Ah yes I know Lair's Dice. You could also just use the basic version.
I don't know the Common Hand version but it seems like the player has 5 private dices and no table dices.
I also don't know about the rerolling part. I could not find a kind of video online but in my head rerolling as part of the game makes it kind of broken.
The cool thing about the normal version is that it uses all dices, so also the enemy dices. So you could have 4 fours but still lose because there where 5 fours. And you have to taken into account the enemies bets for strategy. The common hand version is a bit more guessing and luck.
There are also other games that uses Lair Dice (Red Dead Redemption had it as mini game if I remember correctly).
The re implementation of the AI sounds pro messing. If you want any playtest for futur iteration, just dm me. I maybe not checking my itch every day if there is no active jam so response might take a while :D