This game requires a bit of prep but is well worth the effort.
Put a small prize (such as a $10 bill) in a small box, tape it well, and gift wrap it. Put the box in a bigger box, wrap that box and put it in another, and so on, wrapping it as many times as you have the boxes and the patience for.
With everyone sitting in a circle, the youngest chooses a number from 1 through 6 and rolls a die, then passes the die to the next player.
The first person to roll the chosen number puts on two oven mitts and tears into the present. The other players continue rolling the die. The next player who rolls the chosen number grabs the mitts and takes over the unwrapping. The person who unwraps the actual box with the prize gets to keep it.