No, in Deadlands the Marshal has one deck for NPC and enemy actions, and the party has one deck for their actions. The only time a player has his/her own deck is when he/she is playing a huckster or mad scientist. But, that's not my question. I was a little unclear.
In the combat, to determine turn order, a player would roll a quickness check and gain up to have five cards. Each one of those cards would be her actions, with turn order starting at aces and ending at 2s. So, she may have a king of hearts and a 4 of diamonds, while another player has a 6 of spades, meaning his action happens between the other player's two actions.
This can make combat go very slowly on PBP. Whereas in games like D&D 3.5, combat would take a while since every player had to post their three actions on each of their turns with regards to the initiative order, in deadlands, every player has a varying number of actions per round that are all spread out around each other, meaning anytime you say "I attack the bandit", there could be three other players who have a hire card than you who also say "I attack the bandit" and kill him before your turn happens.