Handicap Hex

Hi,

I'm rated about 2000 at Hex (goes up and down).

I would like to try some handicap games. If you're 1850- or 2150+ (say, i'll happily play anyone on any handicap, right now I'd prefer not-totally-even) - how about a game where the lower rated player goes first, and there's no swap rule?

If there is a 300pt different then perhaps it could go: lower-rated plays, opponent chooses from A1/M13, lower rated plays again. So almost a '2 stone' handicap.

Please send me an invite!

Niall :)

See you in igGC? At 2000 we should be close.. :)

I think a two stone handicap is almost always too much. I've thought about handicaps (although I prefer games without), and my idea was as follows: The lowest rated player goes first, no swap rule, BUT he cannot play whereever he wishes. He has to play on the short diagonal. A small handicap means playing in the corner (a13 for 13x13), a large (huge!) handicap means he gets to play in the center. Thoughts?

Marius, i agree that one stone (center) is enough for most pratical purposes. Between that and no handicap there are many levels. I don't see the advantage of forcing him to play in the short digaonal?

Obviously it also depends on board size. About Nail's proposal, I think that A1+M13 against center+another isn't that easy for the center+another player.. A1+M13 are very balanced, while the other player is forced to create an asymmetry..

The common TwixT handycaps can be applied to hex too, those are:

1. no swap (the weaker player moves always first)

2. no swap + x rows (also possible on lg if both players agree the x last rows are red)

I am not that good in Hex, but in TwixT a no-swap-handycap is probably about 400 points rating difference. To get smaller handycaps you can choose a move with winning percentage X% (X > 50) from a starting move table.

@maraca: 2. if the distance between the edges are not the same, then an explicit winning strategy is available to the shorter player.

Interesting, I didn't know that. 2. is anyways only suitable for teaching beginners the rules / basic mechanics as I've experienced.

Interesting that you guys think 1 stone is enough. I have now finished two H1 (weaker goes first ,no swap) games, the stronger player won both.

I had a few challenges as a result of this post, most people asking for handicaps that seem too much for me, but I'm happy to see what happens. There is one player who asked me to take two handicap stones :)

To see me get egg on my face, look at:

http://www.littlegolem.net/jsp/game/game.jsp?gid=1321881

:)

You may be interested in Philip Henderson's (and the rest of the Hex team at UofA) on Hex. Particularly relevant is his second presentation on handicap Hex. http://webdocs.cs.ualberta.ca/~ph/research.html

Thanks! I think I'll try a few before getting too into it... but from glancing the key point that the don't expand on seems to be:

"Can easily make strategy explicit by enforcing inferior cell strategies"

I probably just need to read other material of theirs.

... :)

Well, the reason for using the short diagonal is that I think that a) All moves on the short diagonal are winning and b) on that diagonal, a move closer to the center is stronger than a move near the corner. Thus, you can translate a certain rating difference onto a specific opening move. Say, 50-100 points is the corner, 100-150 points is the neighbour to the corner and so on (these are just examples, I have no idea what rating differences should translate to what opening move).

Marius, i disagree with A.. i know up to 8x8 is true, and probably up to a quite larger board size too.. i agree with B, but i would prefer more variety in handicap games.. :)

Ah, the famous Marius conjecture again. I want to believe, but the patterns in Hex are grotesquely complicated, why would there exist such a simple beautiful rule? Also why would a stone in or near the center be better than any other on the short diagonal if they all are winning? What exactly is your definition of a "better move" in this situation?

There's no proof that this is true, and I know that. I still believe it to be true, though. I also believe that on all boards, all moves on your own edge EXCEPT the corner is losing. Still no proof, just a part of my "Hex religion" :-)

As for what is a "better move": In my opinion, it's a move that makes it "easier" for you to win. That's hard to define, so for a definition, I'll settle for "a move which makes the number of moves necessary to win, with perfect play on both sides, smaller". Again, I have no proof that opening stones nearer the center are always better in this sense, but I do believe that they are.

Yes, its hard to define. But lets say we use your definition. Have you tested this with smaller board sizes? Will in fact playing close to the center give shorter wins with optimal play for lets say 8x8?

For all the solutions I have seen so far, this holds true. So it's not proven to be false yet. I think I have only seen data for up to 7x7 on this, though. I've seen diagrams of winning moves for 8x8 too, but not with the necessary number of moves to win.

I tried to locate QueenBee's opening page, but the link didn't work. Perhaps someone knows where we can find this data?

