@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.