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I have this question too. But from the perspective of the dice itself it will tend to be biased to on side of it self. So either it is biased towards the 1, 2, 3, 4, 5 or 6. So those are six bias options. I guess, I am not an expert, that this will reduce your entropy significantly. Let's say you use only one dice that tends towards the side with the number 5 more then the other sides and you throw it 256 times. I think you will throw significantly less combinations, meaning this bias will lead to guessable seeds. I don't know what will happen to your entropy if you would use 256 different dices. Does 256 biased dices lower your entropy? Probably not if they do not have the exact same bias. But maybe an expert can answer this question.
If you had 256 dice so biased that they would only ever show one side, they would still produce one seed with 256 bits of perfect entropy as long as the bias was random and not known to any potential attacker. Entropy is just unpredictably. More realistic: does it really matter if you use casino dice or board game dice? No. There is no known *general* bias in toy dice. So an attacker gains no ability to narrow their guesses unless they get your specific personal dice and roll them a over and over in a machine or something to analize the bias. And it would have to be strong bias to be much use. The moral is we are all overthinking this. What happened is not really about entropy. It is about trust. The source of entropy betrayed us. The device. Dice won't do that to you. They are too simple. Don't overthink it. Just make sure there is nothing complicated between you and the source of randomness. Complicated things involve trusting third parties. That's the part you need to worry about.