"you have three turns to run" without a context seems unnatural. Could it possible mean "You have 3 turns left" (You have 3 turns until its my turn) ?
It's "an opportunity or obligation to do something that comes successively to each of a number of people" (From oxforddictionaries.com: http://www.oxforddictionaries.com/definition/english/turn)
This is helpful. Here is how I would describe the situations for use of the word. “Opportunity” or “chance” as in “It is your/my/her/his turn” in a game or sport. “Obligation” as in “It is your/my/her/his turn” for family chores, work tasks, military orders. BTW, for years, I have used Oxford dictionaries as a source for not only definitions but also for usage and history of usage.