No one can "prove" they are a winner and that includes Singer. The big difference is people like Dancer start out with a mathematically PROVEN advantage. They could still lose as no one is guaranteed to achieve the expected return of a game. OTOH, Singer starts out in negative territory and tries to claim his system will make people luckier. Of course, that is silly nonsense that no one with any intelligent would ever believe.

Here's a reasonable analogy. Dancer is like a 7' basketball player who can easily dunk a shot because he starts with a big advantage. He might miss sometimes, though. Singer is like a 5'2" chunky cook who tells everybody that he can easily dunk a basketball and they can too if they'd only fatten up by buying some of his 2000 calorie chili-cheese dogs.