Hacker Newsnew | past | comments | ask | show | jobs | submitlogin
Chess World Championship: Stockfish live-analyzing game 7 (sesse.net)
119 points by tosh on Nov 18, 2018 | hide | past | favorite | 115 comments


Magnus Carlsen with a rating of 2835 is playing against Fabiano Caruana with a rating of 2832.

This is their 7th game. They tied for all the previous 6.


They're called draws. The match will be tied if it's 6-6 after 12 games, then they'll go to tiebreaks - 4 rapid games, then if still no winner, up to 5 mini-matches of 2 blitz games, then ultimately an Armageddon game if needed.

https://en.wikipedia.org/wiki/World_Chess_Championship_2018#...


In the highest form of chess, perhaps all games will be a draw. I wonder if someday we have to modify the rules or use a different variant that prevent draws, like Shogi for example.


Sure, maybe one day. People were speculating on the coming 'draw death' of chess 100 years ago,[1] but it hasn't really been a problem so far. What was a problem, was players agreeing to an early draw without playing the game out (Imagine, say, tennis players 'agreeing to a draw' after 10 minutes) A lot of tournaments nowadays have rules prohibiting draw offers before move 30, or draw offers at all.[0] The best players are just much better at defending than people were 100 years ago, and they're very good at bailing out to a draw when in inferior positions. Also, computers have taught humans a lot about defensive possibilities, which are larger than people had thought.

The situation in matches is different to that in tournaments, where it's no good drawing all your games if you want to win the tournament. In this match, drawing every game, then drawing all the tiebreak grames, then getting black in the Armageddon game and drawing, will make you world champion. And historically, if a world championship match was tied, the champion automatically retained their title. (Tiebreaks are a recent development)

[0] https://en.wikipedia.org/wiki/Draw_by_agreement#Steps_taken_...

[1] e.g. Here's Capablanca (world champion 1921-7) writing at length about it in 1925 http://www.chesshistory.com/winter/extra/capablanca7.html

He created a version of chess with 2 new superpowered pieces to avoid the 'draw death' problem https://en.wikipedia.org/wiki/Capablanca_Chess (that page mentions some other similar variants)


Wow I can’t believe these guys are now the guys playing for the world championship. I remember playing Fabiano in the local chess park when he was like 14 :)

They’ve come a long way indeed!


Did you win any game?


Caruana was a GM at 14. Unless EGreg is a very strong player, I don't think he was able to beat Caruana.


EGreg said it was when Caruana was "like 14" suggesting he isn't sure of the age. If the park was in the US, Caruana was probably actually 12, because that was when he moved from the US to Europe.

At 12, he was "only" around 2150 FIDE.


I happen to be pretty strong :)


National ELO of 1896, in case anyone else is curiy. https://chess-db.com/public/pinfo.jsp?id=3012853574


The curious thing is that Carlsen’s ELO didnt’t get nibbled even after all theese consequent draws. They’re too close.


That's because ELO only gets updated at the end of a tournament, not every game.


At https://2700chess.com/ you can see the live rating with the effect of each game since the last periodic FIDE update. Expanding either Carlsen's or Caruana's rows will show you a list of the seven games since the last update, with a change of 0.0 next to each.


FIDE also calculates a game-by-game "live" rating. It's not normally published but it is used for some title requirements.

For example the requirements for the most common way to earn the GM title include a requirement that your rating has reached 2500. The live rating is used for that.


That's interesting. Do you have a source for that?

I always believed it is because either FIDE ratings are only updated once a month (see 7.1[1]) or because their ELO is too close, therefore the prob. of winning is 0.5 for both anyways.

[1] http://www.fide.com/component/handbook/?id=172&view=article


That's not true about Elo being updated particularly at the end of tournaments - either official/FIDE ratings or live ratings.

I heard (possibly from the Chess24 commentators) that if their difference in rating was 4 or more, each draw would bring them closer together in live rating - Magnus would lose rating with each draw; but as it's 3, their ratings don't change. i.e. anacleto was right, thomasahle wrong.

Also, Elo isn't an acronym (ELO) as one might think - it's named after its inventor Arpad Elo. https://en.wikipedia.org/wiki/Elo_rating_system

Interestingly, when I first looked at this page, most of the good/correct comments were voted down, most of the bad ones not, it was weird. (It made me suspect that other HN pages are like that but I don't know it! - I know chess better than most subjects discussed on here) But that has now almost totally been corrected.


