Hi
instead of party bags, we always play this game at birthday parties.
Buy a selection of small gifts, one per child - hairslides, bags of sweets, temporary tattoos etc. The pile them up in the middle of the table and the kids take turns to thw a dice. If you get a 6, then you can take a gift. However, anyone throwing a subsequesnt 6 can either take a present from the pile or take your present. If you throw a 6 again, you have to swap what you've got with someone else. Eventually everyone ends up with a present. we usually set the timer for 15 minutes for this game and when the timer goes, you keep the present you've got. It's always worked out really well, amazingly kids don't get upset about it - not in our experience anyway. They get to take home the present instead of a party bag, and I also give a slice of cake as well.
We also play a version at Christmas with family, but with the twist to the rules in that if you throw a 6 you can just take a present from someone without having to swap, so someone can end up with three or four presents whilst someone else has none. I wouldn't suggest that version at a birthday party though!