To answer the game related questions, the Skills needed depend on the games.
Card games generally rely on Bluff and Sense Motive.
Dice games are more luck. Knowing the odds helps, but it doesn't change them. All that can do is keep you from walking into sucker bets, and at that point we're back to Sense Motive.
"Spin the Wheel" games are the same: Know the rules/odds enough not to fall for a sucker bet, and then luck.
Want to propose sucker bets? Back to Bluff.
Remember, today's rules for games like rhymes-with-taps, with the standard house odds are relatively recent. Older versions of the games were different, and side bets could run at any odds someone would take.
So Gambling, as a profession, would be my first, most general Skill to use. Bluff and Sense Motive might give Synergy bonuses, in a short and simple resolution. You can Rp in as much detail as you like.
Side note: "Casting lots", a term you've perhaps heard, didn't involve dice. It involved five flat sticks. You can use popsicle sticks if you like, though originally they were half-rounds with a single flat side. Just paint one side of the popsicle stick black.
"Cast" them on the table from a closed fist and count the number of black sides that come up. If there aren't any (i.e. all light sides) that counts as six. High number wins.
You could use that as a game-flavor way to resolve how much a character wins or loses on a given evening. You and the player agree on the scale (low stakes games gamble coppers, higher stakes games gamble silver or gold or whatever you like.) Apply skill modifiers to the final result. You aren't limited to five sticks, of course, if you want more granularity and wider range.