Lucky Seven is a game played with seven coasters numbered one to seven. The object is to turn all seven coasters number-side up. The coasters are shuffled and dealt number-side down; the first player turns over any coaster, and leaves it in place. The exposed number on the coaster determines the position (always reading from left to right) of the next coaster to be turned over, and so on. If the player turns over a coaster that has a number denoting one already turned, he or she is out.
What are the odds of turning all coasters over and how has it been calculated?