

“How boring.”

“How many?”

“Seven.”

“A prime? How original.”

“Says the one who picked cards.”

We each retrieve the specially made cards from the boxes of provided objects. On the back are simple tessellations – mine dominantly hexagons–hers triangles. The fronts are all blank save one with a red circle. We show each other the cards, counting them and proving that there is a red circle among them, then erect the partition on the playing table to block sight of each other.

The objective of the game is to divine the location of the hidden object– in this case the card with the red circle– before your opponent does. Play is divided into two phases. The first in which the partition is up and both players arrange their occulting objects to conceal the objective from their opponent’s divinations. Any number of your own divinations may be performed at this time to block theirs. The most common first defensive divination of course being, ‘In this arrangement, where will my opponent guess first?’ though more questions are advised.

Once both sides have made their desired divinations, the partition is removed and both players take turns guessing which occulter their opponent’s hidden object is under and are allowed to perform one divination before each guess. The one who guesses correctly first wins the round, and then it starts over until one side has won five rounds and two more than their opponent.

Alan calls it a pseudo intellectual guessing game, since it’s impossible for an onlooker to know if a guess was smart or just random. Though of course he would be biased against it since knights are limited in what divinations they can perform, and so tend to fare poorly in these types of contests. At the very least I quickly got to the point where I beat him in every practice game… We stopped after that. He said playing more against him would teach me bad habits, while I just got bored.

I can already tell from my preliminary divinations that this opponent will be much more fun– her divinations more potent. I go through a half dozen arrangements that my rod tells me will quickly get seen through until I find one that seems to work– three clusters, two of two, one of three, taking up about half my allotted space in a triangle pattern. I make a bit of a gambit with the three cluster by stacking two of the cards on top of each other – one orientated horizontally, the other diagonal (left end up). It's risky because the rules say she can flip both cards over in one guess, but it can also help confuse her divinations.

The three cluster makes up the top part of the triangle, with the third card being orientated vertically below the stack (with farther away being up). The cards in the other clusters are side by side. The left one (my perspective) in each is also orientated vertically while the other in the right cluster is diagonal left up, and the last card (left cluster, right card), being the one with the red circle, is orientated horizontally.

DLU/H

V V H(O) V DLU

The reason for the complexity of arrangement is to take advantage of what is called ‘the transitive property of properties’ in magic. If we just placed them all in a neat line, then the opponent could just divine “is it on the left half” and quickly eliminate all the cards in a few guesses– often getting it in one. But arranged like this, asking the same question could result in false positives depending on the relative strength of the divinations.

Being satisfied with my arrangement, and sensing that more defensive divinations might cause distortions, I ring my bell to let her know I’m done and put on the thin veil provided to hide facial reactions.

A few seconds later she rings her own bell, and we take down the partition to reveal our arrangements. I’m immediately excited by what I see. A skewed cross: each point equidistant at right angles from the centre except for the top (her perspective) which is about 10 degrees to the right. Like me she stacked two cards together in the centre, though orientated them on opposite diagonals. The seventh card isn’t part of the formation but is far away, up and to the left, from the rest of the cards, orientated diagonally and perpendicular to the centre.

Stolen content warning: this tale belongs on Royal Road. Report any occurrences elsewhere.

Each point of the cross is a different one of the four orientations (there’s little point in being fiddly with the angles as that can be ignored, or even used against you. Likewise, while some card sets have more complicated patterns on the back which gives them an effective top and bottom to double the orientations, the academy has gone with simplicity.) with the top point being diagonal left up, bottom point diagonal right up, left vertical and right horizontal.

DRU DLU V DRU/DLU H DRU

“An interesting pattern.” I comment as I think about which question I should ask first.

“Thanks, I designed it myself. Yours is, um, pretty standard, but has some interesting implementations.”

The tone is completely different from our verbal sparring as our focus is bent towards each other’s pattern. We don’t need to get on top with words anymore, so we can afford to compliment each other’s strategies.

Having rolled high, it’s my guess first, so I turn the sand timer. It’s a difficult formation, and the stack in the centre is causing all sorts of problems. For instance, if I ask if the circle is diagonal, and it’s not, then the divination might still be positive because the circle would be in a strong line with the diagonal stack. So, part of me wants to just eliminate the stack with the first guess (it’s up to the guesser whether to remove or leave in the card they turned over, which will affect future divinations). Then it should be safe to ask if it’s diagonal. If it’s not then I can turn over either horizontal or vertical on the second, and then the other to win on turn three at the latest.

But assume it’s diagonal, what then? Turn over the bottom point which matches the outlier and then divine the isolated remaining two? It shouldn’t be more than three turns either way, which is good, but can I do better? She might find a way of guessing mine in two, in which case I’ll be hard pressed to catch back up. I can already tell her divination method is about as strong as mine, so losing a round where I have the advantage of going first will likely mean losing the whole match.

The skewed cross point feels like the key, but I can’t figure it out. It’s not in a strong line, though it is still associated with the middle and the horizontal one it’s leaning towards on the right. What’s the point of it? It reduces transitivity, which also isolates the two it’s associated with. So maybe she’s trying to stop me from riding a transitive chain towards the circle… No, I see, she doesn’t want me to divine the whole line of diagonals at once, which would otherwise let me get it in two. But I don’t see a way to use it to my advantage.

