5 ms·

Winning White Elephant Gift Exchanges Using Game Theory

33 points by aaronbrethorst 11y ago

schwap 11y ago
I think the model needs to be expanded to include the popular "maximum steal count" rule, that a gift can only be stolen, say, 2 times at which point it becomes "un-stealable". EDIT: d'oh, should've read the code. This is accounted for.
kitwalker12 11y ago
doesn't it kind of translate to always steal unless you don't want to steal
- bmh100 11y ago
  You have the essence of the strategy: Unless there is a limit on the number of times a gift can be stolen, always steal a gift valued above the average of all currently opened gifts. Limits on the number of times a gift can be stolen are popular, making the strategy more useful. In that case, you should open a gift if none of the available gifts are above average.
colin_mccabe 11y ago
No big surprises here... knowing the distribution of prizes helps a lot, like you might expect. I was a bit surprised that being the first player was better than being the second in their modeled game (I figured later was always better). The configuration is fiddly enough that I wonder if a slightly different configuration would remove that advantage. It would be more interesting if someone could come up with a "fairer" version.
pasbesoin 11y ago
> Of course, as with any gift exchange, the real goal is to win. And that's where these things lose me. Turning a community event into a competitive event. And yet, in many places, if you don't participate, you are viewed as shunning the community.
- ufo 11y ago
  Sounds like you skipped the footnotes.
  - pasbesoin 11y ago
    I saw the footnotes, although admittedly quickly. I see I'm downvoted, but I was serious in my comment. In the scenario described, as well as in a significant fraction of other "social" behavior including in work settings, I encounter a lot of competition. And I am one for whom such competition simply is not fun. I guess if I consider it a bit more, a lot of it seems to be centered around attitudes of "zero sum gain"; someone must "win", and correspondingly others much "lose". By contrast, I am... oh, I forget the corresponding terminology, but I prefer social gatherings that are a "net gain." Another area where I find this: Sports. For sports with teams and/or competition, you need more than one participant in order to have the game. Yet instead of enjoying the game and thanking them for their participation, too often there seems to be an excessive amount of focus on "winning" and on "ragging on" or criticizing (actually, verbally abusing) the losers. I enjoy participating and it is thrilling to win. But I do NOT enjoy "ragging on" nor berating the loser. I guess I'm taking this secret santa thread/response too far. But I've observed that I'm not the only one. There is a greater than miniscule fraction of the population who does not enjoy such things, nor a lot of sports, because during this event meant to strengthen social cohesion, once again they find the group picking winners and losers. And some of them aren't very nice towards the losers -- even when they cloak this behavior in a facade of "good cheer."
    - moftz 11y ago
      Why bother doing anything in life if you can't give yourself a challenge every now and then? White elephant exchanges aren't exactly a win-lose type of game. You are only winning in your mind if you can nab the non-crappiest gift. Everyone gets a prize, some are nice, some are lame. But the whole point is to have fun and enjoy the experience of it. In reality, it is a net gain. Everyone brings something and everyone comes home with something. There is no loss of gross dollar amount however you might come home with a crap gift when you brought a nice one. The net gain comes from the fun and enjoyment people have in playing these dumb games. Its not really a test of skill, its mostly luck. You can sometimes game the system like in the article but if you open up a real piece of crap, then you're stuck with it. That part isn't as fun but you should be able to laugh at your own misfortune. My extended family does one of these games every year. Sometimes there are nice things in there like giftcards and booze, sometimes its one of the old knickknacks thats been passed around for years (like this gaudy ceramic high-heel shoe). If you get crap, you just regift it next year and laugh at the person that ends up with it next. Everyone does it and everyone should know what to expect. If you can't contain your emotions for getting "ragged on" for ending up with the crap gift, then you really need to grow up.
