I stand by not needing a programmed mini-game for things of this nature. The simpler solution, and one I feel is more in line with SoT in general, would be to give us all a new item on our Radial - Dice (a pair of them).
Every Pirate has them, and they would have a design similar to other Tools. Idle would be holding the Dice and cupping them a little in hand so that only your Pirate can easily see the results. Primary Action would be to close and shake your hand (producing a RNG result for the Dice). Secondary Action would be extending your hand to show results to other Pirates near you. They could have all sorts of skins for them like other Tools.
These could then be used to make any games we like for the most part honestly, people can get creative with it. You could still make bets by just staking Loot on the game you cook up with other Crews. People could Cheat at games being played by just attacking during the game (and trying to steal) or trying to sneak in a quick unnoticed reroll. You could also use them for things other than games. Random number generation, high low results, etc. which would facilitate other interesting uses (tools not rules). You wouldn't be confined to using them in only a specific area so they would be no more distractions than our Instruments or Tankard now really. You wouldn't have programmed gambling involved, which means not having to be concerned about how that might impact the games rating in various regions.
To me, this is the more elegant solution to people desiring games.