The monster can know if he can win or not at any time, likwise the lady.
They cant 'agree' to enter a phase where the probability that either wins is something other then 0% or 100%.

If the lady cant win, so the monster wont win if she stays in the lake, they can toss a coin to determine her faith.

The monster can know if he can win or not at any time, likwise the lady.
They can't agree to enter a phase where the probability that either wins is something other than 0% or 100%.

If the lady can't win, so the monster won't win if she stays in the lake, they can toss a coin to determine her faith.