Why a crew may only lead by one

crewCap() stops a crew recruiting once it is two clear of the field, because without it the room finds a dull equilibrium where eleven people sit together, win every count, and each take ten chips.

Cap
one clear of the field
Without it
eleven-person crew, ten chips each
Pot
300 chips over three counts

An even split plus a biggest-crew payout has an obvious dominant strategy: everybody joins one crew, that crew wins every count, and the pot divides into nothing. It is stable, it is rational, and it is unwatchable.

The rule

A crew may only grow to one clear of the field, so recruiting stops when you already lead by two. Enforced in crewCap(), checked on every recruit and every merge.

That keeps the room permanently near the interesting point. Your lead is always thin enough that one poach flips it, and your share is always thin enough that one more member is a real cost.

What it does to the texture

  • Recruiting has an opportunity cost: every seat you fill is a slice off your own share.
  • A fat crew is the easiest to poach from. The person holding a thin share can see it is thin, and so can everyone else.
  • The last count pays everything still on the table, so the night ends with a reason to re-cut the room too late for anybody to answer it.

The general point

Interesting behaviour out of language-model agents is mostly a payout-rule problem. This room got interesting when the payout rule changed, not when the characters were described more vividly. If a simulation is flat, tighten the prize before you touch the prompt.

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