Could it just be that the most recent comments were listed first? I think HN does that to give them a chance to get read and voted on.


7 ties now!


Watching the game live with this open in another tab is cool. On Friday, it showed that Caruana had a winning position with a mate in around 30 moves. It was so non-intuitive that no chess player would have ever found it. But it is cool to see that the game "could have been" won.


True – yet extremely hard to find especially in a fortress situation end game when you can’t afford to wait cognitive brain to calculate new variations after each single move.


And also, Caruana would have had to trap his knight in a corner to get the win. To quote Kasparov:

The computer shows Black wins with 68..Bh4 here. But had Caruana played the incredible 69.Bd5 Ne2 70.Bf3 Ng1!! they would request metal detectors immediately! No human can willingly trap his own knight like that.

https://twitter.com/Kasparov63/status/1063576827850096640


Personally, I’m not convinced that the win was beyond the ability of any human to find. Previous generations of players spent much more time studying the endgame (as opposed to endless openening preparation), and I can see Fischer or Capa, or maybe Botvinnik, finding it over the board.


Live analysis for people: https://youtu.be/Je_2zaLr5gU


Grischuk makes those amazing draws bearable. Svidler and him make a surprisingly funny and informative team.


Am I understanding correctly that the score of 0 at the top means that the chess engine thinks their positions are exactly equally good?


When it's close to 0, it means the engine thinks the position is equal. But usually when it's exactly 0, the machine thinks the best move to play next must lead to a draw. As, in the next best move will lead to a worse position for the player making the move.


Huh, never thought of it that way but that makes sense


Exactly 0.00 can also mean that the engine has no idea what's going on.


Err...sorry no. At least not for Stockfish (maybe for AlphaZero or LeelaZero).

0 means that the position is exactly equal (material + positional)

The engine always has an idea of what's going on through simple material calculation + positional heuristics (although it maybe be flawed)


Yes


Chess aficionados know this, but for casual readers ...

Back in 1972, during the Cold War, we had the chess "Match of the Century". In one corner the USA, in the other the Soviet Union. Bobby Fischer soundly defeated Boris Spassky.

All before the Internet and before computers analyzing chess. So the local PBS station in NYC had chess master Shelby Lyman analyzing moves, for hours and hours, as they came in from Iceland. Perhaps 5 or 10 minutes between moves.

It kept me amused one summer during high school.

https://en.wikipedia.org/wiki/World_Chess_Championship_1972


Dumb chess question from a person that's never competed, why are international chess rankings divided by Male or Female? There are even olympic sports now that are mixed-gender such as Curling.


Chess is mixed sex. I'm guessing you're looking at the FIDE URLs like https://ratings.fide.com/top.phtml?list=men as provided on the FIDE (international governing body for chess) page here [1]. That URL seems to clearly specify men in spite of being linked to as "Top 100 Players", but the list includes both sexes. You'll find Hou Yifan on that list in place 91. The next highest rated female is Ju Wenjun who is 350th.

The reason for being able to see lists by the other classifications is because it's the same way that tournaments are frequently divided. Beyond having rating sections in tournaments there are generally also events that are only open to people below a certain age (or seniors events for players above a minimum age), or only to females. Females are also granted certain female only titles. For instance Hou Yifan holds the title of Grandmaster as well as the title of Female Grandmaster. The latter having substantially easier requirements.

To be clear, these divisions are all completely undirectional. Females, young, and old players can compete in any event and be rated against any player. Hou Yifan is regularly invited to top level events. For instance this year she was invited and competed in both Tata Steel and the Granke Classic closed events, competing against players including Magnus Carlsen and Fabiano Caruana. She scored a total of 0 wins, 10 losses, and 12 draws.

[1] - https://ratings.fide.com/toplist.phtml


There aren't different ratings, but there are women-only tournaments, championships, and so on. The reason is just that there are a lot fewer women in elite chess than men.

For example, Hou Yifan, the #1 woman in the world in terms of rating, is 91st overall.


How is chess allowed to make a move like this in 2018? Imagine if facebook in response to complaints about not enough female representation responded by creating female only teams?

They really should get rid of these archaic female only leagues.


