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Topic: Essay by Christian Freeling on inventing games (Read 522059 times) |
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MHowe
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Re: Essay by Christian Freeling on inventing games
« Reply #525 on: Jul 30th, 2011, 10:30pm » |
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Now that was pretty funny.
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #526 on: Jul 31st, 2011, 12:18am » |
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on Jul 30th, 2011, 10:30pm, MHowe wrote:
Now that was pretty funny. |
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 I may have been a tad hasty reading and responding to Christian's post. Being right all the time has made me complacent. Christian has accused me so many times of "misrepresenting" unspecified things, that if I've now finally, at long last, actually misrepresented something, I don't care.
That being said, and getting back to the subject, I love Christian's definition of soft finitude. I think it applies perfectly to a wide variety of gambling games. Trouble is, I've never seen an abstract game fitting the description.
Name one abstract game that has soft finitude. And I don't mean a trivialized non-game with two pieces on the board. If you can (truthfully and convincingly) do that, I'll stfu (on this particular topic).
Let's let Christian field this one, Mike. With your phenomenal mastery of logical debate, and I mean that in all sincerity, you might convince me of something illogical.
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lightvector
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Re: Essay by Christian Freeling on inventing games
« Reply #527 on: Jul 31st, 2011, 2:09am » |
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If by "any one player can break a cycle and win" we mean instead that "any cycle can be broken by at least one player and still win" (depending on the game, one may need a further qualification that the cycle in question is relevant to optimal play from the opening position), then a number classic games have soft finitude. To give a few examples...
5x5 go with only simple ko prohibition (no long cycle or "superko" prohibition) is one such game. Both players may cooperate to produce longer cycles of captures and recaptures, but the optimal lines of play do not depend on any long cycles. I believe 6x6 go has been solved also, with the same conclusion. 7x7 has not been formally solved, but it is almost certain that it too has no dependence on long cycles. And on larger boards, while long cycles are possible, they are very rare in practice.
Ataxx on a wide variety of board sizes also. Both players can prolong the game indefinitely by only jumping their pieces, but this does not appear to be optimal in practice, nor is it optimal for solved board sizes, and either player can unilaterally choose to stop and eventually force the game to end.
Chinese checkers (a suitable version with rules to prevent a player from indefinitely blocking his home area) also has soft finitude as well. Cooperative cycles are possible, but obviously are not optimal play.
Arimaa is a game that appears to exhibit a property similar to soft finitude in practical play. Of course, it is not known theoretically because we don't know optimal play. But in practice, nearly all games by strong players end with a winner after a reasonable number of moves, and nearly every position occurring in practice seems to provide strong ways to make progress for at least one player. Yet, both players could cooperate to make the game last essentially forever just by shuffling pieces. Strictly speaking, the 3-fold repetition rule would prevent a truly infinite game, but would not stop a game from lasting billions of moves if the players cooperated to this end.
Chess and some of its variants, even without the "50 move rule" are still theoretical candidates, because it has not been disproven that one side or the other can force checkmate from the initial position. Although, practical evidence suggests that optimal play is more likely to lead to a draw.
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| « Last Edit: Jul 31st, 2011, 2:11am by lightvector » |
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #528 on: Jul 31st, 2011, 5:30am » |
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on Jul 31st, 2011, 12:18am, MarkSteere wrote:| That being said, and getting back to the subject, I love Christian's definition of soft finitude. I think it applies perfectly to a wide variety of gambling games. Trouble is, I've never seen an abstract game fitting the description. |
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That may be because you don't understand the definition. I've never seen a gambling game fitting it.
on Jul 31st, 2011, 12:18am, MarkSteere wrote:| Name one abstract game that has soft finitude. And I don't mean a trivialized non-game with two pieces on the board. |
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In Draughts variants, one-on-one opposition, be it men or kings, is one of the first things to consider. It leads to common knowledge such as generally needing at least 4 kings to trap a lone one in Draughts, 3 in Hexdame, 2 in Checkers, Croda, Dameo, to name a few.
In Checkers, depending on the position, the player who is able to take opposition may even win a one-on-one kings endgame.
Pommel is unique in that a one-on-one kings subgame is hard finite: the alignment rule makes that one of the players will have to expose his captain and the other must (!) capture. No cycles.
