I am making a probability game for my Data Management class, and have a few things I am unsure about. Essentially, each player has 6 objects located in locked boxes numbered one through six. Players take turns rolling a die that produces the key to the box that corresponds to the roll. The winner is the one who is able to retrieve all their items first. My question is, if the players are able to choose where each item is placed (i.e. multiple items in some boxes, no items in some boxes) and each attempt can only recover one item max, would the chances of winning be the same? The average number of rolls to roll all numbers from 1-6 should be the same as the average number of rolls to roll any combination of 6 numbers from 1-6, right?