Yes, its hard to define. But lets say we use your definition. Have you tested this with smaller board sizes? Will in fact playing close to the center give shorter wins with optimal play for lets say 8x8?

Here are diagrams of winning moves:

http://www.hexwiki.org/index.php?title=Small_boards

But I have never seen any data of minimal length with optimal play. That would be very interesting data. I suspect that maybe the shortest games are not found in the center but just along the border of the red and blue areas. Or at least about the same. Some numbers would settle this.

Sorry for double post. It's quite poor that the forum post another post when you go back in browser history.

well the two browsers I use (Chrome/IE) warn you that you're about to resend what you just sent, and are you sure you want to do that. What else could they do?

I HAVE seen this data for games up to 6x6, at least (I think even up to 7x7, but I'm not absolutely certain about this). For all these sizes, I remember that the center was always the opening with the fewest moves (although sometimes there were alternatives with the same number, but never fewer). I'm pretty sure also that on the short diagonal, moves farther away from the center never had fewer moves than those closer to the center. But it's been some time since I saw these numbers, so I'm not 100% sure about that last one.

We need these numbers.

1x1 and 2x2 are trivial, as there are only centers along the diagonal. 3x3 is easy to see also - it takes 3 moves to win when opening in center, and 4 when opening in the corner. I think I could do 4x4 also with a little time, but 5x5 and 6x6 takes more time to solve (not to mention 7x7!), and the data are out there somewhere, so I'm not gonna dedicate much time to do this.

Another interesting property is perhaps number of hexes needed to win. The more opponent stones you can add while still having the win, the better position one may argue. In 3x3, starting with B2 you need only 4 hexes, while C1 you need all 8.

Not until size 6-7 can we really read anything into these numbers though. Is B6 or F5 as "good" as D4 in the case of 7x7 for example. That I would like to know.

Better for humans also means less need for precision to convert the win. That's what makes it hard to define, though. You can say the greatest number of future paths that win, but humans will be very good at heuristically paring some paths so a mechanical counting doesn't capture the actual difficulty.

Marius, do you agree that A(N-1), B(N-3), C(N-5)... are all losing with a sufficiently large N? if this is so, then wouldn't it be really surprising for the short diagonal to be winning despite being surrounded by losing moves?! In fact I've done some experiments with this and I'm inclined to believe that for large boards A(N-1) is easier to use than A(N).

I'm not sure I agree that that is the case, lazy. But even if it is, I still believe that yes, every move on the short diagonal will be winning. As for your experiments on large boards: It is very possible that the winning line is so complex that other openings, though actually losing, may seem "easier". But all of this is just guesswork, of course.

It would be very interesting to see if A9 in 9x9 is winning or not. As far as I know this hasn't been computed yet.

I guess I think of a 'better move', given two that are winning, would be one where I had as many subsequent moves to win as possible. That said I don't just want to maintain as many kikashi as possible. So I guess overall I have to cede to Jonathan's "allows your opponent to fill in as many hexes as possible while maintaining your win" is better.

The first of my games has had a win for the weaker player (I predict). I managed to win with a 2 stone handicap against NakedFace :)

N

Niall, we're still waiting to see games won by the stronger player? :P

Hey folks,

(1) I would like more handicap games! Whatever you think is appropriate, but my sample size isn't very big :)

(2) Games won by stronger player:

http://www.littlegolem.net/jsp/game/game.jsp?gid=1319754

http://www.littlegolem.net/jsp/game/game.jsp?gid=1314525 (this one is slightly odd, me and gpallis agreed that I got an extra point if I could connect all 4 sides...). We're having a revenge match now :p

The only other finished game is an over-handicapped game, win for weaker:

http://www.littlegolem.net/jsp/game/game.jsp?gid=1314525

Pretty confident that stronger will win:

http://www.littlegolem.net/jsp/game/game.jsp?gid=1319880

N :)

Sry, win for weaker was: http://www.littlegolem.net/jsp/game/game.jsp?gid=1321881

Stronger were lucky in game 1319754 that weaker gave up. Seems to me weaker has the win. :)

Oh? Sequence?

Niall, fine examples.. i've seen some on 11x11 too, so they're not totally surprising.. but can we conclude that one stone is 300 rating points at 13x13? I'm not so sure same result can be replicated with games between higher rated players..

To be clear, nonetheless i would like to see handicap stones as an option for unrated games.

