On Thu, 22 May 2025, MK wrote:
2. Will the weaker player's probability of coming out
ahead increase or decrease if the cube is in play?
Yes, just replace "probability" with "ratio" of points won
and we may be talking about the same thing, which is to
compare one ratio with another ratio.
There's a more direct way to investigate the question as I've formulated
it. Fix some number of games, say 10, and define a "session" to be 10
games (either cubeful or cubeless). Play a session between the stronger
bot and the weaker bot. Record who wins (meaning just who comes out ahead
at the end of the session; ignore the margin of victory). Of course, the
stronger bot will usually win, but not always. Repeat the experiment many
times; e.g., play 1000 sessions, and record which bot wins. Then ask the
question, does the weaker bot win a greater fraction of the 1000 sessions
when the cube is in play?
Tim
