One Move of the Algorithm

  • Start at a standard knowledge state over (x,y,z).

  • Read a request rz. (The case r = z is trivial.)

  • Update the estimator. No payment either way.

  • Move the distribution. We pay.

  • Adjust the estimator. The adversary pays us.

  • Optionally forgive; lower the estimator selectively. No payment.

  • Las Vegas. Randomly pick a subsequent according to
    an appropriate distribution. No payment: "fair" wager.

  • We are at a standard knowledge state over
    (x,y,r), (y,x,r), (x,z,r), (z,x,r), (y,z,r), or (z,y,r).