Chapter 48 You Can Actually Play Like This

Jianfeng stood frozen, holding a number of slips and counting them separately in her left and right hands.

Gradually, she began to grasp the Young Lord's intention behind this move, but she still couldn't help asking, "At twenty copper coins per Martial Kinship Lottery ticket, it is indeed not expensive."

"Yet, it is not fear of the probable, but fear of the accidental."

"Should someone actually guess all nine matches correctly and win the hundred-tael prize, we would need to sell five thousand tickets just to earn it back!"

"However, you once said that our Great Xu Royal City has a total population of forty thousand at most. It is impossible for everyone to come and buy lottery tickets!"

"The moment even one such ticket is sold, we will suffer a massive loss!"

Chai Xiao tapped the stone table lightly with a large tree leaf, beginning to draw the second diagram, which was the layout for the second set of nine matches.

"Indeed! You are now capable of calculating the probability of payout!"

"Rest assured! Seeing that twenty copper coins is so cheap, they will surely buy more!"

"In fact, there is an arithmetic problem hidden here."

"What we just discussed was merely the first batch within the first group."

"There are thirty-two groups in total. To be conservative, let us arrange twenty people per group, fighting in pairs. Calculate how many matches each group must conduct."

Jianfeng muttered to herself under her breath.

"Twenty people per group, fighting in pairs, one, two, three..."

Since Jianyu was not present, she found the calculation arduous. Besides her two hands, she wished she could use her toes to count as well.

As a result, she became utterly confused after just a few moments.

Chai Xiao smiled.

"This calculation method is somewhat similar to the 'doubling and summation' we discussed earlier. You can find the pattern step by step."

"Let us start with the simple ones!"

"For instance, if there are only three people in a group, the pairings are one-two, one-three, and two-three—three combinations in total."

"If there are four people, there are six combinations: one-two, one-three, one-four, two-three, two-four, and three-four."

"If there are five people, there are ten combinations: one-two, one-three, one-four, one-five, two-three, two-four, two-five, three-four, three-five, and four-five."

"This is equivalent to: for three people, taking three minus one, which is two, adding one, making three multiplied by two, divided by two."

"For four people, three plus two plus one, equal to four multiplied by three, divided by two."

"For five people, four plus three plus two plus one, equal to five multiplied by four, divided by two."

"Therefore, for twenty people, it should be..."

Jianfeng was not particularly skilled in mathematics, but the Young Lord's summary gave her great inspiration, and she immediately answered,

"Adding from nineteen plus eighteen all down to one equals twenty multiplied by nineteen, divided by two, which is equivalent to ten times nineteen, making one hundred and ninety!"

Chai Xiao applauded.

In fact, these were the problems of "permutation" and "combination" in modern mathematics.

High school curricula contained explicit calculation formulas for them.

"Permutation" involved order, whereas "combination" did not.

The initial calculation formulas for both were identical: the "factorial" of the "total number," divided by the "factorial" of the "total number minus the chosen number."

The difference between the two was that "combination" required an extra division by the "factorial" of the "chosen number"!

Since these were pairs fighting one-on-one, one only needed to divide by an extra "one multiplied by two," which was simply "two."

"For the first group alone, there are one hundred and ninety matches. With nine matches drawn on each lottery ticket, we will need at least twenty tickets."

"At twenty copper coins per ticket, one group amounts to four hundred copper coins."

"Across thirty-two groups, that is twelve thousand eight hundred copper coins, which translates to twelve taels and eight Mace of silver."

"Twelve taels and eight mace compared to one hundred taels—that is merely a ratio of one to eight."

"Looking now at the hundred taels that appear when someone strikes gold by getting all nine matches right, you won't feel so worried anymore, will you?"

Jianfeng smiled, and the other Golden Hairpins nodded repeatedly.

Viewed this way, there was indeed no need to worry about losing too much.

The large tree leaf in Chai Xiao's hand stopped drawing the "nine-match diagram" and instead sketched the pattern of a one-hundred-tael "flying money" silver note.

"Let me provide a safety net for you. If someone truly guesses all nine matches correctly, I will pay out that hundred taels!"

"Of course, risk and reward are relative; I cannot let you take advantage of me for nothing!"

"If, looking across the entire event, not a single one-hundred-tael grand prize is won, you will contribute twenty taels from the silver you earn in this event. How does that sound?"

Jianfeng's eyes lit up with radiant joy and she was overjoyed.

"Many thanks to the Young Lord for providing the safety net!"

"To avoid the peril of this hundred-tael grand prize, this subordinate is willing to put up these twenty taels as a counter-stake."

Chai Xiao burst into laughter, glancing sideways at Imperial Concubine Yun and Zhuque.

"In your minds, am I simply the image of a giant six-sided die, constantly plotting to gamble day and night?"

Zhuque, Jianfeng, and the Golden Hairpins could not help but smile.

Did even need to ask?

Was that not precisely the case?

Only Imperial Concubine Yun did not see it that way; her face was wreathed in smiles, her gaze filled with anticipation and admiration.

