Gamers Are Fierce

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Hohenheim reacted instantly and asked: This doesn't seem fair, does it?

The coin is yours and you make the toss, so how can I determine the fair nature of the game?

If I intend to harm you, I won't appear in your sight.

Claude pointed at the corpse of the giant wild boar under the stone pillar and said casually: Did you see that wild boar? There are countless creatures that are several times stronger than it in this forest.

No matter how well-prepared you are, if you can't find the pattern of the forest automatically changing its position, you will still be consumed alive in this forest.

And I only need to wait quietly in the distance to harvest the materials and props from you.

Claude indifferently threw the coin in his hand towards Hohenheim.

Halfway through the air, the coin was caught by a transparent mage's hand released by Hohenheim and hovered in mid-air.

Don't you have a magic book?

Claude pointed to the Book of Sand in Hohenheim's hand and said, You can use it to test coins and see if I'm cheating.

You actually agreed to my use of magic?

Hohenheim's eyes narrowed slightly, and the Book of Sand he was flipping in his hand paused imperceptibly, then quickly locked on a few pages and released several identification spells with different functions.

This coin is made of brass alloy, with even thickness and smoothness. On the front is a human head with traces of wear, and on the reverse is a snow mountain. The diameter is 40 mm. It weighs more than coins in the real world. It is a bit like a special commemoration. currency.

No traces of the paranormal detected...

Hohenheim silently reduced the mana output of detection spells,

Claude took the coin from the magic hand and said: The head is up and the snowy mountain is down. In order to be fair, I will start the first round.

The sequence I chose is, anyway, reverse.

That is, the snow mountain - the avatar - the snow mountain.

...

Hohenheim thought for a moment, Then I choose, anyway.

Oh? You responded quickly.

Claude said with a grin, and Hohenheim smiled lightly without explaining.

I'm starting to vote.

Claude's arm in the middle of his chest caught the coin with his thumbnail and flicked it upward.

The coins were raised high and spinning in the air, reflecting the sunlight that penetrated the dense canopy of trees.

Hohenheim's pupils suddenly shrank, and he used the detection spell released by the Book of Sand in his hand to frantically calculate the kinetic and potential energy conversion trend of the coin, mapping and predicting the trajectory of the coin's rotation, flying, and falling.

In the short time that Claude explained the rules just now, he already understood the rules of this game.

[Both sides choose a sequence of heads and tails of three coins, and keep tossing coins until the sequence appears, it is counted as a victory. 】

This rule seems fair, but in fact it is not equal. The party who chooses the sequence later has a huge advantage? No matter what sequence the first player chooses, the second player can have a relatively better solution.

Take the positive and negative of Crowder’s selection in this round, namely 010, as an example?

Anyway, the one Hohenheim chose, namely 001?, is better than the former in terms of probability.

Because in an infinitely long sequence (assuming that coins are being tossed all the time), the winning condition of 001 is that 1001 appears, or 0001 appears?

If 010 wants to win, the only possibility is 1010.

Because if the sequence 0010 appears,

So whoever chooses 001 will win directly before 010.

It is equivalent to having one less possibility of winning than your opponent.

From the perspective of 001 chosen by Hohenheim, one of the prerequisites for the opponent's victory is actually the basis for our own victory?

Unless the result is directly thrown in the first three throws at the beginning, the probability of 001 will always be in the infinitely extending ray-shaped sequence, taking precedence over 010 - because the rule of the game is [the corresponding sequence appears first], not [Find in an infinite sequence].

Snapped.

Claude caught the coin with the back of his left hand, covered it with the palm of his right hand, and then slowly opened it.

The side of the coin facing up is the portrait of the character, which is the positive side.

Ah, no one hit the first shot.

Claude grinned, Come again.

He continued tossing the coin.

Second shot, positive,

The third shot was reverse.

The first three shots were heads or tails, and no one could guess it.

Hohenheim remained silent. The probability of hitting all the first three shots was too low. The next few shots were the beginning of the game.

The fourth shot, positive,

The fifth shot, positive,

The sixth shot, reverse,

The seventh shot, reverse,

The eighth shot... is right.