You are correct, I think; chess does not need to be segregated by gender. It also does not need to be segregated by skin colours, religions, or how many letters in your name.

Rather, to have the segregation by blitz or full time controls, but some players can be in both if they want to do.


If people don't like that tournament, then they should feel free to not compete in it. That's their choice. Don't like it? Then ignore it.


That is true, yes. But still I think that tournament is unnecessary. They can have such tournament if they want to do (since, nothing stops you from also having other tournaments too, which can include everyone), but I would not advise it.



There's no "men's" competition in chess. In tournaments, you see men, women, children, blind and other chess players battling each other. Moreover, some women (Judith Polgar who was top 10 for a long time, is the best known example) refuse to compete in woman-only events. However the main reason why there is a separate competition for women, children, blind, ... is that there is a market for it.


Almost all tournaments are mixed. I have never played a men's only tournament in my life and I have played fair bit of them in my chess career life.


[flagged]


Women aren't naturally less interested in or good at chess. There must be some other explanation for the top 90 chess players all being male.


What evidence is there that this is true?


There exist women who are good at and interested in chess.


There are also women who are two meters tall, but that doesn't mean that women are naturally just as tall as men.


I suppose then that you're imagining they got that tall by unnatural means?


You're talking past each other because you're using different definitions. I'd propose one of these definitions:

- "Women on average are less good / equal to / better at chess than men on average"

- "The best women at chess are less good / equal to / better than the best men"

- "The best n% of women are less good / equal to / better than the best n% of men at chess"


The simplest and most likely explanation for the disparity is that women are naturally less interested in and/or not as good at chess, on average.


No. Instead it is culture that tends to make less women be interested in chess. This is still a problem, though.


It might be culture; it might be biology. It’s probably a combination of both. Either way, why, exactly, is it a problem?


Considering AlphaZero was orders of magnitude stronger than stock fish, it would be interesting to see AlphaZero's analysis if it was available.

Edit: Alphazero's record against Stock Fish is 28 wins, 72 ties and 0 losses.

In a 100 game matchup, AlphaZero had 28 wins 72 draws and 0 losses. I'd classify that as orders of magnitude better.

https://www.chess.com/news/view/google-s-alphazero-destroys-...


AlphaZero was playing Stockfish 8. This is done using Stockfish dev which is more than 110 ELO higher than Stockfish 8 (see https://github.com/glinscott/fishtest/wiki/Regression-Tests) and higher than what was reported for AlphaZero.

Check out the Leela project, which is trying to reproduce and improve the AlphaZero project to also beat Stockfish dev: http://lczero.org/ (at this point they are about equal with Stockfish 9)


A 100 ELO difference is about a player twice as stronger. With a 100 ELO difference, Stockfish would have won some games.

28Win 72Draw and O Loss in my opinion reflects at least 300 ELO (8 times stronger).


Elo is not a matter of opinion. There's a formula for it, and 28 wins, 72 draws and 0 losses represents almost exactly a 100 point Elo difference.

https://www.3dkingdoms.com/chess/elo.htm


You are right, thank you for the pointer.

I guess that the spectacular 28-0 was somehow confusing my ELO opinion engine by concealing the fact that 72 draws are a lot more difficult to achieve than 12 draws (28-12-0 would have been a 300 ELO difference).


The A0 vs Stockfish 8 match also didn't use endgame tablebases.


It's not orders of magnitude stronger. But I agree, it's be interesting to see Alpha's analysis.


In a 100 game matchup, AlphaZero had 28 wins 72 draws and 0 losses. I'd classify that as orders of magnitude better.

https://www.chess.com/news/view/google-s-alphazero-destroys-...

But yeah, it would be interesting to see a side by side comparison of alphazero and stockfish's live analysis of these games.


Wasn't Stockfish crippled in that set of games? Such as no opening book, which would give a computer like AlphaZero an initial advantage? And a relatively weak CPU setup, compared to the massive computer AlphaZero used?


So, 70 million nps or about ~3x 2950x threadrippers [2] is relatively weak cpu compared to 80 thousand nps or approximately 2x 2080tis [3] for Alphazero?

> AlphaZero compensates for the lower number of evaluations by using its deep neural network to focus much more selectively on the most promising variation [1]

Even if you compare CPU to GPU by price, and not speed, it seems pretty even. It clearly has to sacrifice speed by making more intelligent pruning decisions than stockfish.

