Warning: don鈥檛 play rock, paper, scissors with a large group of people unless you have a lot of time to spare. The game time increases exponentially with the number of players. So with 100 people participating, you may have to wait for a hundred thousand trillion rounds or more for the emergence of a winner.
Rock, paper, scissors is often no more than a bit of fun or a way to decide where to get lunch between friends. However,听with more than听a few players involved it can get a little out of hand.
By mathematically analysing the game, Hyun Jae Yoo and his colleagues at Hankyong National University in Korea derived a formula to predict how many rounds of rock, paper, scissors a certain number of participants would need to play before the emergence of a single winner.
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In their version of rock, paper, scissors everyone displays their move simultaneously. If across all the players only two of the moves are chosen 鈥� rock and paper, rock and scissors, or paper and scissors 鈥� then the normal rules apply, with everyone who throws a losing move eliminated.
But if rock, paper, and scissors all make an appearance then the round is considered a tie and a new round begins. New rounds keep being played until a single winner remains.
The game goes on
Yoo and his colleagues found that the average number of rounds needed before a winner emerges increases exponentially with the number of players. The听exact number is difficult to compute, but simpler versions of the team鈥檚 formula allows them to work out the upper and lower bounds more easily.
In a 10-person game, the average number of rounds needed is between 19 听and 19,221. For a 100-person game, the average number of rounds needed shoots up to somewhere between one hundred thousand trillion, also known as a quadrillion, and one hundred sextillion 鈥� a number with 23 zeros. Both of these numbers are so large that all of the players would be long dead before a winner was found.
The team鈥檚 formula also shows that there is no upper limit on how long a game will last if there is an enormous group of players. 鈥淚t could be longer than any given time,鈥� says Yoo.
However, the game is听more complicated than this analysis听because participants tend to form coalitions and come up with strategies, says Ethan Akin at City Collage of New York. 鈥淲hen play occurs, players decide whether or not to hold to the agreements they have made,鈥� he says. 鈥淚t makes things more interesting.鈥�
Reference:听arXiv,听
