Is there a winning strategy to the game called white elephant gift swap?

Question

everybody knows there a game around xmas called white elephant.

being a math guru i was seeking a winning strategy or evena probability of winning.

Answer 1

I love white elephant gift swap, but...for all the times I've been involved I was never able to figure out how to come out on top. I did realize, not being first is a good thing. You get a c**p gift, you're stuck with it! Have fun and good luck!

Answer 2

I just learned of this game from wikipedia :)

If by winning means getting the most valued item (by all), then it seems that in general, the latter the turn, the more information you gain, and therefore have more advantage.

However, if there is a limit to the number of steals, then intuitively somewhere around the middle position seems to be best balancing the amount of information and remaining steals.

Let n be the number of items and people. Let m be the number of possible steals. Let p be the proportion of people who would steal the best gift.

P(getting the gift) = P(the gift opened by the kth person) * [P(you are the k+jth person to open a gift) * P(m-1 steal of this gift by the people before you)]

One of the many possible scenario:

The kth person opens the best gift. He considers it the best gift.

Among the next k+1 to k+j-1 persons, m-1 of them consider this gift is worthwhile to steal, and thus steal it.

You, as the k+jth person, who also think likewise that this gift is worthwhile, and choose to steal this gift.

May be running some simulations may give a better picture.

On the other hand, the idea of gift is to give, and thus, to win is to get the least valued item considered by all, then be the last person and steal the least valued among the n-1 already unwrapped gifts, and bet that the last gift is not better:

P(being the last) * P(least valued is not the last one) = 1/n * (n-1)/n.