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Nanana’s Buried Treasure Volume 7 Chapter 6.2

Batako-san’s hand: A, 3, 4, 6, K. Thrown away pairs: 7, 10, j, 8

Ikusaba-san’s hand: Unknown, Unknown, Unknown, Unknown. Thrown away pairs: Unknown, Unknown, Unknown.

Old Maids: Unknown, Unknown, Unknown.

 

Now Batako-san nominates the K in her hand.

「Is it the King?」

One of the Old Maids is turned over.

Because of the right answer Batako-san has the right to guess again.

「2」

「That is incorrect.」

 

Batako-san’s hand: A, 3, 4, 6, K. Thrown away pairs: 7, 10, J, 8.

Ikusaba-san’s hand: Unknown, Unknown, Unknown, Unknown. Thrown away pairs: Unknown, Unknown, Unknown.

Old Maids: K, Unknown, Unknown.

 

Ikusaba-san’s turn. He drew the number 3. Instead of being able to discard it as a pair it stayed in his hand.

Ikusaba-san declared 「3」 with a smile on his face.

「That is correct.」

 

Batako-san’s hand: A, 4, 6, K. Thrown away pairs: 7, 10, J, 8.

Ikusaba-san’s hand: 3, Unknown, Unknown, Unknown, Unknown. Thrown away pairs: Unknown, Unknown, Unknown.

Old Maids: K, 3, Unknown.

 

Ikusaba-san was up again. He thought about it for awhile then declared 「4」.

「That is incorrect.」

Batako’s turn. The card she drew was an A. Since she has the other one she throws away the pair.

 

Batako-san’s hand: 4, 6, K. Thrown away pairs: 7, 10, J, 8, A.

Ikusaba-san’s hand: 3, Unknown, Unknown, Unknown. Thrown away pairs: Unknown, Unknown, Unknown.

Old Maids: K, 3, Unknown.

 

Batako-san smiled fearlessly and declares 「Q」 for her guess.

「Well, that’s it.」

And I hear a voice say 「Correct」.

The result of the first round is that Batako-san won by a score of 2-1.

Lady Ageha tapped me on the shoulder at this point.

「Hey Servant A. What do you mean ‘Well, that’s it’? I mean, even though I’m watching it, I don’t get it at all.」

Lady Ageha is a little annoyed.

「Well, let me explain.」

 

The second round begins.

Batako-san’s hand of 11 cards: A, 5, 6, 8, Q. Thrown away pairs: 2, 3, 10.

Ikusaba-san’s hand of 12 cards: Unknown, Unknown, Unknown, Unknown, Unknown, Unknown. Thrown away pairs: Unknown, Unknown, Unknown.

Old Maids: Unknown, Unknown, Unknown.

 

Let’s start with this. At this stage of the game Batako-san has one old maid in her hand, and Ikusaba-san has two.

「Huh? How do you know? … Oh, I see.」

「Do you understand?」

「In fact, I already knew.」

No you didn’t, you said ‘Oh, I see’.

「Just to be clear, it’s because of the difference in the number of cards in their hands. If you shuffle 13 pairs or 26 cards and divide them between two people then discard the pairs, you will always end up with the same number of cards. That’s because the other player will have the same numbers as each other left over.」

「In a normal game with two players playing together, the player with more cards has the joker.」

「Yes. So, this time there is no Joker and instead 3 regular cards are the old maids. So based on the difference in the number of cards between the two players, you can quickly guess how many each player has.」

「I see… I mean, of course I knew that.」

As the young lady was trying to gloat, the second round got underway.

To start, Ikusaba-san (who starts with 12 cards) takes over from the previous game. He draws the 5 from Batako-san’s hand and discards it face down on the table.

「You know that the number that was just discarded face down is a 5 right?」

「I hope you don’t think I’m an idiot.」

Lady Ageha is a little peeved.

 

Batako-san’s hand: A, 6, 8, Q. Thrown away pairs: 2, 3, 10.

Ikusaba-san’s hand: Unknown, Unknown, Unknown, Unknown, Unknown. Thrown away pairs: Unknown, Unknown, Unknown, 5.

Old Maids: Unknown, Unknown, Unknown.

(The discarded pair of 5 on the table is upside down, so you can’t actually see it, but it’s confirmed through logic.)

 

And now Ikusaba-san guessed 4 was an old maid.

「Maybe Ikusaba-san has a 4 in his hand?」

「Huh, why?」

「Ikusaba-san has 5 cards in his hand, and there are two old maids among them. There is little information in the early stages, so one strategy is to bet on the 2 out of 5 chance that it’s one of his cards.」

「That’s correct」, says President Yuiga, flipping over one of the old maids.

