Disease Game

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New rules, by John Choi, Christian Murphy, Dan Sakamoto, Kristina Wagner:

In an environment where 3 players try to cure their diseases:

3 Patients start with 5 diseases + 3 diseases in the pool (center of the table)
Each turn patients take a decision in Rock Paper Scissors style. Patients can choose Treatment (with possible side-effects) (fist) or Sneeze (open hand).
There are 4 possible outcomes:
Outcome 1 – one patient chooses Treatment: this player takes 1 disease from each other player.
Outcome 2 – two players choose Treatment: these players both give 1 disease to the third player.
Outcome 3 – three players choose Treatment: all players put 1 disease in the pool
Outcome 4 – three players choose Sneeze: the player with most diseases proposes once, without discussion nor barter, how to divide the pool. If at least one player agrees the decision becomes effective. Otherwise, nobody takes anything.
The game ends when the first player is out of diseases. This player is the winner.