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Topic: Essay by Christian Freeling on inventing games (Read 522032 times) |
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #450 on: Jun 9th, 2011, 12:16pm » |
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on Jun 9th, 2011, 9:56am, MarkSteere wrote:Christian:"Hex, without the pie rule, is a proven win for the first player.
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What makes Symple different is that you can't even argue one way or the other"
Hogwash. Hex was not solved, except for on a handful of small boards. There's a difficult, complex, theoretical proof that Hex is a first player win, but nowhere in that proof is any indication of how one goes about winning. |
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Could it be any clearer? Where did I say Hex was solved? I said it was proved to be a first player win. You say "Hogwash. There's a difficult, complex, theoretical proof that Hex is a first player win".
Notice anything? READ what you reply to.
(P.S. It's not all that difficult either, but non-constructive, and yes, I know who gave it).
Concerning the second quote, numerous times did I say that Symple isn't different from any finite abstract perfect-information zero-sum game in this respect:
Quote:Symple is a finite abstract perfect-information zero-sum game and as such completely determined. That means that the truth - in this case a white win or a black win - is locked in the gametree.
About Symple |
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That these games are proved to be completely determined doesn't mean anything for actual play - that's another thing I've referred to many times. Please stop enlightening me with common knowledge.
In Hex you can prove the result, which doesn't mean you can use the proof to achieve a win. Some games allow you to argue towards a result without anything that can be proved. I can argue Draughts is most likely a determined draw. Or that Chess most likely is not a determined Black win.
In Symple and Sygo - with the balancing mechanism in effect - I say you can't, but if you can, please do.
It's not about a mathematical proof, it's about a high resolution balancing mechanism. That in itself is the means of convergence - just like a swap is intended to seek the middle, even if 'the middle' doesn't exist in a game-theoretical sense.
It's the sheer number of positions to consider that it generates (effectively all positions before a first growing move, far more than the 20+ million of a 3-stone swap in hex19) that make that the divergence that would eventually result from exploring the intricacies of one such position, in deep over a long period of time, will never come to be. That's what I'm saying, NOT that Symple and Sygo are different in any fundamental way.
There will be another 'refutation', no doubt. My problem is that I don't say what I'm saying. 
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| « Last Edit: Jun 9th, 2011, 1:14pm by christianF » |
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ocmiente
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Re: Essay by Christian Freeling on inventing games
« Reply #451 on: Jun 9th, 2011, 1:16pm » |
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on Jun 9th, 2011, 11:51am, christianF wrote:
... If someone states that he or she cares about art, music, literature or math, would you voice the same suspicion?
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I would have the same concern if someone stated that someone's illogical behavior toward their person was less concerning than someone's illogical behavior toward any other inanimate entity.
I'm struggling with this thread in general. While I appreciate your contributions, there appears to be some unwritten social rule similar to one of the Bush doctrine's "prongs" that occurs to me, i.e.:
"Make no distinction between trolls and the people that respond to them--and hold both to account."
I suspect that's partially what SpeedRazor had in mind, maybe... possibly... who knows. He has more common sense than I do in not posting to this thread in a while 
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #452 on: Jun 9th, 2011, 1:17pm » |
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on Jun 9th, 2011, 12:16pm, christianF wrote:
Where did I say Hex was solved? |
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I never said you did. Stop putting words in my mouth. What you did say is that reasoning can't even be applied to the question of whether or not Sygo is a first player win. And I quote, "You can't even argue one way or the other." A magical logic shield, lol What next??
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #453 on: Jun 9th, 2011, 1:28pm » |
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on Jun 9th, 2011, 1:16pm, ocmiente wrote:| I suspect that's partially what SpeedRazor had in mind, maybe... possibly... who knows. He has more common sense than I do in not posting to this thread in a while |
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Yes, I can relate to that. It's a pity though.
