I think he is appealing to intuition here, where randomness means you can't predict the next drawn value with accuracy better than uniform. But you're right, y

I think he is appealing to intuition here, where randomness means you can't predict the next drawn value with accuracy better than uniform. But you're right, you can draw randomly according to a different distribution. However, if you allow any distribution in your definition of "random" then you get the constant distributions. It's not very intuitively random anymore. So the question becomes, how do you pick which distributions are allowed and which aren't?