Between the time you first think of a new card idea and it makes it into its final form, how many games does it end up getting tested in (ballpark of typical case)?
Well it varies hugely with how well the card is working. A card that isn't working but seems promising will get more focus on it, specific games where it's played with. Things that work right away will just show up when they show up.
Also if you are counting everybody then it varies hugely with how many external playtesters I have and how much they end up playing.
Me personally, I will play typically two nights a week, 3-5 games depending on number of players and experience level and AP level and how sloggy the games are. The number of months spent on an expansion has varied a lot; if nothing else is pressing to be worked on afterwards then plays won't trail off though accomplishing things will. For Adventures the work was mainly June-October, but we kept playing for months afterwards and tweaks were made.
And then, the number of cards in the set affects how often each card is seen. Typically 5 new cards are in each game, 5 old cards. But Adventures had Events so the math works out differently for them.
And then of course a card thought of late in the going got played a lot less than an early card that worked out. Dungeon got played a lot more than Raze, because Dungeon was early and Raze was later.
I can't do this math, man. There is the information that you could use to make a guess.
Do you have a standard set of cards that you initially test new ideas with or does it vary?
I play the new cards with the other new cards, and with all the old expansions, with whatever individual other expansion each evening.