AC Chapter 411

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Chapter 411: A Complex Chess Game That Turns Crazy

“Alright, let us play a game that tests wisdom and strategy…”

Shi Xiaobai said with a chuckle, “Aeroplane Chess! 1

The Infernal Queen naturally did not know of the unique board game that came from Earth, but since she dared to let Shi Xiaobai decide, it was certain that she was mentally prepared to play something she had never played before.

The Infernal Queen said with a calm smile, “I’ve never played Aeroplane Chess before. Can Darling explain the rules?”

“Alright.”

Shi Xiaobai nodded understandably. He took a piece of white paper meant for drawing from the desk and began drawing the layout of Aeroplane Chess. Each corner was supposed to be evenly divided between the colors, red, yellow, blue and green. However, Shi Xiaobai could not find any crayons, so he could only use text in place of color.

Aeroplane Chess’s four differently-colored regions were constructed in a regular pattern. One simply needed to remember one colored corner to reproduce the rest. Therefore, Shi Xiaobai very easily reproduced the board of Aeroplane Chess.

After that, he found four golden coins and four silver coins from the clutter in the drawer. He used them to represent the airplane pieces.

After Shi Xiaobai was done preparing the chess and chess pieces, he began explaining the rules of Aeroplane Chess.

In fact, the rules of Aeroplane Chess are simple to understand. Every side has four airplane pieces parked in their hangers that are located at the corners of the board. One would roll the dice, and an airplane piece can only be taxied out of the hangar when a 5 or 6 is rolled. Any piece can be chosen, but the number of spaces the piece can move is decided by the number of spaces indicated by the dice. The piece has to fly clockwise around the board before reaching the center base. Whoever first gets all four airplane pieces into the center of the board wins.

Additional rules are the rules of additional rolls, sending a piece back to the hangar, jumping to the next space of its own color upon landing on a space of its own color, shortcut paths, and stacking of pieces.

The additional rules were not that complex and were easily understandable. Aeroplane Chess was one of the many board games that had rather simple to understand rules.

And to most people, the largest factor that depended on victory in Aeroplane Chess was luck. One’s luck at dice rolling determined the outcome. The better one rolled the dice, the more ‘6’ appearing to result in additional rolls allowed one to move more spaces.

Furthermore, if one had bad luck, with the airplane pieces almost reaching the center base, but one just fails to roll the required number. It would result in one unable to successfully reach center base. The advantage of being ahead might eventually evaporate into nothingness.

Hence, to most people, Aeroplane Chess is easy to learn and understand. Also a board game that was more related to luck was considered to be more leisurely than strategy board game. They were most suitable for children.

However, when the Infernal Queen heard all the rules, she fell into silence for a moment before she could not help but look up and say, “Darling, the choice of board game is truly complex. It is indeed a test of intelligence and strategy. However, I need to warn you that my intelligence is something even I’m afraid of. Darling, are you sure you want to choose a board game that consists only of intelligence and strategy?”

Shi Xiaobai said with a laugh, “Sorry, This King also frequently wonders about the existence of such a clever existence like This King. So, competing in intelligence and strategy is also the greatest advantage and forte of This King. No matter how smart you are, you won’t be smarter than This King.”

The Infernal Queen said with a covered smile, “Since Darling is so confident, then why don’t we play Aeroplane Chess?”

Shi Xiaobai said with a nod, “Come on. This King wants you to taste the feeling of despair of what it means to never ‘fly to the finishing point’!”

Aeroplane Chess in the eyes of an ordinary person is an entertaining game that is mostly about luck and a tiny bit of strategy. But to Shi Xiaobai, it was a game that was a grueling test of intelligence and strategy. In the Infernal Queen’s point of view, it was a game that completely tested intelligence and strategy.

Why would it be like that?

Was Shi Xiaobai fooling the Infernal Queen while the Infernal Queen was just playing along with him in sarcasm?

Of course not!

It’s because to the two of them, Aeroplane Chess is truly a game that is much more complicated than other board games. It could even be considered the most complicated board game of all!

You might find it ridiculous. Aeroplane Chess is clearly a board game that depends on one’s luck at rolling the die to determine victory. Furthermore, there were only four pieces that could be controlled! So how could it have anything to do with complexity?

You might think that Shi Xiaobai and the Infernal Queen were joking.

But in fact, you ignored the most important point. The greatest difference Shi Xiaobai and Infernal Queen had from ordinary people was—they did not need luck when rolling a die!

Yes, with their strength and ability to stably control their strength, they could roll the required number at any time they wanted!

Rolling dice was a procedure that could be directly skipped. All they needed was to consider what number they should roll during their turn!

And after completely abandoning the concept of luck, how complicated is Aeroplane Chess? Let me analyze it in detail for you.

Firstly, in Aeroplane Chess, there is an award mechanism. When you roll ‘6’, you are awarded the option to roll the die a second time or not. But in order to prevent players from throwing an infinite numbers of ‘6’, the rules had a catch that if ‘6’ was rolled three consecutive times, one would be punished. All the airplane pieces of the player, including the pieces that had reached the center base would be sent back to the hangar and play passes to the next player.

Therefore, when the player can arbitrarily control the rolling of points, they can easily throw from 1 to 18, with a total of 18 valid choices.

