Thanks for your responses, would have replied sooner but had problem logging back into the site.
I had profiled my code before posting and had spotted a few obvious inefficiencies, for example due to stupidity on my part I was shuffling the deck twice when performing a play through of the Monte Carlo player and still building up logging strings despite not printing them out. Now that I have knocked out the (to me) obvious the largest amount of time by far is spent in random.shuffle(). Briscola is a trick taking game (normally 2 players) where players have a hand of three cards and each round play 1 card then draw one card blind from the common deck. So correct me if I'm wrong but each play through by the Monte Carlo player requires shuffling all the unseen cards to get a new ordering of the deck. That's unavoidable correct? I'm using Python so the shuffling algorithm is linear time and efficiently executed so I can't see much speed up there.
I think I might just have too many "speed of writing code vs speed of code execution" trade-offs in my Python programming style for this task - I should maybe do this in another language to force me to think about it differently.
PRE-EDIT: Actually, writing this post has made me think critically about the code - I may have spotted another couple of gross inefficiencies. I'll let you know how it goes.