Recommend
7 
 Thumb up
 Hide
96 Posts
Prev «  1 , 2 , 3 , 4  Next »   | 

Abstract Games» Forums » General

Subject: On the pie rule and its use to balance 2-player abstract games rss

Your Tags: Add tags
Popular Tags: [View All]
Eric Brosius
United States
Needham Heights
Massachusetts
flag msg tools
badge
My favorite 18xx game for six players is two games of 1846 with three players each.
Avatar
mbmbmbmbmb
ROMagister wrote:
Bidding for small variations of either starting state, in-game resources or end/victory conditions is very common in competitive play of wargames (which mostly are not abstract and symmetrical).

Komi bidding in Go is exactly this.

It works if the variable to bid on is fine-grained enough, like in Go or wargames.

In almost any game, you can bid on how much time the players have to finish the game, and this will be fine enough. So, for example, in Chess, players could bid on how many minutes they are willing to give up in order to play white. This would almost certainly lead to balanced games (though it might not solve the drawishness problem.)
2 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Luis Bolaños Mures
Spain
flag msg tools
designer
Avatar
mbmbmbmbmb
russ wrote:
christianF wrote:
But there are clear exceptions like Othello. But it's hard to tell if there's any turn-order imbalance in Othello in the first place, and if there is (of course there is: the tree, being 'completely determined' and all that, but what's it to humans?) then who has the 'advantage'?

(Minor tangential nitpick: it is possible (as far as we know) that optimal play leads to a tie in Othello, so then there'd be no turn order imbalance in Othello... right?)

Evidence points in that direction:

The Othello 8x8 game tree size is estimated at 10^54 nodes, and the number of legal positions is estimated at less than 10^28. Although not mathematically solved yet, a solution could possibly be found using intensive computation with top programs on fast parallel hardware or through distributed computation.

Some top programs have expanded their books for many years now. As a result, many lines are in practice draws or wins for either side. Regarding the three main openings of diagonal, perpendicular and parallel, it appears that both diagonal and perpendicular openings lead to drawing lines, while the parallel opening is a win for black. The drawing tree also seems bigger after the diagonal opening than after the perpendicular opening. The parallel opening has strong advantages for the black player, enabling him to always win in a perfect play. Although it is not proven yet, practically the game always ends in a draw if both players play perfectly. On standard games, using their opening book, top programs lose less than 1% of the time.
2 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Eric Brosius
United States
Needham Heights
Massachusetts
flag msg tools
badge
My favorite 18xx game for six players is two games of 1846 with three players each.
Avatar
mbmbmbmbmb
Eric Brosius wrote:
A player who wants to avoid well-trodden paths can try an opening move that is "off the book", at least when they are the one to make the first move.

As I think about it some more, I realize a potential problem with the pie rule. A player can choose an opening and study best play for both sides ahead of time. If they are selected to move first, they can make the move they studied and gain an advantage over their opponent, who is not likely to have concentrated on that one opening.

Of course, if the other player moves first, they can pull the same trick. So, in a game where opening preparation gives an advantage, the pie rule gives an advantage to the player who moves first.
1 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
christian freeling
Netherlands
flag msg tools
designer
Avatar
mbmb
Eric Brosius wrote:
So, in a game where opening preparation gives an advantage, the pie rule gives an advantage to the player who moves first.

Do you know The Marquisian Method?
It is a pie about a complete initial position instead of an initial move. It thrives on the 'drawback' of preparation: not a bug but a feature.

Quote:
At the end of the 18th century 10x10 Draughts was still in its infancy and the first wonders of the new game had just started to emerge. They included a very intricate endgame that was used by a not particularly good Draughts player to make some money on the market. He was known as 'the Marquise' and he knew every nook and cranny of the endgame. In the position White was to move and his bet was that he would win with white and draw with black. I'm not sure whether the balancing protocol I used in Swish & Squeeze and Pylyx and that I named after him is exclusively my own invention. But I don't know of any other games that use it.

The protocol can be used for games that allow a variable initial set-up in a placement stage, followed by a movement stage in which the actual goal is pursued. One player makes the complete initial set-up, then the other decides on a color or on playing first. If he chooses a color, his opponent may move first. If he chooses playing first, his opponent decides on color.

The method is very if not only suitable for games with a simple goal and tricky tactics. It gives one player the option of presenting an initial position of which he has studied 'every nook and cranny'. But he can't have it both ways and may end up not playing his preferred color or not moving first. So he needs a trick or two for either case. His opponent implicitly is aware of this and must try to unravel any dark tricks that may be woven into the position, before deciding.
1 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Nathan James
United States
Covington
Ohio
flag msg tools
designer
mbmbmb
Eric Brosius wrote:
So, in a game where opening preparation gives an advantage, the pie rule gives an advantage to the player who moves first.