The unusual thing is that the position in the post that started this subject has 4 pieces and indeed does allow cycles.
So players can cooperate towards a draw: The "if" is necessary for soft finitude. The question remaining is the "and only if".
Zillions gives a win in 13 for whoever starts. It makes that this particular subgame has soft finitude, but it still leaves matters inconclusive with regard to soft-finitude for the game as a whole. A white swan doesn't mean swans are white.
But matters would be settled by a black swan, of course, that is: a position in which a player can force a cycle against his opponent's best opposition. Like a king in a tric-trac corner in Checkers for instance.
The problem if you don't find a forced cycle is: how do you prove it cannot exist?
The outcome doesn't affect the necessity of a rule like 3-fold: cycles may occur in a soft finite and a non-finite game alike.
Why is this interesting?
Endgames in Draughts variants are notoriously tricky. I've had the honor of working with one of the greatest endgame authorities in 10x10 Draught, Leo Springer, whose father, the late Ben Springer, was world champion from 1928-1931.
Leo made me see just how tricky endgames are, and he made a number problems for Hexdame and Dameo for which I'm ever grateful because he's so much better and faster than I am.
Knowing how tricky they are, and finally realizing the impact of compulsory alignment in endgames (I was a bit slow there I must confess, I've known square Pommel for some time without fully realizing the impact), I predict that this brand new monkey in the cage will make endgames a very rich and interesting class all by themselves.
That's why the finitude issue is important.
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #529 on: Jul 31st, 2011, 7:25am » |
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Black is black?
Here's a position, not all that different from the previous one, that may or may not be the black swan, but in any case is illustrative in terms of my previous post. I'll get to that as soon as I've finished walking with the dogs and in the meantime leave it for your consideration:
Done. Let's first establish that although none of the pieces are aligned with the opponent, the position is legal. It can for instance (but not only) occur after successive promotion on A6 and G4. Let's say it's white's turn.
Concerning exchange two things should be considered by the player initiating it:
1. A capturing captain isn't obliged to align, but rather obliged to stop immediately behind the jumped piece.
2. The resulting 1x1 position is hard finite and one players will win, so the initiating player must take care he's the one.
Considering that a sacifice makes no sense and barring symmetry, white has two moves available in the diagram, 1.A13 and 1.A14:
 
I'm making this up while going, I'm not sure where it leads, just intruiged and bored by sidetracking. Please correct me if I'm wrong, this isn't my forte.
1.A13?
Here black's exchange GB4 wins: 1...GB4 2.A3xC5 G9xB4
3.A6B7? B41+
3.A64? BG4+
3.A63? B49+
1.A14?
Here black's exchange G9B4 wins in a similar matter.
Conclusion: this subgame too is soft finite and gives no decisive answer regarding the game.
Another conclusion is that if a player in a one-on-one captains endgame is forced to align with an 'infield' opponent, he will lose: he can align only under cover of the boardedge, and the infielder takes the opposite end of the line.
Yet another conclusion is that Pommel, if not indeed free of draws (that's the issue here), makes draws very unlikely.
At the same time it is a real Draughts variant, so proving draws cannot occur (unless both players cooperate towards the result) would make it quite unique.
Cage is hard finite, but no Draughts variant, as Benedikt Rosenau and I argue in On the Evolution of Draughts variants.
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| « Last Edit: Jul 31st, 2011, 10:31am by christianF » |
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MHowe
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Re: Essay by Christian Freeling on inventing games
« Reply #530 on: Jul 31st, 2011, 11:22am » |
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Christian, Zillions almost immediately found a win in four for the new position you proposed, so you were correct that it was not the counterexample we're looking for.
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MHowe
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Re: Essay by Christian Freeling on inventing games
« Reply #531 on: Jul 31st, 2011, 11:40am » |
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on Jul 31st, 2011, 12:18am, MarkSteere wrote:
I may have been a tad hasty reading and responding to Christian's post. Being right all the time has made me complacent. Christian has accused me so many times of "misrepresenting" unspecified things, that if I've now finally, at long last, actually misrepresented something, I don't care.
That being said, and getting back to the subject, I love Christian's definition of soft finitude. I think it applies perfectly to a wide variety of gambling games. Trouble is, I've never seen an abstract game fitting the description.
