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# Number Line

November 22, 2021 by Jorge Zhang

Idea behind this game: A friend and I were considering a situation in which 3 players had to guess a number between 1-10. The person who guessed the closest number won. What is the best strategy and how can each player maximize their chances of guessing the right number? Interestingly, the strategy here is somewhat complex. If the first person simply chooses 5, they can be "surrounded" by the other 2 players who guess 6 and 4. Thus, this game was born. Ultimately, I think this problem is technically solvable. In this game, round 1 is essentially this initial solvable state, which is somewhat unfortunate because solved games are boring after a while. Although with all multiplayer games collusion is generally possible, so I think there is still more to explore there. "Round 2" is a more gamified version where a decoy card can spice things up because this allows for bluffing.

This game is a competitive game in which players try to earn the most points across two rounds.
SET UP: Place the number cards 1-10 face-up in a row, ordered lowest to highest. The Starting Player is the player who can calculate 17 * 34 the fastest in their head.
Win when: At the end of round 2, have the most points.
Round 1: Each player chooses a color and gets those respective cards. Players take turns starting with the starting player and continuing clockwise by playing 1 card on top of a number card that does not already have a number on top of it. The round ends when all players have placed exactly 1 card. Score this round, then reset the game to the SET UP position.
Round 2: This is the same as round 1, except players now continue until they play 2 cards. Additionally, 1 card is a "decoy" that does not count during scoring.
Scoring: Players get 1 point for every number their card is closer to than any other's card. This includes the number that their card is on. Neither player scores points for ties.
Changing the starting player: The starting player should rotate clockwise between rounds, and you can keep track of this with the starting player card.
Ties: If 2 or more players are tied at the end of round 2, then play a third round.
Round 3: This is the same as round 1, except now the decoy card also counts during scoring. Additional rounds: If there continue to be ties, play additional rounds under round 2 rules but remove the highest number each time. This can make it so that a move is impossible because there are no available numbers to play a card on: in this case, immediately end the round.