Now that alpha is complete, I've done a few bits of analysis.

Gold Drop Rate

First up, we have the gold drop rate:

Rare golds are the rarest apparently, but mostly hanging out around the 1.8-1.9% drop rate compared to their regular peers.

Regular Max Level Cards

Here we have the number of potential maximum cards by rarity. So for regular commons, there can be 130 max level cards (bound by the minimum value in the cohort) out there if nobody else has any.

Gold Max Level Cards

Here we have the number of potential maximum cards by rarity. So for gold legendaries, the limit is 6 max level gold legendaries.

Meta

On both the regular and gold max level limits these are limits from combining. Once battles start and cards can gain XP, this number will go up.... very slowly.

Right now the rarest cards in terms of potential max levels in existence are the Flesh Golem, Giant Roc, Pirate Captain, Silvershield Knight, and Skeleton Assassin all coming in at 130.

On the gold side Lightning Dragon is the rarest card in max level combination terms.