Name one abstract game that has soft finitude. And I don't mean a trivialized non-game with two pieces on the board. If you can (truthfully and convincingly) do that, I'll stfu (on this particular topic).
Let's let Christian field this one, Mike. With your phenomenal mastery of logical debate, and I mean that in all sincerity, you might convince me of something illogical. |
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No worries, Mark. Looks some some possible examples have been put forward. And if I ever convinced you of something illogical, it would be accidental. And if we discovered it I would retract. Always just looking for the truth.
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #532 on: Jul 31st, 2011, 11:50am » |
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on Jul 31st, 2011, 11:22am, MHowe wrote:| Christian, Zillions almost immediately found a win in four for the new position you proposed, so you were correct that it was not the counterexample we're looking for. |
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Yes, it would, considering the ply depth. Handy tool, Zillions. Please keep experimenting or otherwise think deep and see if you can come up with a proof. I'm back to Sygo now because we've got another interesting game going, and to Havannah because the match is about a year away now and players were passing me by left and right in the ratings at LG, lately. I'm just back in the top-10 after dropping out of the top-20 recently.
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| « Last Edit: Jul 31st, 2011, 11:51am by christianF » |
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #533 on: Jul 31st, 2011, 12:39pm » |
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on Jul 31st, 2011, 2:09am, lightvector wrote:
If by "any one player can break a cycle and win" we mean instead that... |
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No, no, no, no, no. Christian's definition of "soft finitude" is succinct, objective, and very clear. (Did I just say that?) There's no room for equivocation.
"A game has soft finitude if and only if both players are required to cooperate to reach a draw."
[snip lightvector's exhaustive diatribe answering wrong question]
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #534 on: Jul 31st, 2011, 12:58pm » |
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MS: "I love Christian's definition of soft finitude... Trouble is, I've never seen an abstract game fitting the description."
on Jul 31st, 2011, 5:30am, christianF wrote:
That may be because you don't understand the definition. |
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It's too late Christian. You carelessly uttered something perfectly sensible.
"A game has soft finitude if and only if both players are required to cooperate to reach a draw."
You can't take it back now and inanify it.
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lightvector
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Re: Essay by Christian Freeling on inventing games
« Reply #535 on: Jul 31st, 2011, 1:08pm » |
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Actually, most of the games I presented do answer the right question, although I wasn't as clear as I could be about the definition.
A infinite cycle that neither player is willing to relent on, is in many games (such as Ataxx) considered to be a draw. Sometimes, the versions of the rule set may not explicitly state this case, of course, but the reason is precisely because it is not needed, because of this property - a draw can only be achieved by cooperation, that is, at least one player can always break a cycle to win. If the game provides no other ways to draw, then this definition, which I used, is equivalent to Christian's definition.
The statement "any one player can break a cycle and win", which I rejected, is actually the odd definition out. It would be very strange to require that for every cycle, *both* players have a way to deviate from that cycle and win. If the game contains only cycles where player A can deviate and win, but where player B would actually prefer to cycle (such as if deviating causes B to lose), then the game still has soft finitude, because cooperation is still required to achieve a draw. If player A refuses to cooperate, he can win, rather than draw.
Additionally, the definition "both players are required to cooperate to reach a draw" leaves unspecified whether this is to apply for every legal game state, or whether only from the opening game state. Interpreted the second way, it could also allow games that contain mandatory infinite cycles but where none of those infinite cycles can occur following optimal (or merely even "strong") play by the winning side from the starting position. Either definition is interesting.
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #536 on: Jul 31st, 2011, 1:19pm » |
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on Jul 31st, 2011, 7:25am, christianF wrote:
Got that right. Hard finitude, which defaults to the simpler "finitude" in abstract games, is not a badge of dishonor. Picture a state of the art American tank. Brutish yet sophisticated.
on Jul 31st, 2011, 7:25am, christianF wrote:
but no Draughts variant, as Benedikt Rosenau and I argue |
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This is a potentially serious issue. You're telling me that Cage doesn't meet the arbitrary, English language definition of "variant" by a couple of foreigners? lol
It must be a bragging point in Europe. "My English is so good, I have to instruct Americans on proper discourse, [chortle, guffaw]."
