Update: I read one of the comments below and now I'm convinced by the argument. Here's the intuition for what's happening. (I wish the article had spelled this

Update: I read one of the comments below and now I'm convinced by the argument. Here's the intuition for what's happening. (I wish the article had spelled this out sooner) 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't hurt you, then R landing somewhere else not between A and B doesn't hurt you either. So you've gotten a strategy that, once in a while, helps you separate A and B, and doesn't hurt you otherwise.