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #454 on: Jun 9th, 2011, 2:14pm » |
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on Jun 9th, 2011, 12:16pm, christianF wrote:| Where did I say Hex was solved? |
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on Jun 9th, 2011, 1:17pm, MarkSteere wrote:
I never said you did. Stop putting words in my mouth. |
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Yes, bad habit isn't it? 
on Jun 9th, 2011, 9:56am, MarkSteere wrote:| Hex was not solved, except for on a handful of small boards. |
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So this bold reply wasn't meant to 'correct' me on this point?
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #455 on: Jun 9th, 2011, 2:50pm » |
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on Jun 9th, 2011, 1:16pm, ocmiente wrote:| He has more common sense than I do |
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That much?? 
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #456 on: Jun 9th, 2011, 2:56pm » |
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on Jun 9th, 2011, 1:28pm, christianF wrote:
Ocmiente wrote: "He has more common sense than I do in not posting to this thread in a while"
Yes, I can relate to that. It's a pity though.
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Is it really a pity? Your "guest" thread has already bloated to proportions that dwarf the host forum. You remember - the Arimaa forum?
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omar
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Re: Essay by Christian Freeling on inventing games
« Reply #457 on: Jun 9th, 2011, 5:42pm » |
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Quote:| Christian and Nanojester are barely capable of formulating a sentence, never mind a coherent logical premise. |
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Mark, I'm afraid I have to ask you to stop posting here. I have warned you before and you have again violated the posting guidelines. So please refrain from posting. Thanks.
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Sconibulus
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Re: Essay by Christian Freeling on inventing games
« Reply #458 on: Jun 9th, 2011, 11:20pm » |
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In response to the initial premise, I'll admit that while I can't claim to have played any piece-placement games skillfully, it does seem that black has an advantage in these games, because of the balancing mechanism in question. Basically, it feels to me as if Black has a move in hand, and loses far less from exercising his option early as compared to White, because he still gets a growth step.
Basically, it seems that White's window of success on growth-starting is much smaller than Black's, while Black also has the minor advantage of being able to be in a reactionary position in the early placement stage (assuming Black exercises the limits on the growth-starting window in order to gain the first move on White as well)
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #459 on: Jun 10th, 2011, 7:01am » |
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on Jun 9th, 2011, 11:20pm, Sconibulus wrote:In response to the initial premise, I'll admit that while I can't claim to have played any piece-placement games skillfully, it does seem that black has an advantage in these games, because of the balancing mechanism in question. Basically, it feels to me as if Black has a move in hand, and loses far less from exercising his option early as compared to White, because he still gets a growth step.
Basically, it seems that White's window of success on growth-starting is much smaller than Black's, while Black also has the minor advantage of being able to be in a reactionary position in the early placement stage (assuming Black exercises the limits on the growth-starting window in order to gain the first move on White as well) |
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That's an interesting question to which I have no immediate answer. In my games against Rendong You the button is pushed very early sometimes (the current one is an example) but there's not much to go on yet for at least two reasons:
1. The complexity of the game itself.
2. Tactical threats early on, mainly threats to isolate and kill a particular stone or the group it is intended to form.
The first requires getting to grips, strategically, with the fast growing rate and the tactical implications. Any mistakes made may have a greater impact than the value at stake in terms of the balancing mechanism. There are as yet no strong players.
The second one may force you to grow in a local conflict whereas you'd rather place a single stone in view of the overall position. The example below has moved beyond Black's prerogative because he cashed in on the second move, but it may wel happen very early on, before growth has taken place.
In the current game my opponent initiates a local conflict with 7. ... E8. Two moves on I felt compelled to grow for defensive reasons, and my opponent did not follow suit. My stones are fairly densely packed in the bottom left section and may yet be forced to connect (depriving me of growing options).
By placement he now has 9 groups, while I have 8. In the local conflict things look save, so I felt I should follow suit this time with placement (10. D12 that's as far as it stood when I posted this).
The game also illustrates that it isn't simply a 'placement stage' and a 'growing stage'.