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MarkSteere
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Re: Essay by Christian Freeling on inventing games
« Reply #537 on: Jul 31st, 2011, 2:46pm » |
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on Jul 31st, 2011, 1:08pm, lightvector wrote:
Actually, most of the games I presented do answer the right question, |
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Lightvector, it isn't:
"A game has soft finitude if and only if both players are required to cooperate to reach a draw in optimal play on a tiny board, but, if, and, but, and, if, but, but, and, if......"
It's simply:
"A game has soft finitude if and only if both players are required to cooperate to reach a draw."
Are you saying that a non-cooperative, cyclic draw can't occur in Ataxx? Not to "put words in your mouth", Lightvector. I'm just trying to glean some meaning from among all the buts, ifs and ands.
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The_Jeh
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Re: Essay by Christian Freeling on inventing games
« Reply #538 on: Jul 31st, 2011, 3:12pm » |
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on Jul 31st, 2011, 1:08pm, lightvector wrote:
Additionally, the definition "both players are required to cooperate to reach a draw" leaves unspecified whether this is to apply for every legal game state, or whether only from the opening game state. Interpreted the second way, it could also allow games that contain mandatory infinite cycles but where none of those infinite cycles can occur following optimal (or merely even "strong") play by the winning side from the starting position. Either definition is interesting.
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You must also be careful with the word "cooperate." Two fallible players might both believe that to deviate from a cycle leads to their own loss, even if one of them actually has a forced win by doing so. In a sense, they are not trying to "cooperate," yet the game is not doing its job of judging their play. (Edit: Well, maybe it is punishing the player that could win for not seeing the win.) Presumably that is why Mark prefers hard finitude, not that I myself am attracted to it. But I know what you are trying to say by "cooperate."
Also, I would abstain from defining "soft finitude" in terms of "cycles." Endless shuffling is not "cyclical." Rather, I would say soft finitude exists if "a forced win exists from all reachable game positions, but from the initial position players could choose moves extending the game forever (for practical purposes)."
Finally, I might add that the term "soft finitude" itself does not include any hint that you are applying it only to games that are forced wins from every position. A finite game might also conclude in a draw, so you need to refer to more than just the game's finitude.
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| « Last Edit: Jul 31st, 2011, 3:32pm by The_Jeh » |
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christianF
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Re: Essay by Christian Freeling on inventing games
« Reply #539 on: Jul 31st, 2011, 3:38pm » |
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on Jul 31st, 2011, 1:19pm, MarkSteere wrote:| This is a potentially serious issue. You're telling me that Cage doesn't meet the arbitrary, English language definition of "variant" by a couple of foreigners? |
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Yes, we foreigners have the considered opinion that Draughts has a spirit. It's an important point indeed, so we've put it on our homepage. It's a spirit implemented one way or the other in every culture of the world.
We also have the considered opinion that compulsory capture is at the heart of its spirit. See for instance the chapters "Did Alquerque have compulsory capture?" and "I'll huff and I'll puff and I'll blow your house down" in the history section of "On the Evolution of Draughts Variants".
Cage has no compulsory capture and no spirit. It may be considered a shuffle variant or something, but not a draughts variant. All in the best of spirits, but that's our opinion  .
P.S. I'm surprised this comes up now. We've always stated it in the rules. Allow me to Quote:| "The absence of mandatory capture makes that the impact of captures is mainly local and their interaction in combinations all but absent. As we've argued elsewhere, compulsory capture is the soul of Draughts. A game without it is not Draughts. Cage is a forced march towards the center that can't get stuck. Like black and white marbles falling through a hole in a cone, one will eventually come out as last, and that's the winner. The important feature of the game is that it shows that a draughts type game can be decisive and drawless, but in Cage it comes at the price of loss of combinatorial power with all emphasis on strategy, a price most Draughts players are not eager to pay." |
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Pommel is so unique because it is a real draughts variant that appears to have soft finitude, which is very unusual for a draughts variant. Ossetian Draughts is hard finite and drawless and has no compulsory capture, but it has "no legal move" as its object. It's slow and lacks combinatorial power. It's a lot like Cage in that respect, but it needs far less rules.
Stapeldammen is a hard finite drawless column checkers variant that has compulsory capture, even precedence of majority capture, but it also settles for "no legal move".
Pommel requires elimination. I like that.
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| « Last Edit: Jul 31st, 2011, 4:13pm by christianF » |
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