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alisontate

Posts: 157
Registered: Nov 27, 2008
Age: 30
Re: Universal first mover advantage
Posted: Sep 19, 2009, 5:38 PM

Removed by Alison


Message was edited by: alisontate at Sep 22, 2009 5:29 AM



up2ng

Posts: 542
Registered: May 9, 2002
From: Northeast USA
Age: 38
Re: Universal first mover advantage
Posted: Sep 20, 2009, 7:20 AM

VVVVVVV
1. If you are firm on the idea that a perfectly balanced game IS in fact a draw because it would go on forever (your apparent definition of a draw), and we are excluding games with draws, then of course my position makes no sense since balanced games (while perhaps possible in theory) are excluded.
^^^^^^^

Hmm, while reading over this new post and subsequent postings between you and Zoey I'm starting to think that our positions actually agree after all. I could have sworn that you had written somewhere previously that it should be possible for a snapshot position in a turn-based game with NO draws or infinite results to be balanced in the sense that either player can still win with perfect play. You have since clearly stated that you agree that this is not possible. Either your position has changed slightly along the way or we were not understanding what you were trying to argue in the beginning.

I continue to believe that in turn-based games that will end in victory with perfect play, one side OR the other always has the advantage -- there is never a balanced position. It seems we are now in agreement on this.

VVVVVVV
2. In your second paragraph about looking at things from the back end, you have simply assumed a winner (the last player to move) and worked backwards to find the unsurprising result that there was an advantage.
^^^^^^^

Actually, I'm not sure you were reading this or following the thought process of his argument here in the same way that I was. I thought this was actually a very good example and was similar to one of the ways that I was trying to explain how I view the whole thing (Watsu and I seem to be on the same page on this topic).

VVVVVVV
The intent of my comment was to refer to all possible two player zero sum games of which there are those thousands that exist and an infinite variety that could exist but don?t. ... but I think we should not be quick to dismiss the possibility that in just one of the infinity of other possible (non Pente) game designs, that a game situation could be constructed that meets the requirements of my thought experiment.
^^^^^^^

Yes, I didn't mean to keep coming back to Pente except that it made for some good examples that we would all be able to follow because we are all familiar with the game so it provided good context. While thinking of your questions I was trying to think of lots of different types of turn-based games such as Stratego, Go, Chess, etc. Many of these allow for draws under certain conditions (in many cases to prevent infinite play -- in Chess a King vs. a King, you could continue on making lots of different moves but no one can ever win, so the players just recognize this and declare the position a Draw). Similarly, I thought of other types of NON-turn-based games such Diplomacy where, at least the way I played it BITD, everyone declared their moves at the same time on little scraps of paper, and these would all be reconciled afterwards. Now, in Diplomacy there may be some inherant geographical advantages, but one might design another game with these same mechanics which, in theory, could yield a balanced game. But this game is NOT turn-based! To me, that is the whole key. Turn-based games by their very nature are and remain unbalanced.

VVVVVVV
It should not be a surprise therefore that we have a sense of there being something about turn-based games that gives an insurmountable advantage to one player with perfect play ? the popular games we play were designed that way.
^^^^^^^

I can see your point on this. Certainly, many games have been designed in such a way that the result is that generally someone achieves victory within a reasonable amount of time with respect to our every day lives. However, I would say that these games have generally been designed with enough complexity that humans who play it to completion within a reasonable amount of time cannot generally be expected to play it perfectly. These varying degrees of human skill and human error (and subsequent human learning) is part of what makes these games interesting. In this discussion we are talking about the theoretical scenario of all players always playing perfectly. This is unrealistic, but it serves as an important assumption when trying to determine whether a given game state has an inherant advantage. Because of the complexity of many games, these advantages are small enough that humans cannot be expected to always have the skill to capitalize upon it and it is even beyond our current computer capability to "solve" these games through brute force. But just because we are not able to demonstrate that there is a definitive advantage does not mean that we cannot "proove" conceptually that there must be one.

VVVVVVV
I know that you strongly believe that it would not matter if the game took 1,000,000 moves to complete because there is an inherent imbalance in turn based games that cannot be overcome.
^^^^^^^

Yes, if the game will definitely end in victory within these 1,000,000 moves, I'm saying that during each and every position along the way SOMEONE had the advantage whereby with perfect play victory is guaranteed. If, instead, the game has a possibility of continuing infinitely, that's a little different. I was still maintaining that in that scenario one player still has an advantage, under a slightly different definition -- but now I'm rethinking that as I'll talk about next.


