Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Simple Set Game Proof Stuns Mathematicians

quantamagazine.org

Post reply on HN
Print view View original

71–80 of 86 posts

Re: Simple Set Game Proof Stuns Mathematicians

#71

Post by lmm »

tamana wrote: post #61
Nadya wrote: post #33

Earlier quoted context omitted.

If you want to lose friends and be disowned from your family - learn to play Monopoly by the actual rules and follow this strategy: http://imgur.com/a/vX3zm I can confirm that it works and nobody wants to play Monopoly anymore. Instead we play more fun board games

This strategy works when one person plays by the complicated rules and everyone else plays for fun. When you go pull out some BGG game, you'll have the same problem: the board game geek rules lawyer playing strategy and trouncing players who play for fun.

In any competitive game the majority of players will be losing. So a good game is one that's fun even when you're losing.

Re: Simple Set Game Proof Stuns Mathematicians

#72

Post by dkurth »

zem wrote: post #35
henrik_w wrote: post #12

Nice to read about mathematics that involves Set! I found out about Set here on Hacker News several years ago, when I read Peter Norvig's blog post on the odds of not finding a set in the 12 cards [1]. I had never heard about the game before, but tried it and really liked it. The simplicity of the rules, the mathematical nature of it, and the fact that adults and kinds can play together makes it such a great game. I…

the similar but easier game "spot it!" works better for playing with kids, i find. (i prefer it as an adult too - i thought i'd love set, but playing it feels more like work than fun to me.)

There's some interesting analysis of the math behind Spot It! on stackoverflow [1].

That post mentions the Fano Plane, which, incidentally, I first read about in the book How Not to Be Wrong by Jordan Ellenberg, a mathematician quoted in the article about Set that started this thread. In the book, he uses the Fano Plane to explain how to pick numbers for a specific kind of lottery.

[1] http://stackoverflow.com/questions/6240113/what-are-the-math...

Re: Simple Set Game Proof Stuns Mathematicians

#73

Post by lowtolerance »

dhekir wrote: post #9
pnut wrote: post #2

I did really well in school, and am a professional developer now, and my wife utterly destroys me at this game. She can find sets in real time as the cards are being dealt, while singing along with music, it's maddening.

Could it be somehow related to better peripheral vision? I met a woman once who could gather four-leaf clovers nearly instantly, at the same spot where me and my male friends had spent minutes searching. I've seen written in some places (but could not find a worthy source) that women might have better peripheral vision due to food gathering in prehistoric times, but this might just be some old sexist construct (if an…

My mother is like this with four-leaf clovers. We can be walking together and having a conversation, and she'll stop mid-stride and pick up a four-leaf clover that any normal person would have had to stop and hunt for. I definitely did not inherit this skill - I can't recall ever having found one.

Re: Simple Set Game Proof Stuns Mathematicians

#74

Post by function_seven »

tamana wrote: post #60
function_seven wrote: post #50

Earlier quoted context omitted.

I like how you introduce a correlating attribute in the beginning of your comment, get me thinking about the relationship between musical ability and set-identifying ability, then clobber whatever hypothesis I was putting together just as fast with the confounding "field trips" variable. Nice work :)

But why is set so popular on band trips, but not football trips?

I'd guess that the players on a football team would be reviewing the playbook all the way up until kickoff. Meanwhile the band isn't going to be practicing their performance on the bus.

Re: Simple Set Game Proof Stuns Mathematicians

#75

Post by Nadya »

tamana wrote: post #61
Nadya wrote: post #33

Earlier quoted context omitted.

If you want to lose friends and be disowned from your family - learn to play Monopoly by the actual rules and follow this strategy: http://imgur.com/a/vX3zm I can confirm that it works and nobody wants to play Monopoly anymore. Instead we play more fun board games

This strategy works when one person plays by the complicated rules and everyone else plays for fun. When you go pull out some BGG game, you'll have the same problem: the board game geek rules lawyer playing strategy and trouncing players who play for fun.

To be fair - Monopoly is a partially luck-based strategy game. And while having fun is certainly a big part of board games - so is winning and winning is pretty fun for most people.

I see it as a split between "casuals" and "competitive" players. Competitive players find fun in attempting to win or giving it their best shot while casual players see winning as a bonus and just want to have fun. Which may or may not involve playing with the best strategies or giving it their best.

I also agree entirely with lmm. The best games are games that are fun even when losing. If you can't have fun while losing (eg: Monopoly) then I don't consider it a good game.

Re: Simple Set Game Proof Stuns Mathematicians

#76

Post by xom »

dhekir wrote: post #9
pnut wrote: post #2

I did really well in school, and am a professional developer now, and my wife utterly destroys me at this game. She can find sets in real time as the cards are being dealt, while singing along with music, it's maddening.

