The uniform distribution is in some sense the most random distribution you can choose, given that you have a finite number of cards. Formally, it's the maximum entropy distribution on a finite domain.
But what if the domain isn't finite? e.g. the entire real line? Then we can't define a uniform distribution, because the total probability can never sum to one. We can still define a maximum entropy distribution, but only by making some more assumptions. The normal distribution is the maximum entropy distribution on the real line, given a particular mean and variance.
Other examples: on the positive real line, the exponential distribution is maximum-entropy for a given mean. Poisson distribution is the equivalent on the non-negative integers.
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The uniform distribution is in some sense the most random distribution you can choose, given that you have a finite number of cards. Formally, it's the maximum entropy distribution on a finite domain.
But what if the domain isn't finite? e.g. the entire real line? Then we can't define a uniform distribution, because the total probability can never sum to one. We can still define a maximum entropy distribution, but only by making some more assumptions. The normal distribution is the maximum entropy distribution on the real line, given a particular mean and variance.
Other examples: on the positive real line, the exponential distribution is maximum-entropy for a given mean. Poisson distribution is the equivalent on the non-negative integers.