tunesmith 11y ago
I'd just be tempted to steal the least valuable gift to make it less stressful for myself and more valuable for everyone else.
JustSomeNobody 11y ago
I win by not playing.
- ibmthrowaway218 11y ago
  ITYM: A STRANGE GAME. THE ONLY WINNING MOVE IS NOT TO PLAY.
rtkwe 11y ago
This doesn't seem to cover the rule I've always played with where the first person to pick gets to swap at the end of the game with anyone. Is that not a common rule? Under that 1 is the best (can always get whatever gift they want) but they usually get stuck with a mediocre present until the very end.
- strictnein 11y ago
  That's Footnote #3 in the article: > "There are lots of variations on these rules, such as capping the number of times a gift can be stolen or letting the person who went first take another turn at the end."
  - rtkwe 11y ago
    Ah serves me right for skipping them. Wonder how those variations are spread out. Do they cluster geographically or is it more localized to families?
Zikes 11y ago
I recently read a theory that the origin of the name "white elephant" is due to an Asian ruler gifting albino elephants to people he did not like, as they were very high maintenance and would become a financial burden.
- freshyill 11y ago
  A delicious white elephant is never a financial burden.
- at-fates-hands 11y ago
  Sounds about right considering the Wiki page states something similar: The term white elephant refers to a gift whose maintenance costs exceed its usefulness. While the first use of this term remains a matter of contention among historians https://en.wikipedia.org/wiki/White_elephant_gift_exchange https://en.wikipedia.org/wiki/White_elephant_gift_exchange
murbard2 11y ago
The rules, as stated, make the game particularly uninteresting. I would suggest instead doing some type of Colonel Blotto game. For instance: Give each player 1000 points^. Points can be used to secretly bid on gifts and/or on players. When the bids are revealed, each gift is temporarily assigned to the highest bidder, but then, immediately re-assigned to the highest bidder on that player. So if you want to get a specific gift, not only should you bid on that gift, but you should also bid on yourself to avoid the gift being reassigned. Or you could put a high bid on someone you think will snatch that gift. ^ or a suitably large number to avoid issues of divisibility.
- strictnein 11y ago
  It can be interesting because you've typically spent the previous couple of hours drinking.
  - murbard2 11y ago
    Not if you're in the company of people who like intractable game theory problems.
    - TallGuyShort 11y ago
      * you're. Oh... Oh I see your point.
      - murbard2 11y ago
        (thanks, fixed)
gragas 11y ago
This seems really trivial. There always has to be at least one gift that is of average value or greater. Also, there probably aren't a large number of gifts in white elephant gift exchanges, so it's not so safe to generalize the average value of the opened gifts to the entire population. I was really hoping for a more rigorous proof and a more non-intuitive strategy.
- wrsh07 11y ago
  Agree that a more rigorous proof / non-intuitive strategy would be welcome, but all gifts could be of equal value. [eg if you go second]
- Vraxx 11y ago
  Seriously.. They tried to complicate it by bringing expected value, which isn't terribly complicated even still, but the whole strategy can be summed up with the following. Do you like any of the gifts here more than than the "average" gift, if so, steal. Is this really news? I appreciated the sentiment of this post, but not the content.
helipad 11y ago
My wife took part in one of these. She chose to "steal" a gift, whereby the owner said "no", quickly realizing the participant was serious. And that, folks, is where grudges come from.

