What do you mean suit doesn't matter? In cribbage, you get 4 points if all 4 cards in your hand are the same suit. If you want to prove that no hand with a 5 isn't worth at least 2 points you HAVE to consider suits. You can easily use Re: Iterating over combinations
to generate the hands. The hard part is the scoring.
On the other hand, it is a lot easier to prove that there is a hand of 5 cards containing at least 1 five that is a total of less than 2 points.
- 4 cards (your hand) must not all be of the same suit
- Must not contain any cards with a value of 10
- Must not containing any combination (excluding the 5) whose sum is 10
- Must not contain any 2, 3, or 4 of a kind
- Must not have any sequence of greater than 2
I don't have an implementation yet, but it certainly does reduce the problem set.