Won.

A flash of light flashed deep in Hohenheim's eyes,

Claude sighed, looked at him and smiled: You're lucky. You won the first round.

Hohenheim narrowed his eyes slightly. It was not luck, but a simple probability calculation. Two-thirds of his 001 sequence, that is, almost 67% chance, was better than 010.

This does not mean that 001 is the optimal solution. As he calculated, among the eight possibilities (000, 010, 001, 100, 110, 111, 011, 101) of the three-digit sequence of 0 and 1,

The winning probability of 111 and 000 is the lowest. 011 and 100 both have a seven-eighths, or 87.5%, probability of winning.

Sequences such as 100, 001, 011, and 110 are mutually superior and inferior solutions, forming a cycle of mutual reinforcement and reincarnation, like rock-paper-scissors.

For a gambler, a 55% winning probability is already a huge advantage. If you can control the winning probability to 67% or even 75%, you can almost bet all your money, and there is no reason not to continue to follow the bet.

Claude said slowly: Best of five rounds. In the second round, you choose first.

...

Hohenheim thought for a moment and said slowly: I choose, pros and cons.

Although a cycle will be formed between the number sequences, the probability of being restrained by 011 and 100 is relatively low.

Claude smiled and said: Then I choose, pros and cons.

Sure enough, Hohenheim's heart sank. The number sequence chosen by the opponent was more likely to be better than his first solution, but... there might not be a chance of a comeback.

The result of the second round of throwing is.

Anyway, anyway, anyway.

Victory again.

Hohenheim's frown relaxed slightly. The only way to win with his forward, reverse, and reverse shots was to make three consecutive forward shots in addition to the first three shots to break the opponent's forward, reverse, and reverse suppression, and basically win again. , cast your own results.

It is equivalent to a double judgment, and the probability of winning is not high.

Wow, it looks like luck is really on your side.

Claude whistled, tilted his head, and raised the corner of his mouth with a strange arc, We have reached the match point. Then in the third round, I choose, Zhengzhengzhengzhengzhengzhengzhengzhen.

Um?

Hohenheim's eyes narrowed and he looked at the opponent deeply. The probability of being positive three times in a row was not high. If he chose to suppress the positive situation anyway, then the opponent's winning rate would be infinitely lowered.

You have to make the first three shots and get positive results to win——

Because once the number sequence exceeds the first three, then there will inevitably be a situation [before the right, there must be a tail]. No matter how you choose the side of the head, you will not lose.

The probability of winning is... 87.5%.

I choose, anyway.

Under the cold probability calculation, Hohenheim had no reason to choose other solutions and gave the answer immediately.

Very well, then, I'll start.

Claude's thumbnail flicked up the coin.

The round thin piece of brass alloy rotated slowly and rapidly in the air, and finally fell on the back of Claude's hand, and was caught with a force.

The result is displayed as...[positive]

“The first shot was pretty good for me.”

Claude grinned and ignored the dense monitoring techniques that were like probes in the void. He placed the coin again on his thumbnail and bounced it up again.

clang--

Still, [positive].

The atmosphere around Hohenheim suddenly changed. His 87.5% winning rate was based on the fact that he couldn't make a positive shot in the first three rounds.

For the opponent to win, it means that the probability is one-half times one-half times one-half, for a total of only one in eight possibilities.

Third round...

Claude flipped the coin nimbly with his fingers and tossed it up again.

The brass alloy coin whirled, fell, and was caught in the palm with a snap.

【just】.

There's a one-eighth chance that I win.

Claude whistled easily, Fourth round...

Wait a moment.

Hohenheim raised his palm and said, How about I throw the next two rounds?

He has never been a person who believes in probability. As a player, he also believes that the system will not set up a kind-faced and magic-rich old man as a considerate guide for players in difficult dungeons.

The other party must have used some means to make him fall into a trap...

OK.

Unexpectedly, Claude nodded generously and tossed the coin to Hohenheim.

As before, Hohenheim held the coin with his invisible mage's hand, and examined it more carefully using his detection spell.