I agree! It's very uncertain. I wish more people would challenge me and join in :)

In go it's amazing to see strong players lose handicap games. Even professionals can losse on H2 (I think - they say 3or4 pro ranks ~1 handicap). My guess is that the same will hold for Hex. I am not at all sure of beating Koontz with the first move. In fact my money would be fairly strongly on koontz winning.

There is nobody 300 points above him, but if there were a player who could beat Maciej every time... then I think he would give koontz a hard time even if koontz went first. On 19x19 the handicaps would get a lot bigger too...

N

I'm willing to give handicaps but i play only real-time.. :)

Niall, heh, it's true, in 1319754 you're still losing at the end because 33 D8 wins! 28 D3 could have given you the win in practice, but you probably were losing from the begin to the end. As you can see, it is very hard to compensate the one move disadvantage. You can lose in millions of way, and you've to patiently reduce the number of losses at each move..

Well, I will ask subsequent players not to resign until it's totally clear. I am confident that I would have won that game. Suppose he plays D8 (which he may not):

My moves in ():

33: D8 (E8) D9 (C9) , ladder to the left. If there is a way out of that for red there are also lots of ways to get it wrong too. My opponent resigned as he could find no way.

You're right that 1 move is a challenge, but I think it's a mistake to think that it's insurmountable! I expect to win most of my games as stronger player on H1.

Is there really any reason people think Hex should be so different to Go in its handicaps? My guess is that people just haven't played that much handicap hex to see how challenging it could be. Lazy, you might have to challenge Maciej or Daniel, but try it! Of course, experience as the stronger player is important too, they may need more than one try to work out how to make it hard, but I bet they could!

N

I've already tried to give one stone handicaps because I also like the idea of giving everyone a fair chance. And this is why I'm aware of how difficult it is to find a win in a maze of losses! My guess is that with a larger board there are more chances of blundering but center is also more important and optimal! I'm not sure how much it is an human problem (= we all play quite bad) and how much it is an hex problem (= center is overpowering). See you! :)

So as to test this hypothesis that moving first with no swap is always too much... I have now also added 5 (unrated) games in the waiting room, if people don't want to reply.

I'll let people know how they go. Also, if other people play any handi games I'd like to hear about them. Lazyplayer (the loudest proponent of the idea that you can't win against H1) recently H1 on 11x11 on iggamecenter, and won despite his disadvantage :p

N :)

Well, all i've said about H1 is this: "Marius, i agree that one stone (center) is enough for most pratical purposes.". I think that there are very few decent lines for the player giving the handicap and therefore they're very hard to find. You've no idea how many handicap games i've lost (or won by opponent's blunder) just to find the one decent line you've seen.. :)

Hmm, and I've also made a vague argument about larger boards. It means simply that I don't know if the situation improves a lot for the player giving the handicap by going from 11x11 to 13x13. Apparently it does, but apparence may be misleading. The game IS longer but center IS more important. Isn't it?? :)

Oh sure, if my opponents make no blunders then H1 should be enough!

The point of handicap hex is more to provide a game between players of different strengths so that it's unclear who'll win at the start - as some people find this more fun than knowing that lazy will always win :p

Interesting questions, for me are:

(1) What handicap should an 1800 player give a 1600 player?

(2) Is it the same handicap that a 2000 player should give an 1800 player?

(3) Is it possible to beat a 2100 player with H2 (on 13x13). (I think that it is, even if not every time. )

As ratings are essentially a measure of a series of statements like:

P1 can beat P2 75% of the time

P2 can beat P3 75% of the time

...

P9 can beat P9 75% of the time

etc.

It's then interesting to ask: Is the game between P1 and P5 about the same as the game between P5 and P9?

Then also, does the handicap required for P1 vs P5 to be even match the handicap required to make the game between P5 and P9 even?

In go although this doesn't quite hold up, it's amazing the degree to which it does! The funny thing is that the direction in which it changes is that a 4dan playing a 1dan on H3 has a really _good_ chance of winning, in most rating systems. Yet a 12kyu playing a 9kyu probably doesn't win quite as often. At least that is my understanding. As a novice I would have imagined the reverse!

Sorry for boring you all... :)

N

In chess it is the same: as rating goes up, white winning chance go up as well. Wikipedia has a good article on this: http://en.wikipedia.org/wiki/First-move_advantage_in_chess#Winning_percentages. Probably the same happens in Hex and so it is all normal and good. I give plenty of handicaps so stop accusing me :P

I'm still very skeptical. Is handicap games really a good learning strategy? Why not play a real game. Yes the weaker part will probably lose, but learn a lot more. Isn't that the point?