And in Aeroplane Chess, there were same-colored jumping of pieces (if a plane piece lands on a space of its own color, it immediately jumps to the next space of its own color), as well as shortcut squares (when a plane piece lands on one of the shortcut squares of its own color, it may take a shortcut, traversing a quarter of the board. It would complete a move as high as 16 moves). These two jumping rules made the player have way more than 16 possible moves.

And according to the calculations, from sending the airplane pieces out of the hanger, with all three dice rolls used on the same airplane piece can at best move it by 42 spaces!

That also meant that in one round, there were 42 possible outcomes available to the player for each airplane piece!

And the player has a total of 4 airplane pieces!

Furthermore, the player can choose to not throw 6 to prevent the triggering of the reward. Each round, the player can choose to move once, twice or thrice, a total of three choices.

Then, how many variations can a player have in his own round?

The answer was on the order of the product of 42, 4, and 3—504 combinations!

In addition to the possibility of stacking pieces (when a plane lands on another plane in its own fleet, the player may “stack” the pieces and move them as one piece until they reach the center) or attacking (when a player lands on an opponent’s piece, the opponent returns that piece to its hangar). These two change the possible variations of the control of the pieces.

A player was facing way more than 504 combinations during his single round. It was even more than a thousand!

What did this mean?

It means that during one’s turn, one has a thousand possible moves to make. Furthermore, after your round, you have to consider what the changes the other party’s thousand possible moves would do to the situation.

And this was just one round of the game. We all know that really talented chess players would typically calculate three to four rounds, or even up to ten rounds. And in Aeroplane Chess, if one wanted to consider ten rounds ahead, how many combinations would be needed?

1000 to the 20th power!

It could be considered so complex that it turns crazy!


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  1. Also known as Ludo

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23 thoughts on “AC Chapter 411” - NO SPOILERS

      1. Not always, according to what I read, you race tokens according to die. It’s possible to force the die to land on a number. If it’s from a cup, then I’m not too sure.

    1. But I’ve been wanting lust to die
      I assume Kali was wrath
      Glutony was killed
      Envy?
      Sloth?
      Greed was our doge
      Pride? Maybe was dead from the get go becuase on honestly SXB

      1. Gluttony wasn’t killed, he became part of Shi Xiaobai.

        Remember the part he said why are you hiding?

        About the dog?

        The only reason the dog probably surrendered is because he is the original sin of calamity(HE IS INDEED)

        Because he has the memories of the old man and the king. Or… HIS SWORD IS THE ORIGINAL SIN OF CALALAMITY

        It’s one of those.

        1. Honestly, even if I don’t really disagree, I would avoid making hypothesis too specific. This author makes so many plot twist in a minor arc that I don’t expect the main plot to be that straightforward.

        1. Exactly because she’s rarely angered that she’s wrath, Wrath doesn’t mean angry all the time, basing off Meliodas from Nanatsu no Taizai, similar to Kali, Meliodas wasn’t angry in his normal state but once he became angry he turned into something else, does that seem similar to the corruption of the pixies?

          1. But Gluttony always consumed his surroundings and Greed always stole riches from people. And the Corruption isn’t something exclusive to Kali, therefore not exclusive to the sins of calamity.

          2. I don’t think Kali is wrath cause of one thing simple, she has already encountered the other Seven Sins from the Other Calamities, and Each time they perished or hiding or seal, then they will reincarnated or something, like the Original Sin of Calamity. So you can’t expected something that’s Already Exist(as in Kali) to be something else that’s Also Exist at the same time(as in Wrath).
            Unless the Author pull some Twists move again like how Kali is being possessed by Wrath or other Seven Sins or something, there’s literally No Chance for Kali being part of the Seven Sins.
            Unless the Author pull some Twists move again like there is a clone of Kali or something….

    1. Things wrong with the authors math:
      1. Attacking does not change whether or not you can move a piece to a given location. I does provide an additional effect to that particular move, but does not create an additional possible move
      2. Stacking planes does have its own merits and possible disadvantages to consider, but in fact reduces the number of possible ways you can move in future turns. From what I read, once planes are stacked they must remain stacked until they reach the center. This means you no longer have 4 possible planes to move with each die roll. After your first stack is created, you will have 2 planes and 1 stack (3 targets) that can be moved with each die roll. This reduction of targets reduces the total number of permutations you can have to the board state.
      3. The fact that the shortcut can move you forward 16 squares doesn’t mean you have 16 additional places you can stop. What I read doesn’t indicate that you can stop halfway through a shortcut. All I can see is that landing on a shortcut provides you the option of moving immediately to another specified square on the board. This means one possible move now gained a SINGLE additional outcome. This same logic can be applied to jumping, if jumping is optional.
      4, The author was sloppy with his counting and double counted some possible moves. If you roll a 6 and move plane 1 forward 6 spaces, roll a 6 on the bonus roll moving plane 2 forward 6 spaces, and roll a 5 on the second bonus roll to move plane 3 forward 5 spaces, you will achieve the same effect as rolling a 6 and move plane 2 forward 6 spaces, rolling a 6 on the bonus roll moving plane 1 forward 6 spaces, and rolling a 5 on the second bonus roll to move plane 3 forward 5 spaces.
      5. There may be more, but it is hard to identify them with this already drastically incorrect math.

      My analysis of the problem says there are at most 168 moves you can make if you already have 4 planes on the board. This number was calculated by being very generous and treating every space as one that provides an optional jump/shortcut to be taken. The actual number of possible moves should probably be even lower, but I don’t know enough about the board to accurately model the frequency of shortcut/jump spaces.

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