During the Spring Festival, in addition to eating and drinking, many people will also play some sports with relatives and friends, such as egg hunting.
Egg Hunting is a card game that originated and is popular in Huai'an City, Jiangsu Province and its surrounding areas. The slogan of the "egg breaker" is "If you don't break eggs before eating, you don't eat." If you don't break eggs after a meal, you are eating for nothing." In recent years, this slogan has begun to become popular in all circles across the country.
Screenshot of Weibo.
In 2017, Huai'an Egg was included in the "National Fun Chess and Card Official Competition" by the Chess and Card Sports Management Center of the General Administration of Sports of the People's Republic of China.
In 2023, the General Administration of Sports of China held the National Egg Cracking Open, and there were even news reports that 2023 was the "first year of egg hunting".
Notice from the Chess and Card Sports Management Center of the General Administration of Sports of the People's Republic of China **Network screenshot.
The Spring Festival is approaching, people are returning to their hometowns for the New Year, and the eggs may "penetrate" into a wider area with the crowd of returnees.
In that case, can you learn a winning strategy for egg cracking in advance, and turn yourself into a well-known "egg master" in ten miles and eight towns?
Is there a winning strategy for cracking eggs?
In fact, there is no winning strategy for egg hunting.
In 1913, the mathematician Ernst Zermelo proposed the "Zermelo theorem". This theorem says, "In a finite game of two, if both players have complete information and the factor of luck is not involved in the game, then either the first or the latter must have a winning (undefeated) strategy." ”
If you are not familiar with the rules of egg hunting, you can simply understand it as a team of two people competing for the top, with a total of 4 people participating. And in the process of breaking eggs, there will be an element of luck involved, for example, you can use some strategies to make a bad hand easier to play, but still can't stand the opposite hand full of bombs.
In addition, a game like Egg Hunting is an imperfect information game, which means that everyone knows the rules of the game, but they don't know what the opponent's cards are.
And there is a human element involved in the process of playing cards, so it's hard to know what kind of strategy your opponent will use. For example, if you can make a pair, if you can make a straight, someone will make a straight, and someone will make a pair.
Playing Cards **pixabay**.
You can't even make sure that your teammates will help you. For example, when you have a card left in your hand, your teammate may throw a pair.
These factors make it impossible for an egg-breaking strategy to win. Similarly, games such as mahjong and landlord fighting also have no winning strategy.
It is precisely because of the randomness of games like Egg Hunt that people are willing to play it over and over again. Moreover, the egg card rises level by level, and it often takes an hour or two to play a big situation, which also makes it a sharp weapon for pastime before and after meals.
Is there really a winning strategy in games?
Many people may not know that in fact, many of the games we usually play have a winning strategy.
In order to make it easier to understand, let's start with the familiar "tic-tac-toe". Tic-tac-toe is to draw "x" and "o" in turn on a "tic-tac-toe" shaped chessboard, and whoever joins a line first wins.
Tic-tac-toe **wikipedia
To illustrate, some people may think that as long as the first mover occupies the middle position, he can win. But no, the winning strategy of tic-tac-tac tac is to occupy a corner. If the first hand does not occupy this position, it is also possible to be undefeated as a second hand to occupy this position (if you don't believe it, you can find someone to try it).
In fact, the way to find a winning tic-tac-toe strategy is very simple and crude, we just need to draw all the possibilities of the game and find a move that will never fail.
Strategies for winning first on Wikipedia
Not only tic-tac-toe, but many games have a similar strategy of winning (undefeated).
Tic-tac-toe, for example, is a finite game for two (which will eventually end), where both sides know how they and their opponents can move, and there is no luck involved. Therefore, according to Zermelo's theorem, such a game must have a winning (undefeated) strategy.
In addition to tic-tac-toe, our common chess, chess, Go, etc., all belong to this type of game. So theoretically, these games also have a winning strategy, but it's too difficult to find their winning strategy.
For example, tic-tac-toe is already a very simple game, with 12 possibilities already appearing in the second move, and in fact, its game tree complexity is 10 to the 5th power.
Tic-tac-toe "game-tree" *wikipedia
For example, the complexity of the game tree in Chinese chess is 10 to the 150th power, and Go is 10 to the 360th power. So even with a computer, you can't exhaust everything (AI doesn't need to exhaust all possibilities when playing chess). So according to the "Zemelo theorem", there is a winning or undefeated strategy in these games, but it has not yet been found.
Did you break eggs this Spring Festival? It should be noted that there is nothing wrong with having fun with relatives and friends during the Spring Festival, but remember not to participate in gambling. Also, don't forget to eat even if you're whipping eggs. After all, if you want to break eggs "before and after meals", the most critical information has to be "rice".
Resources. 1]
2]schwalbe u, walker p. zermelo and the early history of game theory[j]. games and economic beh**ior, 2001, 34(1): 123-137.
*The content represents the author's views only.
It does not represent the position of the Institute of Physics of the Chinese Academy of Sciences.
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*: Popular Science China.
Editor: Yue Yue.