To share with the class:

The cyclic property of this scoring system is given a fancy name: Intransitivity Intransitivity What does that mean? A Transitive function or property is something in which all comparisons are performed according to the same dependent criteria. For example, if Albert is older than Bob, and Bob is older than Charlie, then we know that Albert must be older than Charlie too.

This is because "is older than" is a Transitive function.

This is because "Friendship" is Intransitive. You can read a little more about intransitive games on my posting about How to win free drinks from your friends using dice. Rock, Paper, Scissors There are numerous articles on the web that talk about strategy from the psychological perspective.

If you want to read more on that angle, Google is your friend. Imagine there are three organisms living on a fictitious island in the Pacific Ocean. The Rock Wolf feeds entirely on the Scissors Rats. None of these animal species is cannibalistic to their own species.

Each animal has a unique prey, and a unique nemesis. On this island, there is a natural state of dynamic equilibrium with the three species balancing each other out. Now imagine what would happen if, suddenly, half the snakes disappeared?

How would this effect the ecosystem? How would it change the balance and the ecosystem? Back to Rock, Paper, Scissors Imagine there are a lot of people in a room, and they are going to play a giant game of rock, paper, scissors. However instead of autonomy in selection, their choice of Rock, Paper, Scissors is pre-ordained.

They are automatons and always play the same move. To play each round, two random people are selected from the pool the players still in the game and challenge one another. The winner goes back into the pool to fight another day. The loser leaves the game. In the event of a tie, both players return back to the pool.

Over time, the number of people in the pool gets fewer. Because, obviously, when we are down to just one remaining class there is nobody who they can attack, or they can get attacked by.

The class that survives is determined to be the winner this could be as few as one person. Mixtures The probability of being the winning tribe depends of the concentrations relative ratios of the starting players. The starting conditions effect the chances of surviving to the end.

Obviously, if the ratios of Rock, Paper and Scissors at the start of the game are the same, the probabilities of being the last tribe standing are the same This should be obvious from symmetry, and from the fact the intransitive property that each class is the same with exactly one strength and one weakness each.

To work out what happens with non-equal starting conditions, we need to model the system. Monte-Carlo Simulation To model this system, I wrote code to perform this contrived Rock, Paper, Scissors game using a random number generator to select two opponents for each round.

Each game was played to completion.The probability of a tie in an odd-number-of-weapons game can be calculated based on the number of weapons n as 1/n, so the probability of a tie is 1/3 in standard rock-paper-scissors, but 1/5 in a version that offered five moves instead of three.

How to Win at Rock, Paper, Scissors. You might think that winning at rock, paper, scissors was purely a matter of chance – after all mathematically each outcome has the same probability. We can express the likelihood of winning in terms of a game theory grid: It is clear that in theory you would expect to win, draw and lose with probability 1/3.

Probability Worksheets: Rock, Paper, Scissors Probability Worksheet (could be easily extended for grade probability) Probability Worksheets Science Worksheets Math Resources Math Activities Grade 6 Math 7th grade math Fraction Activities Fifth Grade Math Math & School.

Worksheets: Rock, Paper, Scissors Probability Awesome for students to engage in! Is the probability for rocks, paper, and scissors the same? If the rock-paper-scissors (RPS) robot is asked, "What is the probability of the robot throwing a rock?", the desired outcome is rock, which is 1 since only one rock is present, and the total outcome is 3, since rock, paper and scissors are present.

(8) Compare the theoretical probability and experimental probability of one player (you choose which player) throwing rock, paper, and scissors. Rock: theoretical= experimental.

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Probability - Rock Paper Scissors : probabilitytheory