power
uh-oh, the game in trouble
Not sure why monte carloing this was necessary
Scenario 1 has probability 27/41 (65.85%) the great player wins
Scenario 2 has probability 589/903 (65.23%), which is slightly less.
These are both relatively straightforward to compute as (.6*.9)/(.6*.9 + .4*.6 + .4*.1) and (.62*.95)/(.62*.95 + .38*.8 + .05*.2)
Scenario 1 has probability 27/41 (65.85%) the great player wins
Scenario 2 has probability 589/903 (65.23%), which is slightly less.
These are both relatively straightforward to compute as (.6*.9)/(.6*.9 + .4*.6 + .4*.1) and (.62*.95)/(.62*.95 + .38*.8 + .05*.2)