I think the model needs to be expanded to include the popular "maximum steal count" rule, that a gift can only be stolen, say, 2 times at which point it becomes "un-stealable". EDIT: d'oh, should've read the code. This is accounted for.

kitwalker12 11y ago

doesn't it kind of translate to always steal unless you don't want to steal

bmh100 11y ago
You have the essence of the strategy: Unless there is a limit on the number of times a gift can be stolen, always steal a gift valued above the average of all currently opened gifts. Limits on the number of times a gift can be stolen are popular, making the strategy more useful. In that case, you should open a gift if none of the available gifts are above average.

colin_mccabe 11y ago

No big surprises here... knowing the distribution of prizes helps a lot, like you might expect. I was a bit surprised that being the first player was better than being the second in their modeled game (I figured later was always better). The configuration is fiddly enough that I wonder if a slightly different configuration would remove that advantage. It would be more interesting if someone could come up with a "fairer" version.

pasbesoin 11y ago

> Of course, as with any gift exchange, the real goal is to win. And that's where these things lose me. Turning a community event into a competitive event. And yet, in many places, if you don't participate, you are viewed as shunning the community.

ufo 11y ago
Sounds like you skipped the footnotes.
- pasbesoin 11y ago
  I saw the footnotes, although admittedly quickly. I see I'm downvoted, but I was serious in my comment. In the scenario described, as well as in a significant fraction of other "social" behavior including in work settings, I encounter a lot of competition. And I am one for whom such competition simply is not fun. I guess if I consider it a bit more, a lot of it seems to be centered around attitudes of "zero sum gain"; someone must "win", and correspondingly others much "lose". By contrast, I am... oh, I forget the corresponding terminology, but I prefer social gatherings that are a "net gain." Another area where I find this: Sports. For sports with teams and/or competition, you need more than one participant in order to have the game. Yet instead of enjoying the game and thanking them for their participation, too often there seems to be an excessive amount of focus on "winning" and on "ragging on" or criticizing (actually, verbally abusing) the losers. I enjoy participating and it is thrilling to win. But I do NOT enjoy "ragging on" nor berating the loser. I guess I'm taking this secret santa thread/response too far. But I've observed that I'm not the only one. There is a greater than miniscule fraction of the population who does not enjoy such things, nor a lot of sports, because during this event meant to strengthen social cohesion, once again they find the group picking winners and losers. And some of them aren't very nice towards the losers -- even when they cloak this behavior in a facade of "good cheer."
  - moftz 11y ago
    Why bother doing anything in life if you can't give yourself a challenge every now and then? White elephant exchanges aren't exactly a win-lose type of game. You are only winning in your mind if you can nab the non-crappiest gift. Everyone gets a prize, some are nice, some are lame. But the whole point is to have fun and enjoy the experience of it. In reality, it is a net gain. Everyone brings something and everyone comes home with something. There is no loss of gross dollar amount however you might come home with a crap gift when you brought a nice one. The net gain comes from the fun and enjoyment people have in playing these dumb games. Its not really a test of skill, its mostly luck. You can sometimes game the system like in the article but if you open up a real piece of crap, then you're stuck with it. That part isn't as fun but you should be able to laugh at your own misfortune. My extended family does one of these games every year. Sometimes there are nice things in there like giftcards and booze, sometimes its one of the old knickknacks thats been passed around for years (like this gaudy ceramic high-heel shoe). If you get crap, you just regift it next year and laugh at the person that ends up with it next. Everyone does it and everyone should know what to expect. If you can't contain your emotions for getting "ragged on" for ending up with the crap gift, then you really need to grow up.

tunesmith 11y ago

I'd just be tempted to steal the least valuable gift to make it less stressful for myself and more valuable for everyone else.

JustSomeNobody 11y ago

I win by not playing.

ibmthrowaway218 11y ago
ITYM: A STRANGE GAME. THE ONLY WINNING MOVE IS NOT TO PLAY.

rtkwe 11y ago

This doesn't seem to cover the rule I've always played with where the first person to pick gets to swap at the end of the game with anyone. Is that not a common rule? Under that 1 is the best (can always get whatever gift they want) but they usually get stuck with a mediocre present until the very end.

strictnein 11y ago
That's Footnote #3 in the article: > "There are lots of variations on these rules, such as capping the number of times a gift can be stolen or letting the person who went first take another turn at the end."
- rtkwe 11y ago
  Ah serves me right for skipping them. Wonder how those variations are spread out. Do they cluster geographically or is it more localized to families?

Zikes 11y ago

I recently read a theory that the origin of the name "white elephant" is due to an Asian ruler gifting albino elephants to people he did not like, as they were very high maintenance and would become a financial burden.

freshyill 11y ago
A delicious white elephant is never a financial burden.
at-fates-hands 11y ago
Sounds about right considering the Wiki page states something similar: The term white elephant refers to a gift whose maintenance costs exceed its usefulness. While the first use of this term remains a matter of contention among historians https://en.wikipedia.org/wiki/White_elephant_gift_exchange https://en.wikipedia.org/wiki/White_elephant_gift_exchange

murbard2 11y ago

The rules, as stated, make the game particularly uninteresting. I would suggest instead doing some type of Colonel Blotto game. For instance: Give each player 1000 points^. Points can be used to secretly bid on gifts and/or on players. When the bids are revealed, each gift is temporarily assigned to the highest bidder, but then, immediately re-assigned to the highest bidder on that player. So if you want to get a specific gift, not only should you bid on that gift, but you should also bid on yourself to avoid the gift being reassigned. Or you could put a high bid on someone you think will snatch that gift. ^ or a suitably large number to avoid issues of divisibility.

strictnein 11y ago
It can be interesting because you've typically spent the previous couple of hours drinking.
- murbard2 11y ago
  Not if you're in the company of people who like intractable game theory problems.
  - TallGuyShort 11y ago
    * you're. Oh... Oh I see your point.
    - murbard2 11y ago
      (thanks, fixed)

gragas 11y ago

This seems really trivial. There always has to be at least one gift that is of average value or greater. Also, there probably aren't a large number of gifts in white elephant gift exchanges, so it's not so safe to generalize the average value of the opened gifts to the entire population. I was really hoping for a more rigorous proof and a more non-intuitive strategy.

wrsh07 11y ago
Agree that a more rigorous proof / non-intuitive strategy would be welcome, but all gifts could be of equal value. [eg if you go second]
Vraxx 11y ago
Seriously.. They tried to complicate it by bringing expected value, which isn't terribly complicated even still, but the whole strategy can be summed up with the following. Do you like any of the gifts here more than than the "average" gift, if so, steal. Is this really news? I appreciated the sentiment of this post, but not the content.

helipad 11y ago

My wife took part in one of these. She chose to "steal" a gift, whereby the owner said "no", quickly realizing the participant was serious. And that, folks, is where grudges come from.