I’ve even heard people use “die” as both the singular and plural! It’s the only singular/plural pair I know of where 3 of the 4 permutations show up in common parlance. I’ll be thrilled if I ever hear someone use dice as sing. and die as pl.

Some constructs in English can indeed feel a bit dicey.

Mouse, mice therefore singular of dice is douse!

From the OED: "As in pence, the plural s retains its original breath sound, probably because these words were not felt as ordinary plurals, but as collective words".

Here is another interesting article about the etymology and singular/plural usage: https://www.grammarphobia.com/blog/2016/10/dice.html