The Master watched as Svetlana studied the board. He would save his brain-washing and mind tricks for later in the game. After all, he would first need to gauge whether she was worth the time. He'd met plenty of humans over the years that had seemed to have potential to begin with, then they turned out to be much less than he'd expected. Humans were fickle, and he'd never understood why the Doctor had to protect them, even love them. They were an inferior race that could only live a single lifetime. Time Lords could live for centuries. True the Time Lords were a largely extinct race now thanks to the Time War, but that wasn't the point.
This where this game of chess would prove crucial. He could see how Svetlana's mind worked. If it turned out she was crafty enough, he'd use his mental prowess to draw out her secrets, perhaps even use them to cause some trouble if they were there. After all, he was bored, and he needed some entertainment. If he could get that through causing tension between Svetlana and others, he'd do that. He wasn't positive he would see the results, but it would be all right. He'd make sure the trouble happened regardless of his being able to watch it.
He saw the move and found it to be an interesting one. It was his turn to study the board, deciding which move he should make. He would take a subtle approach, lead Svetlana into traps. He would see if she could recognize the traps before it was too late. That would tell him whether she was worth his time or not. He made his first move, an unassuming, seemingly harmless move. The trap would come in several moves yet, but the groundwork was laid.
"Do you play chess often?" He asked after making his move. It was idle chit chat. He wasn't certain how she'd respond to it, if she was a talker or not, but it would at least give them something to start a discussion on.