Lesson 12

It turns out that no matter which die you choose, I can choose another one (from the remaining two) so that my winning probability will be higher! Indeed, \(\Pr[\text{\(A\) beats \(B\)}]=5/9\). The same applies to the pairs of dice \((B,C)\) and \((C,A)\). That is, \(A \succ B \succ C \succ A\)! This is another example where intuitive reasoning about probabilities fails.