Symple has no capture and suffers from these tactical disruptions to a lesser degree. But Sygo is more fun .
I'll ponder your remarks carefully. I don't know if you have a point, but that may very well be. I'll have to sleep on it.
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| « Last Edit: Jun 10th, 2011, 7:21am by christianF » |
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #460 on: Jun 11th, 2011, 3:13pm » |
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on Jun 9th, 2011, 11:20pm, Sconibulus wrote:In response to the initial premise, I'll admit that while I can't claim to have played any piece-placement games skillfully, it does seem that black has an advantage in these games, because of the balancing mechanism in question. Basically, it feels to me as if Black has a move in hand, and loses far less from exercising his option early as compared to White, because he still gets a growth step.
Basically, it seems that White's window of success on growth-starting is much smaller than Black's, while Black also has the minor advantage of being able to be in a reactionary position in the early placement stage (assuming Black exercises the limits on the growth-starting window in order to gain the first move on White as well) |
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I've slept on it and I fear I don't see matters any different than before.
For arguments sake, let's assume Sygo's move order advantage mirrors the one of Go, say six points.
'Pushing the button' means for white that he uses a turn to grow his groups instead of placing a single stone, for black that he uses a turn to grow his groups and place a single stone.
In a more or less regular opening position, after five moves each, both would probably have claimed influence in corners and along sides, but barring tactical involvement, stones would still be wide apart.
In such a position, life and death being no issue yet, what is a single stone worth, as opposed to a 2-stone group? One point for the extra stone for sure. But there's no difference in the rate of growth, so the rest is 'influence'.
I don't know, but for argument's sake let's say that's worth one point too. So a 2-group in such a position would be worth two points more than a single stone.
Here's a table with subsequent positions in terms of numbers and some commentary.
I'm not entirely sure of the value of the second parameter (i.e. "a 2-group in such a position would be worth two points more than a single stone"), but the general idea is clear and I don't see any difference in the 'size' of the window wherein to push the button, for white or black, nor in the weight of the decision. I also fail to see a 'reactionary position' that would work in black's favor.
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| « Last Edit: Jun 12th, 2011, 1:41pm by christianF » |
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #461 on: Jun 18th, 2011, 7:38am » |
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on Jun 10th, 2011, 7:01am, christianF wrote:In the current game my opponent initiates a local conflict with 7. ... E8. Two moves on I felt compelled to grow for defensive reasons, and my opponent did not follow suit. My stones are fairly densely packed in the bottom left section and may yet be forced to connect (depriving me of growing options).
By placement he now has 9 groups, while I have 8. In the local conflict things look save, so I felt I should follow suit this time with placement (10. D12 that's as far as it stood when I posted this). |
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The game ended after white-21 by resignation. My opponent lost a local battle after the cut-off of the black stones at E8 and E11 and secured not quite enough territory in return.
At white-19 I start a new group bottom right and black doesn't reply immediately, but even now I'm not sure it lives. You can't create eye-space by capture in Sygo. Maybe I could have gotten some life in it with one eye, supported by a seki situation around a black attacker, but black would lose (by a small margin) even if he kills it, so my opponent thought the best of it.
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #462 on: Jun 21st, 2011, 8:04am » |
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For those interested in combinatorial games like Clobber and Konane, especially from a programming point of view, here's an interesting development regarding Grabber.
Greg Schmidt of The Axiom Universal Game System Project wrote this:
Quote:Hi Christian,
I've had a little bit of time recently to revisit Grabber. I've searched high and low looking for some issue in the programming that's creating a bias for blue and I just can't find any problems. Of course that doesn't prove that there still isn't an issue.
I now suspect that there is a strong 2nd player bias on the 6x6 grid. Here's why I say that:
1) I created the next smaller even sided version, the 4x4 (with 2 pieces, rather than 4 being removed at start of game). Axiom can solve this game. It is a guaranteed win for blue.
