"Wait,"

Hohenheim reacted instantly, and asked rhetorically, "That doesn't seem fair, does it?"

The coins are yours and yours are the ones to toss, so how can I be sure of the fair nature of the game? ”

"If I had deliberately harmed you, I wouldn't have been in your sight."

Claude pointed to the carcass of the giant boar beneath the stone pillar and said casually, "See that boar?" Creatures that are several times stronger than it, and there are countless of them in this forest.

Even if you are well prepared, you will not find the pattern of the automatic change of position of the forest, and you will be consumed alive in this woodland.

And I just need to wait quietly in the distance to harvest the supplies and props on you. ”

Claude didn't care about throwing the coin in his hand to Hohenheim,

The coin flew halfway through the air before it was grasped by a transparent mage's hand unleashed 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 check coins and see if I'm cheating." ”

Agree to me using spells?

Hohenheim's eyes narrowed slightly, and the book of sand that was being flipped in his hand paused imperceptibly, and then quickly locked on to a few pages, unleashing several identification spells with different functions.

This coin is made of brass alloy, evenly smooth, with a human head with signs of wear on the obverse and a snow-capped mountain on the reverse, with a diameter of 40 mm, which is heavier than a real-world coin, a bit like a special commemorative coin.

No supernatural traces were detected...

Hohenheim silently lowered the mana output to the detection spell,

I saw Claude take the coin from the hand of the spell and said: "The avatar is positive, the snowy mountain is negative, in order to show fairness, the first round, I will start first."

The sequence I chose is, reverse and opposite.

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

“...”

Hohenheim thought for a moment, "Then I'll choose, anyway." ”

"Oh? The response is very fast. ”

Claude grinned, and Hohenheim smiled faintly, without explanation.

"I'm starting to vote."

Claude's arm in the middle of his chest, caught the coin with his thumb fingernail and flicked upward.

The coin is raised high and spins in the air, reflecting the sunlight that penetrates the dense canopy.

Hohenheim's pupils contracted suddenly, and the detection spell released by the Book of Sand in his hand frantically calculated the kinetic energy potential energy conversion trend of the coin, and mapped and predicted 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, and the side that chooses the sequence later has a huge advantage? No matter what sequence the first hand chooses, the second hand can have a relatively better solution.

Take the opposite of Claude's choice in this round, that is, 010 as an example?

The opposite of Hohenheim's choice, i.e. 001? It is better than the former in probability.

Because in an infinitely long sequence (assuming a coin toss all the time)? What are the winning conditions for 001? Is it 1001 or 0001?

And if 010 wants to win, it can only be 1010.

Because if there is a sequence of 0010,

So the side that chose 001 is the backhand? will win directly ahead of 010.

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

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

Unless the result is thrown directly in the first three throws of the opening hand, the probability of 001 will always be in an infinitely extended ray-like sequence? Priority over 010 - because of the rules of the game? It is the corresponding sequence that appears first, not the infinite length of the sequence.

Syllable.

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

On the side of the coin facing up, there is a portrait of the person's head, which is positive.

"Ah, no one hit the first shot."

Claude grinned, "Come again." ”

He continued to flip coins.

Second vote, positive,

The third throw, against.

The first three shots were positive and negative, and no one could guess it.

Hohenheim was silent, the probability of wanting to hit the first three shots was too low, and the next few shots were the beginning of the game.

Fourth throw, positive,

Fifth vote, positive,

Sixth vote, anti,

Seventh throw, anti,

Eighth Throw... Correct.

Won.

A gleam flashed in the depths of Hohenheim's eyes,

Claude sighed, looked at him and smiled, "Good luck." In the first round, you win. ”

Hohenheim's eyes narrowed slightly, not luck, but a simple probability calculation, his 001 sequence, with a two-thirds of the time, that is, almost a 67% probability, is better than 010.

This is not to say that 001 is the optimal solution, as he calculated, out of a three-digit sequence of 0 and 1 with a total of eight possibilities (000, 010, 001, 100, 110, 111, 011, 101),

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

The 100, 001, 011, 110 and other sequences are mutually superior and inferior, forming a cycle of mutual growth and restraint, like rock-paper-scissors reincarnation.

For a gambler, a 55% probability of winning is already a huge advantage, and if the probability of winning can be controlled at 67% or even 75%, then almost all of his net worth can be cast, and there is no reason not to continue to call.

Crowder said slowly: "Three wins in five games. In the second round, you choose first. ”

“...”

Hohenheim thought for a moment and said slowly: "I choose, positive and negative." ”

Although there are loops between sequences, the probability of restraint between 011 and 100 is relatively low.

Claude smiled: "Then I choose, positive and negative." ”

Sure enough, Hohenheim's heart sank, and the number series chosen by the other party was better than his first solution in terms of probability, but... There may not be no chance of a comeback.

The result of the second round of throwing is:

Anyway, anyway, it's positive, it's positive, it's negative.

Win again.

Hohenheim's frowning brow stretched slightly, and the only solution to his head-to-back to win was to shoot three straight shots in a row in addition to the first three shots to break the opponent's head-back suppression, and once again, on the basis of his own results.

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

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

Claude whistled, tilted his head, and raised the corners of his mouth in an eerie arc, "It's time for the match point." Then the third round, I choose, is right. ”

"Huh?"

Hohenheim's eyes froze, and he glanced at the other party deeply, the probability of three consecutive positive occurrences is not high, if he chooses to suppress it anyway, then the opponent's winning rate will be infinitely lowered,

You have to throw a straight result in the first three shots to win-

Because once the number exceeds the first three digits, then there will inevitably be a situation where there must be a negative before the positive, and no matter how you choose the positive side, you will not lose.