This advantage is not really to be blamed on the pie rule, since without it, the first player might still prepare for his preferred opening. It is true that the pie rule does nothing to mitigate that advantage.
2 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
christian freeling
Netherlands
flag msg tools
designer
Avatar
mbmb
NJames wrote:
Eric Brosius wrote:
So, in a game where opening preparation gives an advantage, the pie rule gives an advantage to the player who moves first.

This advantage is not really to be blamed on the pie rule, since without it, the first player might still prepare for his preferred opening. It is true that the pie rule does nothing to mitigate that advantage.

A slight but inherent unfairness of the pie rule is also that it's easier to choose a piece than to cut the pie.
2 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Richard Moxham
United Kingdom
flag msg tools
designer
Avatar
mb

It seems to me that much of this discussion misses the point pretty comprehensively.

Assuming two players each blessed with perfect awareness, simple self-interest will ensure that every pie-ruled encounter achieves the closest possible approximation to parity. The fact that not every pair of flesh-and-blood adversaries will actually be so blessed is not the designer's problem, and certainly not a shortcoming of the rule.

In reality, of course, any real-life encounter you care to take is unbalanced by discrepancies of ability, understanding and experience.
2 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Joe Joyce
United States
Yonkers
New York
flag msg tools
designer
Avatar
mbmbmbmbmb
mocko wrote:

It seems to me that much of this discussion misses the point pretty comprehensively.

Assuming two players each blessed with perfect awareness, simple self-interest will ensure that every pie-ruled encounter achieves the closest possible approximation to parity. The fact that not every pair of flesh-and-blood adversaries will actually be so blessed is not the designer's problem, and certainly not a shortcoming of the rule.

In reality, of course, any real-life encounter you care to take is unbalanced by discrepancies of ability, understanding and experience.

I find myself agreeing with you (which probably just means you're wrong too, now.) You give a couple decent arguments; my reason is much simpler. I've always hated the pie rule. To me, needing it to balance a game seems philosophically to be just bad design being mitigated by a bad kludge. I always avoid pie rule games if I can. But then, I have a terrible memory, which is why I did better with variants than F.I.D.E. chess. And I'm used to having the occasional minority opinion. So let me offer another one: why not either ignore a small imbalance, or play 2 games, 1 on each side, as a balance if there must be one?
2 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Russ Williams
Poland
Wrocław
Dolny Śląsk
flag msg tools
designer
badge
Avatar
mbmbmb
joejoyce wrote:
So let me offer another one: why not either ignore a small imbalance, or play 2 games, 1 on each side, as a balance if there must be one?

If the imbalance is large,then the "play 2 games, 1 on each side" approach seems clearly bad to me. The result of a typical 2-game match will still be a tie (each player wins once as the very advantaged side).


Edited to add: also, this "just play it twice, switching sides" solution feels lazy and annoying to some people (including me). Sometimes I just want to play a game once, or don't have time to play it twice.
3 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
christian freeling
Netherlands
flag msg tools
designer
Avatar
mbmb
joejoyce wrote:
... my reason is much simpler. I've always hated the pie rule.

Much simpler indeed.
1 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Joe Joyce
United States
Yonkers
New York
flag msg tools
designer
Avatar
mbmbmbmbmb
russ wrote:
joejoyce wrote:
So let me offer another one: why not either ignore a small imbalance, or play 2 games, 1 on each side, as a balance if there must be one?

If the imbalance is large,then the "play 2 games, 1 on each side" approach seems clearly bad to me. The result of a typical 2-game match will still be a tie (each player wins once as the very advantaged side).


Edited to add: also, this "just play it twice, switching sides" solution feels lazy and annoying to some people (including me). Sometimes I just want to play a game once, or don't have time to play it twice.

Gonna make me work for this one, huh? Okay, the missing sentence is the winner of the '2 games' - actually 1 longer game - is the person who lasts longer as the disadvantaged side. If you beat me in 10 turns, all we play to in the next round is to 11, tops. Either you hold me under 10 moves and you win, I make an 11th move and win, or we both wound up with 10 moves, and it's a draw, or subsidiary methods of determining a win, like captures, are used. And fwiw, I do consider draws in general to be good outcomes. All my designs, abstract or not, allow draws. It's only when draws become the major to only result that they become a problem, imo.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Russ Williams
Poland
Wrocław
Dolny Śląsk
flag msg tools
designer
badge
Avatar
mbmbmb
joejoyce wrote:
Gonna make me work for this one, huh? Okay, the missing sentence is the winner of the '2 games' - actually 1 longer game - is the person who lasts longer as the disadvantaged side. If you beat me in 10 turns, all we play to in the next round is to 11, tops. Either you hold me under 10 moves and you win, I make an 11th move and win, or we both wound up with 10 moves, and it's a draw, or subsidiary methods of determining a win, like captures, is used.

