I'm working on designing a new card game. Instead of the traditional 52 cards of four suits consisting of 13 cards each, this deck will have 48 cards with six suits and 8 cards per suit.
I'm interested in implementing a poker-like game with this deck, similar to Texas Hold'em. For the rules, I want the order of the winning hands to be based on probability, so that the hardest to hit hands are ranked higher.
If you're familiar with Texas Hold'em, let's assume it's the same basic rules. Each player is dealt two face-down hole cards. Then the flop comes with 3 community cards, then a turn card is dealt, then a river. So there are 5 total community cards, plus 2 hole cards. Each player uses their hole cards plus the community cards to build the best possible hand.
This game will have an Ace that can function as both a 1 or a 9.
The winning hands in Poker, in order are:
Four of a kind
Three of a Kind
In our theoretical game, we could also have 5 of a kind. I'm not sure where that would fall in the rankings.
This is all possible to compute using math, right? Not requiring a computer simulation to predict?
Any insights would be greatly appreciated. Thanks!