「It’s true.」

As Lady Ageha watches in amazement, Ikusaba-san continues his guesses.

「6」

「That is incorrect.」

「Now we have more information.. The old maid is not 6. By the way, since it is in Batako-san’s hand, that means one of the cards in Ikusaba-san’s hand is a 6.」

 

Batako-san’s hand: A, 6, 8, Q. Thrown away pairs: 2, 3, 10.

Ikusaba-san’s hand: Unknown, Unknown, Unknown, 4, 6. Thrown away pairs: Unknown, Unknown, Unknown, 5.

Old Maids: 5, Unknown, Unknown. (6 is not one)

(The cards 4 and 6 on the table are not actually visible, but are determined by logic)

 

Next it was Batako-san’s turn. What she drew was an 8. Since it forms a pair, they are discarded face down on the table.

 

Batako-san’s hand: A, 6, Q. Thrown away pairs: 2, 3, 10, 8.

Ikusaba-san’s hand: Unknown, Unknown, 4, 6. Thrown away pairs: Unknown, Unknown, Unknown, 5.

Old Maids: 4, Unknown, Unknown. (6 is not one)

 

「If it were you, what number would you guess Lady Ageha?」

「Ace or queen right? Either one is possible right?」

「That’s right.」

As expected Batako-san chose ace.

President Yuiga says 「That’s correct」, and flips over an old maid. Batako-san is allowed to continue guessing after getting one right.

 

Batako-san’s hand: A, 6, Q. Thrown away pairs: 2, 3, 10, 8.

Ikusaba-san’s hand: Unknown, Unknown, 4, 6. Thrown away pairs: Unknown, Unknown, Unknown, 5.

Old Maids: 4, A, Unknown. (6 is not one)

 

「So what can you infer from this Lady Ageha?」

「Well, the possible old maids are 7, 9, Jack, Queen, and King. …Wait. Based on the difference in the number of cards, the opponent has the remaining old maid, so it can’t be the queen. Then it has to be a 7, 9, jack or queen.」

「That is right. By the way, one of those is the old maid, and the other three are face down in the discard pile.」

Lady Ageha hears this and nods, 「I see.」

Meanwhile Batako-san has taken awhile to think.

「She’s been thinking about this for quite some time hasn’t she?」

「This is how the game is played.」

「Is that so?」

「It would be really bad if Ikusaba-san got another chance to guess.」

「Huh, why?」

「Because Ikusaba-san is currently in a situation where he can guess the old maid with a 50% chance of being right. On top of that, on the next turn if Ikusaba-san  draws the queen from Batako-san’s hand then he will know for certain what the old maid is.」

「…Um.」

Yeah, that confused face is cute.

「The last old maid is among the four cards in Ikusaba-san’s hand. In his hand is a 4 and a 6 which have already been ruled out. So then Ikusaba-san’s options for guessing are the queen and the card that actually is the old maid.」

「But it’s not the queen.」

「Yes. But you know that because you are looking at things from Batako-san’s point of view. Here’s how it looks from Ikusaba-san’s point of view.」

Ikusaba-san’s perspective

Ikusaba-san’s hand: 4, 6, Q, The Old Maid

Batako-san’s hand: A, 6, a card that isn’t the Old Maid.

Old Maids: 4, A, Unknown (Not the 6)

 

「Really? It’s different for Ikusaba. The old maid is a card in his hand so he doesn’t have to worry about the unknown cards that his opponent discarded.」

「That’s right. By the way, what would happen if Batako-san couldn’t choose the old maid from the 4 choices? If that were to happen, then for Ikusaba-san to lose he would have to not draw the queen from Batako-san’s hand and then guess that the queen was the last old maid. In that case Ikusaba-san would then know for certain what the old maid is, and it would be Batako-san’s turn. On her next turn if she could draw the old maid she would know what it is and win. If she didn’t, she would have no choice but to guess it from the 3 remaining possibilities. And if she guesses wrong, Ikusaba-san would be guaranteed to win…. Are you listening?」

「I understand that this is her chance to win.」

She didn’t understand my explanation.

The battle is the same as it was before the explanation. Batako-san is just staring at Ikusaba-san’s expression. It’s like she’s looking at his heart. Just observing.

Batako-san finally says, 「Don’t make this so difficult, it’s the king.」

「That’s correct.」

President Yuiga turns over the last old maid. It’s a king as he said.

「Yo, that’s amazing! You only had a 25% chance of guessing that Batako-san!」

Lady Ageha next to me also looked surprised as she clapped her hands.

Batako-san has two wins in a row. It’s a great start.