I'm glad, that I was able to bring you to another view of your problem.
In Windows-Forms you primary have one Thread, which is the UI Thread. This thread normally is redrawing the forms and controls and every action concerning that should be implemented within the OnPaint-Methods of your components. Therefore, all your actions, which are not about the UI should be seperated into an extra thread, e.g. this could be a thread you instantiate manually for the human player, and e.g. a Background-Worker thread which you could use for the AI-player.
In fact, It's up to you, how you get these things done. I think an easy and efficient way to solve your problem could be this one:
1) Subclass a Windows-Form or your Picture-Box, you probably need for implementing the custom drawing
2) Implement Event-Handlers for the Picture-Box and Event-Receivers for your class which handles a Player
3) Subclass the Player to be a human player
4) Subclass the Player to be an AI-player (and if you like, include Thread-Handling in the way of a background worker there)
I hope this brings you a little further