VVVVVVVV
I have played many games of chess where the only moves available make the situation worse or just keep things at the state they are.
^^^^^^^^

Your chess example here has forced me to rethink what I had said earlier about games that can go on indefinitely. I too have played games of chess where a couple of things might happen:

1. Perpetual check: One player is all set to win by checkmate on his next move. Perhaps the other player left his king behind his row of castled pawns and he has a rook ready to move to the last rank and force checkmate. Even better, assume it's some other scenario even more unavoidable -- that player WILL win by checkmate on his next move. But, for now, the opponent has found a way to continuously put him into check, over and over, never a chance to force a checkmate or to prevent losing by checkmate unless continuing to keep his opponent in check, over and over. This is each player's best (perfect) move at this time, and by continuing to perform these moves the game will never end (a Draw is eventually offered and accepted).

2. Repeated position: I can't describe a specific example, but sometimes, even when there are still lots of pieces on the board, the best move for each player is to just move a piece back and forth into the same two positions over and over, each one defending and simultaneously counter-punching the other's threats. If either player did NOT play this sequence of moves, they would move into a deadly position and lose quickly. Each player is forced to defend against losing in the near future and thus the position is repeated 3 times, which by rule is a Draw (if it were not a rule, the game would go on forever repeating this position).

I have a hard time calling either of these positions "balanced" although it is clear that there will be no winner with perfect play. In example 1, perhaps one player has only a couple of pieces left and has literally no way of winning the game. BUT, in the given position, he somehow is able to keep his opponent in perpetual check. Player B, however, has a huge army of pieces remaining and has literally dozens of ways to win the game in the very near future -- IF he was just able to avoid being put into Check. This really feels to me like Player B has the advantage in this position, but it's just not enough of an advantage to force a win -- therefore the game will end in a Draw (or it will go on forever and so one player will offer a Draw and it will be accepted). I understand that in the sense that neither player can win, there is no advantage, but that doesn't sit right with me -- which is why I was saying earlier that my definition of advantage might differ from yours, at least with respect to games that can end in a Draw or go on forever.

VVVVVVV
For me it all comes down to one thing. As I said to watsu, if you allow that an infinite and balanced game is not actually a draw, then I think my proposition is correct for the reasons stated. If you consider infinite balanced games to be draws then my proposition cannot stand. I contend that infinite balanced games are not draws, but that is just my opinion.
^^^^^^^

Yes, it appears to me that we actually agree on the heart of the matter at this point. Flushing out the boundary cases to me is just details. I have one view on what it means to have an advantage in an infinite game that is different from the way you see it, but to me this is just a special case and in general we agree on the main point, which deals with Turn-Based Games with consistant, universal rules that does not involve chance or randomness, and that cannot end in a Draw and will not go on forever with perfect play. In that type of game, (as agreed) every position along the way is out of balance and one player or the other has the advantage.

alisontate

Posts: 157
Registered: Nov 27, 2008
Age: 30
Apology to zoey
Posted: Sep 22, 2009, 11:54 AM

Hi everyone,

Zoey and I have had a talk today and afterwards I have given thought to how to approach this. Although during our talk we did not see eye to eye on everything I can say that enough is enough, and it is time to move forward.

I noticed coming in here that zoey has put line-through text on his entries relating to our disagreement. I don't know how to do this so I have just deleted the text completely.

Anyway, I want to say just two things. First, at the time I believed I was initially offering a peaceful outcome to a situation where a disagreement was in place. Later, I felt that this had been taken badly and I felt it had been thrown back at me and I found this upsetting. What I wrote next reflected what I believed to be an appropriate response at the time.

The reality is that zoey's interpretation of my words was different to what I had intended to convey and the effect was the opposite of what I intended. I then overreacted to his words and the whole thing escalated.

I read back over all of this again tonight after speaking with zoey, and I now realise more from his side about how he must have seen my words. I also know that I felt I was being accused of deception and being tricky and I felt that my attempt at conciliation had been rejected, so I reacted.

I know that I have said some things that I shouldn't have and that I have deeply upset zoey. I think there was misunderstanding on both our parts, and this is unfortunate, and I have learned a big lesson from this.

So zoey, this is my public apology. I am deeply sorry for the hurt I have caused you. I apologise not only for what I said but also because I should have spoken to you privately. Also, despite my words I have tremendous admiration for you both on a personal and intellectual level. Please accept my sincere apology.

Regards
Alison

up2ng

Posts: 542
Registered: May 9, 2002
From: Northeast USA
Age: 38
Re: Apology to zoey
Posted: Sep 22, 2009, 11:53 PM

I've seen flame wars on other forums that can get a lot worse than what I saw here. There's something about belonging to an online community that can become emotional and at the same time it provides a degree of anonymity -- a combination which can often cause more heated conflicts than might otherwise happen in person, for example.

My two cents is just try not to take these things personally when it happens. These sites are here for everyone to have fun and be entertained. But at the same time, everyone has a responsibility as part of this community to bahave in a friendly manner and in accordance with the site rules.