1: https://en.wikipedia.org/wiki/AlphaZero#AlphaZero_vs._Stockf...

2: https://sites.google.com/site/computerschess/stockfish9-benc...

3: https://www.reddit.com/r/hardware/comments/9jyts8/rtx_2080_t...


AlphaGo engineers didn't really know how to configure Stockfish correctly.

The computer itself was strong. But the weird timing setup, the disabled databases (ie: both opening book AND endgame book was disabled. Stockfish normally plays PERFECTLY when the board is reduced to 6 pieces or less, as well as perfectly knows the winner / loser in every 6-piece setup. But that was disabled for the AlphaGo games)

Without the ability to run AlphaGo on our own and recreate the test, we have no way in knowing how AlphaGo would work under "fair" conditions.

-------

And btw: 1GB of RAM is a lulzy setup. You put all the CPU time you want, but gimping the RAM down to 1GB is... weird. Its a VERY suspect "test" that none of us can replicate.


It's not that they didn't know how to configure it correctly; some of it was purposefully (and rightfully) disabled to see real difference between stockfish and AZ.

Remember that if stockfish uses tablebases and opening books it's really "cheating" by using human knowledge.

Although I am surprised that they reduced the hashtable so much and also used stockfish 8 when stockfish 9 was available. It was not RAM but just the hashtable size also their "test" has been replicated by plenty of people.

We have our own "replica" of the NN playing chess in lichess.


Opening book I agree, but tablebases are definitely not human knowledge. They are a bruteforced database of every possible position, or in essence a precomputed position. Put simply, giving a massive time advantage to the user during the late middle and endgame.

So if A0 wasn't built to access them, but stockfish did in the match, then that would be an unfair advantage.


> So if A0 wasn't built to access them, but stockfish did in the match, then that would be an unfair advantage.

Why is that an unfair advantage? AlphaZero developers wanted to prove that their AI was better than Stockfish.

They failed to do that. If AlphaZero wasn't built to access Tablebases, then they should have built it to access tablebases. Don't unfairly gimp Stockfish because you're lazy at programming.


Alpha zero can access the tablebase. This proof of concept was to let both the engines play with minimal interference of outside pre computed knowledge.


> Remember that if stockfish uses tablebases and opening books it's really "cheating" by using human knowledge.

I thought the "point" of AlphaZero was that it was better than the sum of human knowledge.

By the way: tablebases are computer generated. There is no human alive who knows all combinations of 6-piece endgames. Tablebases are brute-forced endgames, created by computers to be used by computers.

Stockfish itself was only really designed to play the midgame. Its designed to be used with both tablebases and opening databases.

> It was not RAM but just the hashtable size also their "test" has been replicated by plenty of people.

Citations please. I'd love to see a "proper" test of AlphaZero vs Stockfish.


The programs are different programs. You can try it both ways, with and without the opening books. Because there are different configurations, in order to see who win must be specified by the configuration in use.

One way is to do according to the most capable configurations of each program, so that means Stockfish with all of them. Other way is to specify the same limits of time, memory, etc of each one, although that is still not the excuse to avoid the opening books and tablebases and so on unless they use up more memory than AlphaZero does.


You can estimate pretty well even on average hardware by keeping the same 875x ratio using time odds. However, what is a fair comparison to either side depends on who you ask.


Stockfish was severely crippled in that comparison, Stockfish had no opening book and only like a gig of RAM, as well as a very weak CPU and also it had a fixed amount of time per move, even though variable "thinking" compute time is a major advantage for stockfish


White was winning twice as many points as black (64 points for white, 36 for black; draws give 0.5 points to both players) and points difference is all that matters for Elo. As a matter of fact, 64-36 is pretty much exactly what you'd expect when two players have 100 Elo difference.

Your incorrect perception comes from the fact that, at very high levels (as shown by this match as well), draws become way more common than for lower levels. A 3400 vs 3300 Elo match might be 28-72-0, a 1400 vs 1300 match might be 60-8-32. At the lower level, you see one player winning twice as many games as the other, at the higher level you see one player losing all the time; that looks different to you, but as far as Elo difference is concerned the two results are exactly the same.


According to the ChessNetwork yt channel, Alpha zero does not consistently beat stockfish. But when it does, it does so in a very interesting manner.


