@Factotum I was thinking about trying to have a small card set example. Suppose there is no **synergy **and you have 6 cards with their **card value** equal to their number, 1, 2, ... 6. You could create a deck with 5 cards **D1**, and you could create a deck with 6 cards **D2**. So the logical way to build **D1 **is to put cards 2 through 6 in the deck, and leave out card 1 which has the lowest value.

In this hypothetical situation we start with 0 cards in our hand. Then the draw potential for each deck would be:

D1 draw potential = (2 + 3 + 4 + 5 + 6) / 5 = **4**
D2 draw potential = (1 + 2 + 3 + 4 + 5 + 6) / 6 = **3.5**

If you could generalize this to where you are comparing a deck of size n vs n+1, where the deck of n+1 has all of the exact same cards, plus one more which is guaranteed to be smaller, we want to prove something like:

**sum(n):** the sum of value in deck 1 (avg value * n)

**c:** an n + 1 card that is lower value than the lowest value in the deck

of n cards.

**prove:** draw potential for the larger deck is worse than the smaller deck.

1: sum(n) / n > (sum(n) + c) / (n + 1)
2: (n + 1) * sum(n) > (sum(n) + c) * n
3: n * sum (n) + sum(n) > n * sum(n) + c * n
4: sum(n) > c * n
5: sum(n) / n > c

Seen in this form, we can see that as long as the card **c **has a value less than the average value of the smaller deck, then it reduces the average value of the larger deck. Meaning lower draw potential.

I think this can be generalized to include synergy as well, it just makes things more complicated.

Edit: Math