- There are 7 players, and 7 rounds to the game.
- Every round, every player is given 7 (indivisible) coins in hand. They can allot these coins as they wish amongst the following options:
- The public tax box: After each round, the coins in the tax box are counted, and the number is publicly revealed. The coins are then doubled, and distributed equally to all players who are in the game(rounded down) as that many points.
- The private bank: Money deposited in a private bank is not publicly revealed, and is credited directly to your score.
- The casino: If multiple people choose to put money in the casino in a single round, nobody gets any money from the casino. However, if only one person puts money in the casino, they are awarded 3x the money they put in as payout to their score. If the casino awards money to someone, this will be announced in public, but who it is and how much they got will not be.
- The insurance firm: If 0 < N < 4 people put coins in the tax box, the payout is (4-N) times the amount you put into insurance. Else, you get nothing(note that if nobody puts money in the tax box, the payout from insurance is *0*). Insurance payouts are not public.
- 2 times in the game, if 4 players agree, they can vote to exile a player from the game. The exiled player can no longer participate in the game, and their score is set to zero.
- At the end of 7 rounds, if all players have a score < 78, the dealer wins. Otherwise, the highest scoring player wins.
- Private communication between players is *allowed*. Feel free to conspire with each other to your heart's content! However, if playing online, sharing screenshots of communications with the dealer is not allowed.
I've run the game once with friends, and it ended up being a close finish, the "solution" to the game being deduced just a bit too late for the players to beat the dealer.
The "solution" is not quite a Nash equilibrium, but it is quite close, and interesting to try and figure out on your own.