Could it be somehow related to better peripheral vision? I met a woman once who could gather four-leaf clovers nearly instantly, at the same spot where me and my male friends had spent minutes searching. I've seen written in some places (but could not find a worthy source) that women might have better peripheral vision due to food gathering in prehistoric times, but this might just be some old sexist construct (if an…

quoting https://news.ycombinator.com/item?id=10954918 :

> Go players activate the brain region of vision, and literally think by seeing the board state. A lot of Go study is seeing patterns and shapes... 4-point bend is life, or Ko in the corner, Crane Nest, Tiger Mouth, the Ladder... etc. etc.

> Go has probably been so hard for computers to "solve" not because Go is "harder" than Chess (it is... but I don't think that's the primary reason), but instead because humans brains are innately wired to be better at Go than at Chess. The vision-area of the human's brain is very large, and "hacking" the vision center of the brain to make it think about Go is very effective.

Re: Simple Set Game Proof Stuns Mathematicians

#77

Post by mundo »

function_seven wrote: post #50
mundo wrote: post #39

Earlier quoted context omitted.

Funny anecdata: in my circle of friends, the trait that best predicts Set skill isn't IQ or gender or anything like that, it's musical ability. This came up at a party. Six people playing Set, all of us from different cities, and the three that took band in high school utterly dominated the three that didn't. The reason? Field trips. The Band kids had all played Set for hours on buses, the rest of us had only played…

I like how you introduce a correlating attribute in the beginning of your comment, get me thinking about the relationship between musical ability and set-identifying ability, then clobber whatever hypothesis I was putting together just as fast with the confounding "field trips" variable. Nice work :)

Thank you! I should be writing clickbait headlines.

"Will this STUNNING mathematical breakthrough in a children's card game finally make Kim leave Kanye?"

Re: Simple Set Game Proof Stuns Mathematicians

#78

Post by btilly »

kragen wrote: post #69
Natanael_L wrote: post #66

Earlier quoted context omitted.

Prime numbers used to be useless when first researched (edit: during the previous two centuries, when their properties was studied). We don't always know in advance what will turn up useful.

You say, "Prime numbers used to be useless when first researched," but when the Middle-Kingdom Egyptians were doing their initial research on prime numbers, they needed them for the algorithms they used to calculate with fractions. These were used in the Rhind Papyrus to calculate things like the volumes of granaries. You could hardly have picked a worse example.

No, he picked a famous and perfect example. He just didn't specify it well enough.

Over the last 2 centuries, number theorists developed the theory of large prime numbers. The numbers that they were dealing with were so large that they had no conceivable use in describing the physical universe.

Famously one prominent number theorist, G. H. Hardy, wrote A Mathematician's Apology, a book describing and justifying his life. In it he famously described his field as being utterly useless with no practical applications.

Then cryptography came along, and the mathematics of finding large prime numbers, and factoring hard to factor large numbers, turned out to have practical applications of great importance!

Re: Simple Set Game Proof Stuns Mathematicians

#79

Post by zem »

dkurth wrote: post #72
zem wrote: post #35

Earlier quoted context omitted.

the similar but easier game "spot it!" works better for playing with kids, i find. (i prefer it as an adult too - i thought i'd love set, but playing it feels more like work than fun to me.)

There's some interesting analysis of the math behind Spot It! on stackoverflow [1]. That post mentions the Fano Plane, which, incidentally, I first read about in the book How Not to Be Wrong by Jordan Ellenberg, a mathematician quoted in the article about Set that started this thread. In the book, he uses the Fano Plane to explain how to pick numbers for a specific kind of lottery. [1] http://stackoverflow.com/questi…

thanks, that was a beautiful thread! also a really good diagram explaining the projective plane.

Re: Simple Set Game Proof Stuns Mathematicians

#80

Post by kragen »

btilly wrote: post #78
kragen wrote: post #69

Earlier quoted context omitted.

You say, "Prime numbers used to be useless when first researched," but when the Middle-Kingdom Egyptians were doing their initial research on prime numbers, they needed them for the algorithms they used to calculate with fractions. These were used in the Rhind Papyrus to calculate things like the volumes of granaries. You could hardly have picked a worse example.

No, he picked a famous and perfect example. He just didn't specify it well enough. Over the last 2 centuries, number theorists developed the theory of large prime numbers. The numbers that they were dealing with were so large that they had no conceivable use in describing the physical universe. Famously one prominent number theorist, G. H. Hardy, wrote A Mathematician's Apology , a book describing and justifying his…

Please don't blame me for refuting what he did say, instead of what he would have said if he'd known what he was talking about.
Post reply on HN