What is the branching factor for nondeterministic games? Given a nondeterministic game how could one know the branching factor of it? Is it the number of all possible outcomes?

I have an example game in which you have some cards. The goal is to get rid of all of them. At the start of the game you get 7 random cards. There is a draw pile from which you take cards if you can't (or don't want to) play a card. You can't see the cards in that pile and they are in random order. The amount of card types in the simple version is equal to 52. If I understand correctly that means that the branching factor is at least 52 for every move plus 52 times the number of cards of the player (player's don't know other's cards). Is my thinking correct? It seems to be too big (416 at the start of the game (52 + 52*7) from the perspective of another player and 59 (52 + 7) from the player's own perspective, when Go has "only" 250) but I'm not expert in this.
The branching factor depends on exactly how you model the game.  A standard way to model games that have some randomness is to imagine adding another player (the "dealer") whose only purpose is to make a random choice. 

So if your game involves only one player Alice, we'll add another player Declan (the dealer).  Alice and Declan alternate turns.  During her turn, Alice can either play one of her cards or choose to draw from the pile.  Thus, if Alice has $n$ cards, she has $n+1$ actions she can choose from.  During Declan's turn, if Alice previously chose to draw, Declan selects one of the remaining cards and adds it to Alice's hand; otherwise he does nothing.  Thus, if there are $m$ cards remaining in the pile, Declan has either $m$ actions he can choose from, or only one.

With this model, the maximum branching factor is 53 (assuming Alice can have up to 52 cards in her hand).