Allaying the anxieties of her subordinates was something a "wise ruler" had to do.

This voluntary provision of a safety net brilliantly resolved Jianfeng and the others' greatest concern regarding this "Martial Kinship Lottery."

As for the twenty-copper-coin "counter-stake," since it was to be drawn from her earnings, it would serve to inspire her fighting spirit to earn even more.

Killing two birds with one stone and achieving two goals at once—why not do it?

Chai Xiao caught his mother's approving gaze.

The large tree leaf in his hand pointed toward Jianfeng.

"You should now set your mind to work and consider how to earn ten thousand taels from these tickets priced at twenty copper coins each!"

Jianfeng was pale with astonishment, raising her fingers to begin counting.

"Ten, hundred, thousand—one thousand copper coins equal one tael. Then ten, hundred, thousand, ten thousand."

"Your Highness, at twenty copper coins a ticket, that's fifty tickets per tael. To reach ten thousand taels, we would need to sell five hundred thousand tickets!"

"How is that possible?"

The large tree leaf in Chai Xiao's hand tapped lightly against the stone table.

"The figure of five hundred thousand is correct! But do not be frightened by it!"

"We just calculated the first format of the round-robin lottery, which is win, draw, and loss."

"Thirty-two groups, twenty people per group, with each lottery ticket featuring nine matches of wins, draws, and losses. Each group requires twenty tickets, making six hundred and forty tickets in total."

"Suppose one thousand people wish to try their luck. Calculate how much that comes to!"

Jianfeng hurriedly began to calculate, her mouth falling open in astonishment.

"Six hundred and forty multiplied by one thousand—that makes six hundred and forty thousand! That is more than enough, it vastly exceeds the target!"

Chai Xiao smiled.

"Naturally, that is the maximum possible total!"

"Even if a thousand people wish to buy, given this unpredictable round-robin tournament, most will only pick a few matches to try their luck rather than buying the whole lot."

"However, some people will believe that buying more increases their chances of winning."

"Therefore, your most pressing concern right now is to hurry and work with the Inner Directorate to draw these lottery tickets."

"There is a simple method: you need only draw the matchup diagrams for the twenty tickets of each group, and then make rubbings."

"Create thirty-two small stamps to denote the groups, and stamp them at the very top."

"If we calculate based on one hundred people wishing to make bulk purchases, that is six hundred and forty multiplied by one hundred, which still yields sixty-four thousand tickets!"

"In actual circumstances, the number should be somewhat lower than this."

"Thus, I suggest your first batch of rubbings be around six thousand tickets. Stamp the group designations on them, and print more only as further purchases are made!"

Jianfeng regained her composure and confidence, bowing and accepting the command.

"Understood!"

The large tree leaf in Chai Xiao's hand began to trace a second circle.

"This is merely the first format of the round-robin tournament."

"The second format is guessing the number of moves!"

"Unlike guessing wins, draws, and losses just now, this second format asks you to guess within how many moves victory or defeat will be decided."

"That is to say, if a contestant is knocked out of the ring or falls to the ground three times, victory is declared, calculated based on the number of moves used at that moment."

"It is divided into four tiers, meaning four circles are drawn."

"The first circle: victory or defeat decided within five moves."

"The second circle: victory or defeat decided within six to ten moves."

"The third circle: victory or defeat decided within eleven to fifteen moves."

"The fourth circle: victory or defeat decided within sixteen to twenty moves."

"Each ticket also features nine matches."

"The prize money is identical to the first format: ranging from five correct matches up to nine, from forty copper coins to one hundred taels."

"Twenty tickets per group drawn, uniformly rubbed, and then stamped with the thirty-two group seals."

"This style of play is quite novel; the first batch can have about eight thousand copies rubbed, and more printed as purchases dictate."

Jianfeng and the other Golden Hairpins were stunned by the Young Lord's "novel move-count guessing," taking quite a while to recover their senses.

Shocked though they were, they clearly perceived that this was entirely feasible; they simply had never imagined that such a way to "play" existed.

"Understood!"

The large tree leaf in Chai Xiao's hand traced a third circle.

"The third format of the round-robin tournament: guessing the method of victory."

"Divided into three methods, with three circles drawn."

"The first circle: victory or defeat decided by knocking the opponent out of the ring."

"The second circle: victory or defeat decided by the opponent falling to the ground three times."

"The third circle: victory or defeat decided by points."

"This also features nine matches per ticket, twenty tickets drawn per group, rubbed, and stamped with the group seal."

"This gameplay is also interesting; print eight thousand copies first, and print more upon purchase."

Jianfeng bowed in acknowledgment.

"Understood!"

Seeing the confidence in Jianfeng's eyes growing stronger and stronger, Chai Xiao smiled and traced a fourth circle with the large tree leaf in his hand.

"For the first day of the round-robin tournament, since everyone is unfamiliar with the contestants, we shall start with just these three formats."

"By the second day of the knockout rounds, everyone will have a firm grasp of the situation, and an increasing number of people will purchase lottery tickets!"

"Jianfeng, tell me, how should we set up the formats then?"