The probability of winning has reached... 87.5%。

"I choose, anyway."

Under the cold probability calculation, Hohenheim had no reason to choose another solution, and the answer was given immediately.

"Very well, then, here I go."

Claude's thumb was covered with a fingernail and a coin flicked violently.

The round flakes of brass alloy seemed to spin slowly and rapidly in the air, and finally fell on the back of Claude's hand, where they were caught violently.

The result is displayed as...【Positive】

"The first shot was pretty good for me."

Claude grinned, ignoring the probe-like surveillance in the void and replaced the coin on the thumbnail cover and bounced it up again.

Bell –

It's still, [positive].

The mood around Hohenheim changed abruptly, and his 87.5 percent win rate was based on the fact that he couldn't get straight shots in the first three rounds.

For the opponent to win, it means that the probability is 1 in 2 times 1 in 2 times 1 in 2, for a total of only 1 in 8 probability.

"The third round..."

Claude's fingers nimbly flipped the coin and tossed it again.

The brass alloy coin spun and fell, snapping and being clasped by the palm of the hand.

[Positive].

"One in eight probability, I won."

Claude whistled lightly, "Fourth round..."

"Wait a minute."

Hohenheim raised his palm, "How about I throw the next two rounds?" ”

He has never been a person who is superstitious about probability, and as a player, he also believes that the system will not set up a kind old man with good eyes and full of magic weapons in the difficult dungeon as an intimate guide for the player.

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

"Okay."

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

As before, Hohenheim grabbed the coin with the hand of an invisible mage, and looked at it more carefully with the detection spell.

The head of the figure on the coin is more seriously worn, and it can be vaguely seen that his face is angular, his eyes are deep, the bridge of his nose is straight, his facial features are straight, and he has short curly hair.

From the point of view of universal aesthetics, he is still a handsome man,

It is very different from the three-armed monster Claude in front of him.

Hohenheim looked up and asked, "Who is the avatar on this coin?" ”

Due to the severe wear and tear of the coin, he does not have to worry about the situation that the characters on the coin are extremely well-known in the script world, they do not know them, and they will be suspected of identity by Claude], anyway, he can push the reason to "unrecognizable".

"Who else could it be? O Tishu, the head of the seven pirate kings of the boundless depths, the commander of the invincible armada, and the symbol of all the riches of the world. ”

Claude was a little puzzled, "This copper coin was accidentally picked up by me in this forest, and it is estimated that it was left behind when Hugh and his subordinates came to worship on the Holy Mountain a long time ago.

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

He glanced at Hohenheim strangely, "Could it be that you still think the person on the avatar is me?" Am I that ugly? ”

"Uh, no, no."

Hohenheim resisted the urge to complain, the strange appearance of the three-armed weirdo is enough in the real world to throw into the gloomy scene of a horror game,

When a monster acts as a monster to create the effect of the jumpscare (sudden scare) show, and the handsome guy on the coin is in the sky and one in the ground.

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

But maybe it's normal.,Anything can happen in the killing game.,Maybe Claude's race is aesthetically abnormal.,

There was a fatter player who entered the dark realm of the scripted world, where he was warmly welcomed by a group of drow elves who were fat, killed the skinny handsome guy in the player's team, leaving him alone, and lived happily ever after—although the result was that the group fell into the man-eating spider's web, and everything was an illusion, but it didn't affect the rule to take effect.

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

Claude spread his hands and said, "I chose first in the last round, and in this round, you come first." ”

Hohenheim took a breath, "I choose, pro or back." ”

It was just an accident, and before he saw the problem, the probability-based restraint relationship was still in effect.

Claude grinned, "Well, I choose to go against it." ”

And so it is again!

Hohenheim's heart sank, and the probability of positive and negative was also better than that of anti-anti, and the winning rate was still 87.5%.

In this round, he was the first to choose,

After he chose the positive and negative, the opponent could choose the positive and negative to exercise restraint in the 67% probability of winning, but the opponent did not choose the positive and negative.

Instead, I chose a counter-anti-counter with a win rate of only one-eighth in the end.

Something's wrong...

"Now that you've decided, let's start casting."

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

“... Good. ”

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

The Mage's Hand is an extension of his own magical power, and is even more agile and controllable to use than the palm of his hand.

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

The invisible palm of the hand flicks up the coin, and the coin spun on its own, drawing a straight trajectory in mid-air.

Syllable.

The mage's hand, composed entirely of magic, caught the brass alloy coin at the same height as the toss.

Hohenheim's eyes twinkled, he wasn't cheating, but he already knew the outcome.

The mana-infused monitoring spells in the air, watching each spin of the coin intently, calculated the result before it landed or was caught.

I've already won.

Feeling the loss of mana from his body (the surrounding low-free energy environment is extremely unfriendly to spellcaster-skilled players), Hohenheim uncovered the coin at an extremely slow pace.

Wait a minute

Snow?

Hohenheim's eyes widened slightly, and he jerked his head up to stare at Claude, and said in a low voice, "You cheat." ”

"Yes?"

On the stone platform, Claude smiled, "You tossed the coin, and you caught it."

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

Don't make the situation too ugly just because you're going to lose..."

The three-armed strange man gently scratched his cheek with his right hand, scratched the blood marks, and smiled: "What's more, even if I cheat, as long as you have no evidence to confirm,

The game will still work. ”