The portrait on the coin is severely worn. It can be vaguely seen that the face has sharp edges, deep eye sockets, a straight nose, regular facial features, and short curly hair.

From a universal aesthetic point of view, he is a handsome man.

He was very different from the three-armed weirdo Claude in front of him.

Hohenheim raised his head and asked, Whose face is on this coin?

Since the coin was severely worn, he didn't have to worry about the situation [the character on the coin was extremely well-known in the script world, and if they didn't know each other, Claude would suspect his identity]. Anyway, he could blame it on unrecognizable.

Who else could it be? Tixiu, the leader of the seven pirate kings of the boundless deep sea, the commander of the Invincible Fleet, and the symbol of all wealth in the world.

Claude was a little confused, I picked up this copper coin by accident in this forest. It was probably left behind by Tixiu and his subordinates when they came to worship at the Holy Mountain a long time ago.

Or maybe it was brought in by a certain generation of travelers.

He glanced at Hohenheim strangely, Could it be that you still thought the person in the profile picture was me? Am I that ugly?

Uh, no, no.

Hohenheim resisted the urge to complain. The appearance of the three-armed monster is so weird that in the real world, it is enough to be thrown into the spooky scene of a horror game.

Become a monster that creates jumpscare (sudden fright) show effects, and the handsome guy on the coin is in the sky and the earth.

It's almost the difference between Duan Yanqing and Duan Yu...

But it may be normal. Anything can happen in a killing game. Maybe Claude's race has abnormal aesthetics.

Previously, a fat player entered the underdark area of ​​the scenario world, where he was warmly received by a group of drow elves who regarded fatness as beauty. They killed the thin and handsome guys in the player's team, leaving only him. One person lived a happy life from then on - although the result was that these players fell into the web of a man-eating spider and everything was an illusion, it did not affect the effectiveness of this rule.

Don't talk about beauty and ugliness easily with the natives of the script world.

Claude spread his hands and said, I chose first in the last round. This round, you go first.

Hohenheim took a breath, I choose, pros and cons.

It was just an accident. Before he saw the problem, the probabilistic restraint relationship still took effect.

Claude grinned, Then, I choose to rebel.

That's it again!

Hohenheim's heart sank. The probability of head-to-head was also better than that of head-to-head, and the winning rate was still 87.5%.

This round, he was the first to choose.

After he chose heads and tails, the opponent could choose heads and tails to restrain the 67% winning probability, but the opponent chose not to choose heads and tails.

Instead, he chose the anti-anti-anti with a winning rate of only one-eighth.

There must be something wrong...

Now that you've decided, let's start voting.

Claude glanced at the coins suspended in mid-air, tilted his head, and urged.

...good.

Hohenheim narrowed his eyes slightly, the coin was firmly held in his mage's hand, and the power of throwing was in his hand.

The hands of the mage are an extension of his own magic power, and are even more flexible and controllable than the palm of his hand.

'Let me see if you are cheating...'

The invisible palm bounced the coin, and the coin flew and rotated on its own, drawing a straight trajectory in mid-air.

Snapped.

The mage's hand, which was completely composed of magic power, firmly caught the brass alloy coin at the same height as the throw.

Hohenheim's eyes flashed, he didn't cheat, but he already knew the result.

Those in the air who were infused with magic power monitored the magic spells and watched every rotation of the coin attentively. They had already calculated the result before it fell and was caught.

I've already won.

Hohenheim felt the magic power draining from his body (the surrounding low free energy environment is extremely unfriendly to players specializing in spellcasting), and unveiled the coin at an extremely slow speed.

etc,

Snowy mountains?

Hohenheim's eyes widened slightly, he suddenly raised his head and stared at Claude, and said in a low voice: You cheated.

Is there any?

On the stone platform, Claude smiled and said: You threw the coin and you caught it.

As a mage, you should know very well whether I interfered during the throwing process just now.

Don't make the situation too ugly just because you will lose...

The three-armed weirdo gently scratched his cheek with his right hand, drawing blood marks, and smiled: Besides, even if I cheated, as long as you have no evidence to prove it,

The game is still valid.