[數撚圍爐區] Bounded Operators are Unbounded (58)

Peter and Chris are playing a game. At the beginning, each of them has some balls, where each ball is red, blue, or green. There is also a ball pool which contains more than enough balls of each colour for Peter and Chris to draw.

Peter and Chris take turns to move, and Peter moves first. After each turn, if Peter has exactly one ball and Chris has none, the game will end immediately.

Each move consists of the following steps:
1) If the player has less than two balls, he draws red balls from the pool until he has two.
2) The player chooses two of his balls and throws them into the pool.
3) If the two chosen balls are of the same colour, the opponent player gets from the pool one ball of the same colour. Otherwise the opponent player gets from the pool one ball of colour different from the colours of both chosen balls.

For example, if Peter chooses two red balls, Chris will get a red ball from the pool. If Peter chooses a red ball and a blue ball instead, Chris will get a green ball from the pool.

You are asked to find out the outcome (never terminate/uncertain/red/green/blue) of the game given the initial balls of Peter and Chris.