AlphaZero draws a lot against Stockfish but Stockfish won ZERO games in their 100 game match up.


Stockfish wasn't really configured correctly: they disabled both the opening database and the endgame database in the tests.

I dunno why AlphaGo devs would do that, aside from artificially gimping Stockfish on purpose.


I can imagine them thinking "well, alphazero doesn't employ opening and endgame databases" to which I would counter-argue with "stockfish doesn't use machine learning, either"



Anybody have a suggestion for a site similar to this (engine analysis and all) but also with human commentary to explain things to those of us whose chess skill earlier stage?


Svidler and Grischuk at chess24.com are fantastic, but they're both world class players and beginners will find their commentary and analysis difficult to follow. I'd recommend chess.com - Danny Rensch and Robert Hess are a bit more accessible.


I second chess.com. And the guests they have, Hou Yifan and MVL today, absolutely elite players. Yet they manage to keep them understandable.


ChessNetwork is my choice. Streams on twitch with analysis video on youtube.

https://www.twitch.tv/chessnetwork/events

https://www.youtube.com/user/ChessNetwork


I like https://www.youtube.com/user/AGADMATOR. He goes over many interesting variations with clear explanations.


Second agadmator, lots of personality and humor along with the detailed analysis.


https://lichess.org/ has a great live commentary of every game.


Chess24 has real-time human commentary as well as shorter post-game summary.


It is very fun but I think that to fully follow Chess24 commentary real-time you need to be FIDE 1900+


I don't have 1900+ rating and can follow most of it, although occasionally I need to pause the video to understand why some "obvious" things are indeed obvious.

It's true that without some basic knowledge of chess it would be hard to follow, but that can be said about many sports.


/r/chess on reddit has been good at finding and linking useful commentary.

For example, here's a good move-by-move analysis of game 6, including (around the 33-minute mark) an explanation of the "missed" win:

https://www.youtube.com/watch?v=4yzaG0Ia_fs

And tl;dr for those not following the match: a chess engine analyzing the game found a line Caruana could have used to force a win in game 6 (the actual result was a draw), but it required making such an unnatural and normally bad move (trapping his own knight in a corner) for a relatively distant payoff that commentators pretty much all agree no human would ever have spotted or played it in a live game.

Here's Garry Kasparov, for example:

https://twitter.com/Kasparov63/status/1063576827850096640

But had Caruana played the incredible 69.Bd5 Ne2 70.Bf3 Ng1!! they would request metal detectors immediately! No human can willingly trap his own knight like that.


Another nail-biting draw!


It's the first time since 1978 (Karpov-Kortchnoi) that a world chess championship begins with 7 draws, the longest draw in a raw beggining in a world chess championship !


Carlsen-Karjakin 2016 began with 7 draws.


Welcome to modern, boring chess. I wish we still had hyper-aggressive grandmasters like Mikhail Tal.


These games were all but boring. And nowadays there are great games being played, even if they end in a draw. Check out Carlsen-Svidler from earlier this year.

Players like Tal had their share of boring games, it's just that we remember the crazy ones because they're fun.


We do, they just don't qualify for the world championship.

If Mikhail Tal was alive today, he would play boring chess, too. Otherwise modern GMs would just accept his sacrifices, not make any mistakes, and win.


Late in his career Mikhail Tal put the fireworks away and transformed himself into a supreme technician. He set a record for the longest undefeated streak in chess history. Basically he'd fit right in today.


Interestingly enough, that record was just broken by Chinese GM Ding Liren, who played 100 games before losing to Maxime Vachier-Lagrave at the Shenzhen Masters tournament.


The computer age has unfortunately sort of crushed that style of play :( It's hard to play sacrificially when the engine refutes your attacks


If Leela and AlphaZero have anything to say, it's that there is such a thing as being overly materialistic.


Sacrificing material for positional compensation is hardly a new concept


It's hard to change a game that's so old, but draws shouldn't be allowed, only stalemates.

Imagine if the Lakers played the Warriors, and late in the 4th quarter, the game is tied, and LeBron and Curry decide they are tired, declare a draw and go to their locker rooms. Not particularly satisfying.


Perhaps a doubling cube can be used like in backgammon, ie, one player can up the ante, in a draw-ish situation. Ie, staring at a draw, one player says: let's play for a win, but at double the points, if the other player accepts game continues. If other player rejects the doubling, he is considered to have conceded the game at the original 1pt stake.


