Gamers Are Fierce

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Hornheim reacted instantly and asked, "It doesn't seem fair, right?

The coin is yours, and the tossing is also yours. How can I determine the fairness of the game? "

"If I deliberately cheat you, I won't appear in your sight."

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

Even if your preparations are more complete and you cannot find the rules for the automatic change of forest positions, you will be consumed alive and die in this woodland.

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

Claude indifferently threw the coin in his hand to Hohenheim,

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

"Don't you have a magic book?"

Claude pointed to the book of sand in Hohenheim's hand, and said: "It can be used to detect coins and see if I am cheating."

Even agree to my use of spells?

Hornheim narrowed his eyes, and the book of sand in his hand paused imperceptibly, then quickly locked a few pages and released several authentication spells with different functions.

This coin is made of brass alloy, with uniform thickness and smooth thickness. On the front is a human head with signs of wear, and on the back is a snow mountain with a diameter of 40 mm. The coin weighs heavier than real-world coins, a bit like a special memorial. currency.

No supernatural traces detected...

Hohenheim silently reduced the mana output for detection spells,

I saw Claude took the coin from the hand of the spell and said, "The head is positive, and the snow mountain is negative. In order to be fair, I will start the first round.

The sequence I chose is, anyway.

That is, Snow Mountain-Head-Snow Mountain. "

"..."

Hornheim thought for a moment, "Then I choose, anyway."

"Oh? The response was quick."

Claude grinned and Hohenheim smiled faintly without explaining.

"I started to vote."

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

The coin rose high, spinning continuously in the air, reflecting the sunlight penetrating the dense tree canopy.

Hornheim’s pupils suddenly contracted, and the detection spell released by the Book of Sand in his hand crazily calculated the kinetic energy conversion trend of the coin, and mapped and estimated the trajectory of the coin’s rotation, flying, and falling.

In the short time when Crowder explained the rules, he has understood the rules of the game.

[The two sides choose a sequence of three fronts and backs of the coin, and keep tossing the coin until the sequence appears, which 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 is chosen first, the latter can have a relatively better solution.

Take the pros and cons of Crowder's selection in this round, that is, 010 as an example?

Anyway, Hohenheim's choice, that is, 001? is better than the former in probability.

Because in an infinitely long sequence (assuming that you have been tossing a coin), the winning condition of 001? Is 1001 or 0001?

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

Because if the sequence 0010 appears,

Then the side who chooses 001? Will win directly before 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 to win is actually the basis for his victory?

Unless the result is directly thrown in the first three toss of the opening, the probability of 001 will always be in the infinitely extended radial sequence? Prior to 010-because the rules of the game? It is [the corresponding sequence appears first], not [Find in an infinite sequence].

Snapped.

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

The side with the coin facing up is the head of the character, that is, the front.

"Ah, no one missed the first shot."

Claude grinned, "Come on again."

He continued to toss coins.

Second shot, positive,

The third shot, reverse.

The first three shots were pros and cons, and no one could guess.

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

Fourth shot, positive,

Fifth shot, positive,

Sixth shot, reverse,

The seventh shot, reverse,

Eighth shot... positive.

Won.

A bright light flashed in the depths of Hornheim’s eyes.

Claude sighed and looked at him with a smile: "Good luck. You won the first round."

Hohenheim's eyes narrowed slightly. It was not luck, but a simple calculation of probability. His 001 series had two-thirds, or almost 67% of the probability, better than 010.

This is not to say that 001 is the optimal solution. As he calculated, there are eight possibilities (000, 010, 001, 100, 110, 111, 011, 101) in the three-digit column of 0 and 1,

The winning probability of 111 and 000 is the lowest. Both 011 and 100 have seven out of eight, which is an 87.5% probability of winning.

The sequence of 100, 001, 011, 110, etc., are mutually beneficial and inferior solutions, forming a cycle of mutual growth and restraint, like a reincarnation like rock paper scissors.

For a gambler, the 55% probability of winning is already a huge advantage. If he can control his chance of winning at 67% or even 75%, he can almost cast his entire net worth and there is no reason not to continue calling.

Claude said slowly: "Five games and three wins. In the second round, you choose first."

"..."

Hornheim thought for a moment, then slowly said: "I choose, pros and cons."

Although there will be a cycle between numbers, the restraint probability of 011 and 100 is relatively lower.

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

Sure enough, Hohenheim's heart sank. The opponent's choice of number sequence was better than his first solution in terms of probability, but... there might not be no chance of a comeback.

The result of the second round of throwing is.

Anyway, anyway, positive and negative.

Victory again.

Hornheim's frowned brows stretched slightly. The only solution for his pros and cons to win victory is to make three straight forwards in a row in addition to the first three shots to break the opponent's pros and cons. , Cast your own results.

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

"Wow, it seems luck is really on your side."

Claude blew a whistle, tilted his head, and a strange arc of his mouth raised his mouth, "It's already the match point. Then in the third round, I choose, right."

"Ok?"

Hornheim's gaze narrowed and he took a deep look at the opponent. The probability of three consecutive positives was originally not high. If he chooses to suppress anyway, then the opponent's winning rate will be infinitely lowered.