2) I don't believe Axiom is capable of solving the 6x6, however if I begin by first manually playing the four corners (which gives neither player an advantage), after exploring roughly half a billion positions, Axiom finds a guaranteed win for blue in 19 moves (see attached image).
I consider this to be an important result.
A few more less important observations:
a) Based on further experiments with the 6x6 where I have performed partial runs and watched the score, blue seems to take a fairly early lead and that appears largely independent of the first four moves.
b) I created a 5x5 with a vacant square in the center so that there is an equal number of red and blue pieces. Like the 4x4, only 2 pieces are removed at the start of the game although they can't be removed in a purely "balanced" sort of way. Axiom solves this game and it's a guaranteed win for red. This makes me wonder if there is some sort of parity based on even/odd board size.
Conjecture: Even size boards are a win for blue, odd sized boards are a win for red. I'm out on a limb here with that conjecture, but it seems intuitively plausable to me given these results and given that Grabber is a combinatorial game.
Once again, the 6x6 results do show a guaranteed 2nd player win for blue.
-- Greg |
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Grabber is basically, but not entirely, 'Konane columnified'. Disregarding boardsize and 'columnification', the differences are:
1) In Konane both players remove one man initially and under rather strict conditions, in Grabber both remove two men initially.
2) Multiple capture in Konane is restricted to the direction of the first capture. In Grabber it is not.
I mention this in case comparisons are possible. I'm not up to date in game theoretical issues regarding move order advantage in Clobber or Konane, nor of the current state of programs. Here's what I answered for a first impression (between brackets) and Greg's reply:
Quote:[That's all very surprising indeed, not to mention counterintuitive! I'll have to let it sink in a bit, but at first glance it might even sprout additional interest in the game because this is a somewhat peculiar behaviour, isn't it?]
I think so too.
[Makes you wonder if there's an algorithm of some sorts, something NIM-like.]
Yes, I had a similiar thought, although it might be difficult to divine out by back engineering these results.
[Clobber presumably does not have this issue (or we'd have heard of it) and I don't know of any Konane programs. It would be nice to publish these results in our site at some point.]
I do wonder how many games (outside the mainstream) undergo deeper analysis. Who knows, there could be a few surprises out there waiting to be discovered? Also, I try not to draw too many conclusions from Axiom's game play because it is heuristically based. However, when it is able to solve a game, I do consider that to be a significant result. |
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I've asked Greg to run 4x4 tests removing two men each initially, to see if anything changes in the move order advantage.
For the same reason I've asked to run a few 6x6 tests with one man each removed. I'll keep you posted.
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| « Last Edit: Jun 21st, 2011, 8:34am by christianF » |
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #463 on: Jun 21st, 2011, 1:20pm » |
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on Jun 21st, 2011, 8:04am, christianF wrote:
For the same reason I've asked to run a few 6x6 tests with one man each removed. |
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Tweaking a combinatorial or combinatorial style game for first move advantage is like adding a fourth line to a haiku. I think it subtracts more than it adds. Of course it's your game and you can do whatever you want. Just my outlook on the general topic.
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #464 on: Jun 21st, 2011, 2:56pm » |
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To get things in perspective, I've never considered Grabber as more than a combinatorial quickie.
It is a rather inconsequential game that now appears to reveal a clear bias, for no immediately apparent reason. For a game that's an interesting property, worthy of investigation.
As Greg pointed out, odd/even boardsize seems to reverse the move order advantage.
The test with 2/4 men removal are to see if the advantage stays the same or reverses. I presume the former, but then, I presumed there wouldn't be much of a move order advantage to begin with. And that was a wrong assumption too. In other words, I've got no clue. That's the interesting thing. Where does the advantage 'reside'? Is there something like a NIM-like algorithm possible?
P.S. Does anybody know why Clobber is played on a 5x6 board? Did it perhaps have a similar issue?
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| « Last Edit: Jun 21st, 2011, 3:26pm by christianF » |
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