How many chess moves without capture for a stalemate when you have a king and the other player has two queens and a king?

A "stalemate" does not depend on the number of moves. A stalemate occurs when the king no longer has a legal move or where one opponent has a king and a knight or bishop against a lone king. This is because a king and a single minor piece like the bishop or knight cannot checkmate the king. Since checkmate is impossible, the rules declare it a stalemate. On the other hand, a "draw" may be declared if after 50 moves there is no capture AND if no pawn has been moved during those 50 moves. Although a stalemate and a draw amount to the same thing in practicality, they do have different terminology.