Remember that there are very few admins at this particular site and basically no one is actively monitoring these forums. It is up to the participants to police themselves. It would be a shame for an entire section of the site, such as the forums, to get shut down due to bad behavior by a few individuals (I'm speaking generally here, not about you two). So far, outside of a few incidents that I can remember, this really has not been a problem. The people in this community are generally very nice people and I hope it stays that way.

So, in short, be mindful of your OWN actions, and try not to take things here too seriously.

zoeyk

Posts: 2,007
Registered: Mar 4, 2007
From: San Francisco
Age: 42
Home page
No luck, draw, infinity = one side will have the advantage over the other.
Posted: Sep 26, 2009, 12:59 AM

thank you Alison for your apology. I too am deeply sorry that this occurred. and I apologize for my part in it. I'm just glad we were both able to delete the posts and move forward.

and up2ng, i agree with your post about flame wars.
well said.

i look forward to many more debates on game theories and stuff...

~zoey

Scire hostis animum - Intelligere ludum - Nosce te ipsum - Prima moventur conciliat - Nolite errare
alisontate

Posts: 157
Registered: Nov 27, 2008
Age: 30
Re: Apology to zoey
Posted: Sep 26, 2009, 1:52 AM

Thank you zoey. I value your friendship and am very glad we can more on.


Also thanks up2ng for your post which was very true.

I will respond to your previous post shortly up2ng, as although there has possibly been a slight convergence in our views, I don't think we are as close as you suggest

~Alison

galmacky

Posts: 3
Registered: Dec 10, 2008
From: Seoul
Age: 28
Re: Universal first mover advantage
Posted: Sep 30, 2009, 4:16 PM

Here is my take on this issue.

As others pointed out earlier,

1. It is wrong to say that first-mover always wins in a perfectly balance game since it is a contradiction.

2. There might be draw cases for Pente.
possible, but not proven
- we may have to call certain infinite chain of moves as draw where each player has to put their stones in certain repeating patterns in order not to lose.
- might be only possible beyond the 19x19 limit

Anyways,

3. It is not computable with the current computer machines whether white has a perfect winning path or not. Or it has not been tried with enough resources yet.

4. If first-mover always has a non-losing path in a game, then he/she will at least not lose. For pente and other complex games, this has not been proved yet. (But we're almost sure.)

5. I think Z might want to correct his statement as follows:
For any symmetric two-player game where there is no obvious gain for one player except for the order of playing, first-mover always wins.

I think this might be provable if we can develop 'no obvious gain' into formal set of rules for game rule statement.

zoeyk

Posts: 2,007
Registered: Mar 4, 2007
From: San Francisco
Age: 42
Home page
No luck, draw, infinity = one side will have the advantage over the other.
Posted: Oct 1, 2009, 8:05 AM

galmacky;
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
5. I think Z might want to correct his statement as follows:
For any symmetric two-player game where there is no obvious gain for one player except for the order of playing, first-mover always wins.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^



zoey;
what statement might i want to correct?
and the following is a copy n paste from my very first post in this thread, for the record.







vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
alison;
Z further stated that if there is no element of chance, and no draws possible that the first mover must always win.




zoey;
I Never said in "all games" that the first mover wins.

i said that if there is no draw, and no luck, that one side must have an advantage,..unless the game is not allowed to ever end,..in example; a game based on "Infinity".

you said that there could be rules where No Sides have a advantage, and that "draws" and "luck" do Not play a factor in the victory.

unless infinity is involved this is impossible to be true in my opinion, and possibly is a fact.
and actually if its infinity then obviously there is no victory,.Ever...

further more i agree that it is very easy to give player 2 the advantage by modifying rules (like swap),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^






its possible that what you are meaning has gone over my head.

Z

Scire hostis animum - Intelligere ludum - Nosce te ipsum - Prima moventur conciliat - Nolite errare
zoeyk

Posts: 2,007
Registered: Mar 4, 2007
From: San Francisco
Age: 42
Home page
Re: No luck, draw, infinity = one side will have the advantage over the other.
Posted: Oct 1, 2009, 8:56 AM




back to advantages existing with in a race between 2 players racing the length of infinity.
never ending,...
one car clearly is a little ahead then the other.
so from the observers perspective this looks like the lead player(car) has the advantage.
how ever since infinity has no containable value,
and no value is greater than infinity,
and if both players must travel the equal distance of infinity,
no matter how far they are from each other,
they must always be exactly the same distance from the finish line (which is never),
thus no player was ever even one millimeter more advanced than the other.
in infinity all positions have the same position and value.
length is determined by measuring from one point to another point.
infinity doesn't have 2 points.
it either has one or it has none, meaning a start with no finish (alpha yes, but no omega,
or something that has no beginning and has no ending. (no alpha, and no omega)

further more, my opinion is that draw and infinity are the same thing from my point of view.



