One way to think about the game is adversarially. That is, we first have to publicly reveal our distribution for R, and then the opponent arbitrarily chooses A and B.<p>If our distribution is &quot;always choose 0&quot; or &quot;uniformly choose an integer between 1 and 100&quot;, then the opponent can always pick A and B so that R will never fall between them.<p>But if we pick with a distribution that is positive everywhere (like the normal distribution), it now becomes impossible for the opponent to choose A and B in a way that reduces our chance to zero. She can make that chance arbitrarily small, but it will always be positive.