Update: I read one of the comments below and now I&#x27;m convinced by the argument. Here&#x27;s the intuition for what&#x27;s happening. (I wish the article had spelled this out sooner)<p>As long as A does not equal B with some positive probability, and as long as you choose a separator R with full support, then there is some probability that R lands between A and B. When that happens, you always win the game. Otherwise, if picking A or B randomly doesn&#x27;t hurt you, then R landing somewhere else not between A and B doesn&#x27;t hurt you either. So you&#x27;ve gotten a strategy that, once in a while, helps you separate A and B, and doesn&#x27;t hurt you otherwise.