Dare

Dare is a simple game. It needs a person to act as “Referee” in addition to the players, and its best played with lots of people.

Rules

1. Each person stands up to play.
2. The Referee tosses a six-sided die to start. If the die shows a 2 or 5, the die is thrown again, until a number other than 2 or 5 is shown. Once a first score is thrown, it is read out.
3. Each player decides to sit down (and scores that number for the round), or stay standing to play on.
4. For the second and later throws, either:
   • the die comes up with a 2 or 5, in which case any player standing scores zero for that round, and the round ends; or
   • The die comes up with a number other than 2 or 5, in which case the number thrown is added to the current round’s score, the Referee gives players a few seconds to make their “sit or stand” decision, and the die is thrown again.
5. The die continues to be thrown in a round until all players are sitting, or until a 2 or 5 are thrown.
6. A player may sit at any time between throws to add the current score to their total. Once a player sits down, they may not stand up until the start of the next round.
7. The game is played for a fixed number of rounds (for example, six rounds). The winner is the player with the highest total at the end of that number of rounds.

Tasks

1. Play Dare several times to understand how it works.
2. For any one particular throw, what is the probability of scoring zero for the round?
3. Do you have a strategy to maximise your score? Explain how it works.
4. If the game used an eight-sided die, on average would the rounds be longer (that is, would it take more throws to end a round)? Would the average player scores be higher? Explain your answers.
5. If the game used a twelve-sided die, and the numbers 8 and 11 also ended a round with a zero score, would the rounds be longer? Would the scores be higher? Explain your answers.