Bad example. I can predict the dice game's problem space. E.g. for a single normal die (1-6), I can predict that I'll never observe a 7 [P(7) = 0%]. I can also

Bad example. I can predict the dice game's problem space. E.g. for a single normal die (1-6), I can predict that I'll never observe a 7 [P(7) = 0%]. I can also predict the probability distribution. E.g. for two dice thrown together, the probability of throwing a sum of 7 is 1/6, whereas the probability of throwing snake eyes is only 1/36. Yes, the game's output is random. But what you're talking about is control, not prediction. If random meant "impossible to make predictions about", then statistics wouldn't exist. Regarding winning, there's no way to improve one's chances (besides cheating?). But merely knowing that the game is predicated solely on chance can be useful for other applications. E.g. realizing that the lottery is a scam. Personally, I'm in that camp that says reasoning is a instrumental value towards prediction.