Your analogy doesn't make sense. In basketball, if your opponent gets tired, that gives you a better opportunity to win. In chess, if the game nears the end and neither of you can see a way to win, then there's no good opportunity. Your analogy would make more sense to say the basketball game was tied and there are three seconds left on the clock and both players have broken wrists. Playing three seconds of game to risk injury is not worth it for either player.

It also doesn't mean the game was unexciting.


In a championship match tiredness and losing focus is a big deal. A lot of draws are simply not wanting to risk burning out when there are more games to go.

Saying that, Carlson once had a reputation for not agreeing on a draw and being able to maintain focus while his opponent faded and made a mistake.


You shouldn't comment so confidently about something you don't understand. The position is drawn. There was no way for either side to win.


You shouldn't comment so snarkily to someone you don't know. I understand what a drawn position is, however players will regularly agree to a draw well before it actually happens. They choose to draw because of potential drawn positions. There's no reason for a game not to continue until there is an actual stalemate (or a set of similar circumstances, like a situation in which checkmate is impossible), or a blunder by one of the opponents.


> I understand what a drawn position is

To make this more concrete, the following link is a drawn position (it is trivially easy for either side to avoid checkmate, indefinitely)

http://www.jinchess.com/chessboard/?p=---k------------------...

However, checkmate is still possible (White can checkmate Black if Black makes severe blunders that even beginners probably wouldn't make)

Do you think the players should be forced to play on here?


Yes! Or black should resign. And in addition, they have clocks for a reason - though time is added indefinitely at the end (if a player moves fast enough) - if a player takes an hour more than an opponent (like Carlsen did in the middle of game 8) they should start to feel the pressure of that more severely.


Why do you think Black should lose here? Why is Black's position worse than White's ? If your answer is "White has more material", keep in mind that chess is not about material; it is about checkmate.

But, nevertheless, here's an example with equal material where checkmate is possible for both sides, but not without blunders. Who should have to resign here?

http://www.jinchess.com/chessboard/?p=--------------------k-...

If you really insist on saying "well yes, they should have to keep moving the kings around aimlessly for hours until somebody's clock runs out", you're proposing a game that is so fundamentally unlike chess that it should probably be given a different name.


On a side note: I think Pentagram did an amazing job with the WCC branding [1] in 2014. It's ridiculously non-conventional for a serious organization such as FIDE to adopt it. They did reject the proposal for Shuka Design for the new "pawnographic" (as it was hastagged on twitter) logo [2] for the 2018 championship and only kept the arms tangled up around a chess board. Still, its extraordinary and personally I love it. Oh and they have a King's Gambit perfume [3][4] for sale.

[1] https://www.pentagram.com/work/world-chess

[2] https://www.bbc.com/news/world-42425587

[3] https://www.smellchess.com/

[4] https://shop.worldchess.com/shop/chess-perfume


> serious organization such as FIDE

It's wort noting that up until recently, FIDE had a president who was full-on batshit crazy. He repeatedly claimed in public that he had been abducted by aliens. He (and by implication FIDE under his rule) was sanctioned by the U.S. Treasury for financial involvement in the war in Syria. Corruption was an open secret. It's a bit of a stretch to call FIDE under Ilyumzhinov a "serious organization".


Before such claims one/both of you would have to define what "serious organization" means when you use it, as it would appear that you might be equivocating relative to how he used the term.


I'm glad they rejected the Shuka Design, that thing was over-designed and bad on so many levels. What is the version. What are you referring to by "only kept the arms tangled up"?

I really like the ones from [1], now that's what I call great design.


You can see the modified logo with just arms here: https://youtu.be/3RHo68RDFtU?t=8


The 2014 branding reminds me of the best of mid-century graphic design. Very rare to see it today.


I think the official logo has some Chilly Gonzales Ivory Tower vibes.

Edit: The album art: https://www.chillygonzales.com/wp-content/uploads/2017/09/GE...


Thank you for sharing this. I love the logo, but IMHO the overall look of the 2014 design (type, grid, illustrations) is a little too similar to theguardian.com aesthetic.

Edit: I was commenting on the 2014 design.


Looks a combination of Escher and Picasso aesthetics.




Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: