For a rotation angle of x° the probability of failure for each check+rotate when a bomb is present is sin(x°)^2. It takes 90°/x° repetitions of a rotation by x°

For a rotation angle of x° the probability of failure for each check+rotate when a bomb is present is sin(x°)^2. It takes 90°/x° repetitions of a rotation by x° to get a useful effect in the safe case. So the overall failure rate is 1-(1 - sin(x°)^2)^(90°/x°) or equivalently 1-cos(x°)^(180°/x°). Compute the limit as x goes to 0 and you'll find the limit equals 1. Making x smaller increases the chance of success arbitrarily close to unity.