let expected_reward : (scenario => real) => real =
  (scenario_pmf) => Real.({
    let pr = (s) => scenario_pmf(s) * reward(s);
      let avg = (choice) => {
        let avg = (first_guess) => {
          pr { prize: DoorA, first_guess, choice} +
          pr { prize: DoorB, first_guess, choice} +
          pr { prize: DoorC, first_guess, choice}
        };
      avg(DoorA) + avg(DoorB) + avg(DoorC)
      };
    avg(Stay) + avg(Swap)
  })