[miggol]

This invites a game where models have variants with slightly differing system prompts. Don't know if they could actually sample from their own output if instructed, but it would allow for iterations on the system prompt to find the best instructions.

[energy123]

You could give it access to a tool call which returns a sample from U[0, 1], or more elaborate tool calls to monte carlo software that humans use. Harnessing and providing rules of thumb in context is going to help a great deal as we see in IMO agents.