(i predict someone will disagree with the above said.)

Scire hostis animum - Intelligere ludum - Nosce te ipsum - Prima moventur conciliat - Nolite errare
alisontate

Posts: 157
Registered: Nov 27, 2008
Age: 30
Re: No luck, draw, infinity = one side will have the advantage over the other.
Posted: Nov 16, 2009, 4:06 PM

zoey, you are right in your prediction, someone will disagree with you!

A reading of the work of Cantor and also of Zeno may inform and also fascinate you.

I caution against trying to apply continuous functions to discrete problems as they are not analagous. A continuously moving vehicle is not representative of the step-wise, incremental, and descrete value function of a zero sum two player game. However I will conceed that the introduction of this schema, although not a corrolary to a descrete game, may offer a counterpoint that brings clarity to aspects of the original schema.

To note just a couple of issues with your example: First, the comparative distance to finish is irrelevant in a race until that distance is zero, and also inapplicable to two player board games, so raising the problem of measuring the distance to finish as a coup de gras fails on the grounds of being both erroneous and invalid. Secondly, if a car race is infinite and that the only way to win is to cross the finish line then you have designed a situation where the only way a player can win is to cross the line first. In a zero sum game, we always have the possibility of one or other player winning without the game going for an infinite amount of time, and by definition a win precludes infinity. So in this case infinity is an outcome but not the only possible outcome. Thirdly, since such an event (an infinite race) cannot by its very definition have any other possible outcome but to never complete, it would not matter how far ahead one driver was of the other because the race can never end. But this relative 'distance' is important in zero sum games and it is the very thing that causes the game to end in a win or loss.

Up2ng: In your last post you stated that we had agreed that a no-advantage position within a game is not possible. I had not agreed to that, so I assume you have misunderstood my points on this, or perhaps I wasn't clear enough. In fact I am saying that it must be possible for a non-advantagious position to be reached.


Message was edited by: alisontate at Nov 17, 2009 6:58 AM


up2ng

Posts: 542
Registered: May 9, 2002
From: Northeast USA
Age: 38
Re: No luck, draw, infinity = one side will have the advantage over the other.
Posted: Nov 16, 2009, 9:51 PM

My mistake, Alison. I quoted you directly and talked about why I thought we agreed on certain points, but perhaps I misinterpreted what you had written.

I've run out of ways to explain my viewpoint on this problem and I feel like I've read the opposing viewpoints carefully and have not been convinced, so I will just agree to disagree. I encourage you to read through my points again as well.

A quick point about my Chess examples. I was using Chess as a common context to describe a couple of scenarios which ended up in infinite positions (and a Draw would be agreed to). First, I'm NOT sure that this would happen in Chess if both players played PERFECTLY from the beginning -- but I'm not a chess expert. Secondly, again this describes positions during games that can be infinite or end in Draws. In games that cannot have those outcomes, these Chess examples do not apply.

Lastly, it's interesting to me that you've harped on the fact that this is a discreet, and not a continuous, problem. This is actually a main point in support of my position -- the fact that it is inherantly discreet. I was describing this as "the nature of Turn-Based games", etc, but discreet is an even better description.

During a turn based game, one player has the opportunity to completely change the position of the game in favor of that player while the other player's interest remains unchanged. It makes no sense for a game position to be balanced so that making the next (perfect) move causes absolutely no effect and the position remains balanced -- then the other player does the same, and again, there is no effect and the position remains balanced. Otherwise, the original position was not balanced in the first place. Likewise, there is no way to get to this balanced position during a perfectly played game unless the game actually started out perfectly balanced and remains that way for every move throughout the game -- and yet if there are no infinite games and no Draws, this is just not possible. I will not be convinced otherwise.

alisontate

Posts: 157
Registered: Nov 27, 2008
Age: 30
Re: No luck, draw, infinity = one side will have the advantage over the other.
Posted: Nov 17, 2009, 12:38 PM

up2ng

I understand how you feel and well, getting to a point in a complex discussion where any of us feel we are making little ground is frustrating and can detract from the enjoyment if we go too far. So I am happy to leave it there knowing that out of this conversation many interesting thoughts on all sides have emerged.

I have found it interesting to read back over all of the posts again this evening. But after leaving it for a few weeks, although my opinion remains the same, whole new aspects of the discussion have opened up in my mind relating to points written by all contributors. I guess we could go on forever potentially - unless of course one of us laid out a clinching proof!

Despite the above comments, I am still happy, upon your invitation, to post one last point by point response to all of you posts' points. If not, then know that at any time in the future you want to discuss this or any other topic feel free to send me a message.

So, thanks again to you and the others for a very enjoyable and interesting discussion.

Regards
Alison


Message was edited by: alisontate at Nov 17, 2009 11:05 PM


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