Gambling in ancient Rome. Tossing four astragali was the most popular game of chance in Roman times. Many throws of a present-day sheep’s astragalus show that the approximate probability distribution for the four sides of the bone that can land uppermost are Outcome Probability Narrow flat side of bone 1/10 Broad concave side of bone 4/10 Broad convex side of bone 4/10 Narrow hollow side of bone 1/10 The best throw of four astragali was the “Venus,” when all the four uppermost sides were different.

(a) Explain how to simulate the throw of a single astragalus. Then explain how to simulate throwing four astragali independently of each other.

Chapter 19 Exercises 425

(b) Simulate 25 throws of four astragali. Estimate the probability of throwing a Venus. Be sure to say what part of Table A you used.