They do converge to the same distribution. But they make different predictions about a physical die: the unbiased model predicts uniform outcomes because the die is physically symmetric, whereas the general biased model doesn’t say anything about the geometry of a physical die. So if I see uniform outcomes from a physical die, then that’s Bayesian evidence that the die is physically symmetric.
They do converge to the same distribution. But they make different predictions about a physical die: the unbiased model predicts uniform outcomes because the die is physically symmetric, whereas the general biased model doesn’t say anything about the geometry of a physical die. So if I see uniform outcomes from a physical die, then that’s Bayesian evidence that the die is physically symmetric.
See Wolf’s Dice II for more examples along these lines.