According to experts' statistical analyses, if you're expecting 10 guests for dinner on Christmas day, 15 crackers--those festive cardboard tubes filled with a one-size-fits-no-one paper hat, a small toy, and a groan-inducing joke--should be enough to send everyone home happy. The experts came to their estimation by simulating 10,000 parties, with guest numbers ranging from 2 to 50. Their results are published in Significance .
In the traditional approach, all dinner guests sit around the table, cross arms, and pull crackers with their two immediate neighbors. In this approach, each person has a 25% chance of winning zero crackers, so there are clearly inefficiencies in the system. A better approach would be to use a system that starts by pairing up individuals and having each pair pull a single cracker. (For odd-sized groups one individual will have to stir the gravy or check the goose while this takes place.) Exactly [N/2] crackers are used in this round, with the same number of winners and losers. Those who have not yet won continue as before until only a single individual remains. That individual then pulls a cracker with themselves and we are done.
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Significance