You must make the first three shots and directly cast a positive result to be able to win——

Because once the number sequence surpasses the top three, then there will inevitably be a situation of [there must be a negative before the positive], and the one who chooses the positive will not lose anyway.

The probability of winning is...87.5%.

"I choose, anyway."

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

"Very well, then, I'll start."

Claude's thumb nailed, and the coin flicked up.

The round sheet of brass alloy was spinning slowly and fast in the air, and finally fell on the back of Claude's hand, and was suddenly caught.

The result is displayed as...【positive】

"The first shot was pretty good for me."

Claude grinned, ignoring the dense monitoring techniques in the void like probes, and repositioned the coin on the thumb nail, and bounced again.

clang--

Still yes, [positive].

The atmosphere around Hohenheim suddenly changed. His 87.5% winning percentage was based on the inability of the first three rounds to cast a positive result.

For the opponent to win, it means that the probability is one-half times one-half times one-half, and the total is only one-eighth probability.

"The third round..."

Claude flipped the coin flexibly with his fingers, and tossed it again.

The brass alloy coin spun, fell, and was caught by the palm with a snap.

【positive】.

"One in eight probability, I won."

Claude whistled easily, "Fourth round..."

"Wait."

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

He has never been a superstitious person. As a player, he also believes that the system will not set up a kind-eyed and magical grandfather as a caring guide for players.

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

"Row."

Unexpectedly, Claude nodded openly and tossed the coin to Hohenheim at will.

As before, Hornheim grabbed the coin with the hand of an invisible wizard, used the investigative spell more carefully, and looked at it.

The head of the figure on the coin is more severely worn. It can be vaguely seen that the face is sharp and angular, the eye sockets are deep, the nose is straight, the facial features are correct, and the short curly hair.

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

It was very different from the three-armed weird Crowder in front of him.

Hohenheim raised his head and asked, "Who is the head on this coin?"

As the coin is worn out, he doesn’t have to worry about [the characters on the coin are extremely well-known in the world of scripts, they don’t know, and they will be doubted by Claude]. Anyway, the reason can be pushed to "unrecognizable".

"Who else? The head of the seven pirate kings of the infinite deep sea, the leader of the invincible fleet, and the symbol of all wealth in the world-Tixiu."

Claude was a little inexplicable, "I picked up this copper coin accidentally in this forest. It is estimated that it was left over a long time ago when Hugh and his subordinates came to worship at the holy mountain.

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

He glanced at Hohenheim strangely, "Could it be that you thought I was the person on the profile picture? Am I so ugly?"

"Uh, no no no."

Hohenheim resisted the urge to spit, the strange appearance of the three-armed weird, placed in the real world is enough to throw into the horror game in the eerie scene,

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

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

However, it may also be normal. Everything can happen in the killing game. Maybe the racial aesthetic of Crowder is abnormal.

Before, a fat player entered the dark area of ​​the script world, where he was hospitalized by a group of drow elves who regarded fat as their beauty, and killed the thin handsome guy in the player team, leaving him alone. One person has lived a happy life ever since-although it turned out that this group of players fell into the net of cannibal spiders, everything is an illusion, but it does not affect the effect of this rule.

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

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

Hornheim took a breath, "I choose, pros and cons."

It was just an accident. Before he saw the problem, the pros and cons of restraint in probability still took effect.

Claude grinned, "Then, I choose to oppose."

Again!

Hohenheim's heart sank, the probability of pros and cons is also better than the pros and cons, and the winning rate is still 87.5%.

In this round, he is the first to choose,

After he chooses pros and cons, the opponent can choose pros and cons to exercise restraint in the 67% probability of winning, but the opponent did not choose pros and cons.

Instead, he chose an opponent with a winning percentage of only one-eighth.

Certainly, something went wrong...

"Now that you have decided, let's start voting."

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

"...it is good."

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

The hand of the mage is an extension of his own magical power, and it is even more flexible and controllable than the palm of his hand.

‘Let me see, are you cheating...’

The invisible palm flicked the coin, and the coin flew and rotated on its own, drawing a straight trajectory in midair.

Snapped.

The hand of the mage, composed entirely of magic power, firmly caught the brass alloy coin at the same height as the throw.

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

Those in the air were infused with magic power to monitor and control magic, staring attentively at each rotation of the coin, and before it fell and was caught, they had already calculated the result.

I have won.

Hohenheim felt the magic lost in his body (the surrounding low free energy environment is extremely unfriendly to players who specialize in spell casting), UU reading www.uukanshu.com opened the coin at an extremely slow speed.

and many more,

Snow mountain?

Hohenheim's eyes widened slightly, and he suddenly raised his head to stare at Crowder, his voice low: "You cheated."

"Yes?"

On the stone platform, Claude smiled and said: "You toss the coin and you catch it.

As a mage, you should be very clear about whether I interfered in the process just now.

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

The three-armed weird scratched his cheek lightly with his right hand, drew blood stains, and smiled: "Besides, even if I cheated, as long as you have no evidence to prove it,

The game is still valid. "