So, I’ll go with the centre removal strategy. The only question is how to use my first divination. I can’t think of anything to ask that isn’t negated by the centre stack. If it’s in the cross and I ask, the strong association with the diagonals and the outlier might cause a false positive (same if I ask if it’s not).

The timer is almost out so I go with the only move I can see. I hold the silver rod between the vertical card on the left point and the outlier and chant seeking the red circle. The rod flashes cold and I know it’s neither of them. I sigh in relief. That was risky – a false positive would have cost me at least a turn.

“Clever,” she says, “you used the outlier to break the strong line. What’s your turn?”

“The stack. Remove it.”

“How direct.” She turns the stack over one at a time, revealing blank fronts, then puts them back in the box. “My turn.”

She goes over to my side and places a top in the centre of my formation and spins it. It veers to the right to the two group that does not hold the circle.

“Hm, very irritating,” she says, “you built a double chain so that no matter where I go it could be someplace else. Maybe I can do what you did and break the binding stack, but that would take too long since I think you’re homing in. So, I think I’ll just assume your rod can counter my top and go as far away as possible– left cluster vertical please.”

It’s an effort not to sigh in relief as I turn over the card next to the circle. “Too bad, it was an interesting approach,” I say, genuinely. Alan doesn’t play like this. He only uses strategies that result in the fewest maximum number of turns. But she saw that wouldn’t work, so went with a method to maximize the probability of getting it as quickly as possible. I feel like my skill has grown rapidly just by watching her.

It’s my turn, and I must find the circle now; I have to assume that she’ll guess the circle next turn. It makes too much sense not too. She already assumed her divination was fully countered pre-emptively, and would want to fully remove the left cluster any way. So, what can I do?

It’s down to three possible cards, the top and bottom, and the right. I can divine any two cards at once with a line divination, but if the circle is one of them then I won’t know which. I can’t think of anything to guarantee getting it, so I’ll have to find some way of increasing the odds if logical necessity is failing me. The skewed point. She didn’t want me to divine all the diagonals at once, but if the circle was a diagonal she wouldn’t care since that wouldn’t eliminate anything. So, since she defended against it, I can only assume that it’s not a diagonal. I’ve already eliminated the left point, leaving only the right.

It could be a bluff, so I divine the other two to make sure– resigning myself to a 50/50 if they’re positive. The rod goes cold, and I immediately ask her to turn the right point.

“Well played,” she says, revealing the circle. “I was confident in that formation. Oh well. Was yours the other one in that group?”

“Yeah,” I say, turning it over. “You were unlucky. Your reasoning was impressive.”

“Thanks, but no worries, now it’s my turn to go first.”

The friendly respect for each other’s strategies strains as the rounds go on. We alternate wins, guessing each other’s object in no more than three turns each time. We go through the full range of occulters: decorated bowls, seashells, pendants hanging three dimensionally and others.

We’re evenly matched and go on like this until the eighth round– I have four, she has three. It’s her turn to guess first, and so gets the pick of the occulter.

“Seashells.” She chooses, causing me to sigh. It’s definitely the occulter she seems to favour, having added complexity over cards by each shell being different either in size or type, while still being two dimensional to not hinder her top. “How many?”

I consider. We’re in a pattern that neither seems capable of breaking– the one who goes first wins. I’ll need to try something else if I want to break through before the game draws at ten each. “Two.” I go with the minimum allowed choice.

“Two?” she asks, confused. “Are you just trying to get my win over with?”

“Something like that,” I say coyly.

“Not very sporting, but all right, I admit, I’m excited– I’ve never guessed it in one before.”

I shrug as I erect the partition, then arrange the shell to take up half the space allotted and take out the crystal pendulum. I place the shiny stone under the left one then ask the pendulum which one her divination will point towards. It points right to the empty shell, so I ring the bell saying I’m done.

The partition is removed, and Erika spins her top, which goes to the left shell, so, not trusting it, she picks the right.

“What!?” she exclaims as I reveal an empty shell– a bit too loudly getting us looks from the other contestants in the hall.

“My turn.” I pull out the crystal pendulum, causing her to tense visibly despite the veil. The pendulum struggles to point towards one, so I select the other. She tears the veil off to glare at me as she turns it over to reveal the shiny stone.

She’s silent as we report my win, acknowledging it only with a terse nod. I go to the waiting area to rest before the next round, but she awkwardly, as seems to be a habit with her family, goes to the same room. We wait there several minutes before she speaks.

“That was a mean trick.”

“What trick?”

She glares, causing me to shrug apologetically. She sighs. “I suppose I should have realized what you were doing. But waiting until the end to reveal you had another method wasn’t sporting.”

“It wasn’t against the rules, no?”

“No. It’s just annoying. To think you would use a weaker method so I would assume my divination was countered when it wasn’t. Infuriating.”

“It wasn’t that clever. It’s common to vary the strength of your divination in the field so your enemy doesn’t know what to expect.”

“If it wasn’t clever, why were you so sure it would work?”

“I wasn’t, I just had nothing to lose. You figuring it out wouldn’t have cost me anything since I would have lost the round even if I didn’t do it.”

“You’re still annoying for doing it.”

I shrug. “It was just bad luck I went first. Since otherwise you would have returned the favour, and the game would have turned into a brutal guessing match. You probably would have won then.”

“Which makes it more annoying, not less.”

“Sorry, if it helps I only came up with it from watching your methods.”

“…A little.”

“Good.”

“Next round posting up!” A man shouts into the room, and we all scramble to see who our new opponents are.