[jason1990]

If anyone has the time and desire to work this out, I am curious what the result is.

Suppose you play poker with a deck that has 5 suits and 10 ranks in each suit. The possible hands are the ordinary poker hands plus 5 of a kind. For each possible hand, what is the probability you will be dealt that hand. (Assume you are dealt only 5 cards; that is, we're not talking about a stud or draw or holdem type structure.)

Incidentally, the particular probabilities are not what I'm curious about. I'm curious about the relative likelihood of the various hands.

Also, what about a deck with only 3 suits and 18 ranks in each suit? There is a thread on this in Poker Theory, but I'm sure we can be more mathematical about it here.

Another interesting question: what if there are 8 suits with 6 ranks in each suit? In this case, where does high card rank? Is it still the lowest ranking hand? If so, then in a holdem style game, this hand could not occur. If not, how does that affect which 5 cards out of the 7 make up your hand?

This leads to a more general question. In any kind of deck (modified or not) we can rank the hands under the assumption that we are dealt only 5 cards. Then we could rank the hands under the assumption that we are dealt 7. (For example, the probability of a flush would be the probability that, among your 7 cards, there is a 5-card combination which is flush. These probabilities, of course, would no longer add up to 1, but they would still provide a relative ranking.) For which decks do these rankings agree? (The most important one being the standard 52-card deck.) When they don't agree, does it make sense to modify the hand rankings in a holdem game? Or should they still stay the same as in a straight 5-card game?