4000.
Technically untrue.
The game stops saving at 4000. This means that if you were to buy, say, till you had 3999 cards, went back to menu, waited for save to complete, then reloaded the page, you'd get your account with that save. However, as soon as you buy card #4000, it stops saving. You can continue buying cards, playing ect, but if you are to exit before going back to 3999 or under, you won't get your progress save. Also, it's a *hell* playing with 4000+ cards in your account, since you get an error message each time the game saves (as an example, it does whenever you get back to menu).