Hello,

I would please like some help calculating probabilities for the sum of two cards drawn at random from a deck of 12 cards. Normally I would just use basic COMBIN() functions, but there's an added wrinkle: the 12-card deck is itself assembled in a specific manner that should inform the probabilities. Here's how it works:

The 12-card deck is assembled by adding 2 random cards each from six other decks: yellow, green, purple, red, blue and brown.

Five of the six colored decks (contributing 10 of the 12 cards) have the same number and distribution of card values:

Qty. Value
3 0
9 1
7 2
5 3
3 4
2 5
1 6

The brown deck (contributing 2 of the 12 cards) is a bit different:

Qty. Value
12 1
8 2
6 3

I imagine this is, in some way, a two-step process: Calculating the probabilities of what could be in the 12-card deck from the colored decks, then calculating the probabilities of what the two cards drawn at random from the 12-card deck will sum to.

I would like to keep it a two-step process, because as cards are drawn from the deck, it depletes, and I would like to be able to incorporate this knowledge into the probability calculations. For example, if I draw two cards and see that both are 6's, I would like to be able to remove those 6's from the running so that the probability for the now-10-card deck accurately reflects available knowledge. Or, if I draw two brown cards, I'd like to be able to eliminate the brown deck entirely from the calculation since, because each deck only contributes two cards, I'd know there are zero brown cards remaining.

Ideally, I would like to start by defining each of the six colored decks as a range, where each cell contains the value of a single card: 0,0,0,1,1,1,1... etc. This way, I can make changes to the six colored decks to reflect known cards. Moreover, certain circumstances can make certain colors negative, so if I do it this way, I can easily flip the sign on all the cards in a certain color's deck.

I really hope this was clear; please ask any questions if I failed to explain something well (I didn't anticipate it being this complicated when I set out to write this post)!

Thanks in advance!