That's one way to break ties (i.e. simply add various arbitrary tie-breakers), but I think it's very important to note that this has an unfortunate side effect: it changes the strategy of the core/individual game.

Now instead of simply making what you believe to be the best move to win the game, because "a win is a win", you have to factor in trying to win in the shortest number of turns, or with the most points possible, or whatever other arbitrary tie-breaker is imposed upon the match of two games. Many would find this an unpalatable kludge.

E.g. suppose that instead of using komi to compensate for first player advantage in Go, they said "play 2 games, and whoever wins by the bigger score difference wins the match of 2 games". That would noticeably alter how the game was played.
1 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Richard Moxham
United Kingdom
flag msg tools
designer
Avatar
mb
russ wrote:
joejoyce wrote:
Gonna make me work for this one, huh? Okay, the missing sentence is the winner of the '2 games' - actually 1 longer game - is the person who lasts longer as the disadvantaged side. If you beat me in 10 turns, all we play to in the next round is to 11, tops. Either you hold me under 10 moves and you win, I make an 11th move and win, or we both wound up with 10 moves, and it's a draw, or subsidiary methods of determining a win, like captures, is used.

That's one way to break ties (i.e. simply add various arbitrary tie-breakers), but I think it's very important to note that this has an unfortunate side effect: it changes the strategy of the core/individual game.

Now instead of simply making what you believe to be the best move to win the game, because "a win is a win", you have to factor in trying to win in the shortest number of turns, or with the most points possible, or whatever other arbitrary tie-breaker is imposed upon the match of two games. Many would find this an unpalatable kludge.

E.g. suppose that instead of using komi to compensate for first player advantage in Go, they said "play 2 games, and whoever wins by the bigger score difference wins the match of 2 games". That would noticeably alter how the game was played.

I do agree with you in essence, Russ, but I'm not sure what my reply should be to someone who said that, say, winning with the most aggregate points thereby becomes part of the game. Ultimately, couldn't the same sort of charge you invoke be levelled at the tie-break mechanism for Catchup - a device I'd have been proud to have thought of?

The other thing is that in a sport like soccer, most of the time you just play, and if it's a draw - well, you'd rather have won, but otherwise so what? But in certain tournaments there are local rules (away goals count double - how weird is that?) that simply become parameters which you have to take account of on that specific occasion.

2 
 Thumb up
0.05
 tip
 Hide
  • [+] Dice rolls
Russ Williams
Poland
Wrocław
Dolny Śląsk
flag msg tools
designer
badge
Avatar
mbmbmb
mocko wrote:
I do agree with you in essence, Russ, but I'm not sure what my reply should be to someone who said that, say, winning with the most aggregate points thereby becomes part of the game.


I'd say "Then you're changing the base game itself", which may not be something people who already like the game would want.

But indeed, if everyone's cool with changing the base game, then no problem.

I will say that even setting aside the concern of changing the base game, I think it's still a suboptimal kludge to require people to play the base game twice! That's not just tweaking a rule within the base game, but creating a new "meta" game which is a pair of plays of the original base game.

So "play twice switching sides and use this arbitrary tacked on tie-breaker" seems clearly more clunky to me than a tie breaker built into a single play of the game, like Catchup's.
2 
 Thumb up
0.05
 tip
 Hide
  • [+] Dice rolls
Joe Joyce
United States
Yonkers
New York
flag msg tools
designer
Avatar
mbmbmbmbmb
russ wrote:
joejoyce wrote:
Gonna make me work for this one, huh? Okay, the missing sentence is the winner of the '2 games' - actually 1 longer game - is the person who lasts longer as the disadvantaged side. If you beat me in 10 turns, all we play to in the next round is to 11, tops. Either you hold me under 10 moves and you win, I make an 11th move and win, or we both wound up with 10 moves, and it's a draw, or subsidiary methods of determining a win, like captures, is used.

That's one way to break ties (i.e. simply add various arbitrary tie-breakers), but I think it's very important to note that this has an unfortunate side effect: it changes the strategy of the core/individual game.

Now instead of simply making what you believe to be the best move to win the game, because "a win is a win", you have to factor in trying to win in the shortest number of turns, or with the most points possible, or whatever other arbitrary tie-breaker is imposed upon the match of two games. Many would find this an unpalatable kludge.

E.g. suppose that instead of using komi to compensate for first player advantage in Go, they said "play 2 games, and whoever wins by the bigger score difference wins the match of 2 games". That would noticeably alter how the game was played.

You are absolutely right in what you say, and I expect most will agree with you. I hold the minority opinion: so what if you have 2 games instead of 1, identical except for different winning conditions? That just gives you 2 ways to enjoy the game rather than 1. For me, that's a plus. I'm looking at GOmove now, have played all or part of the games from (1,1) GOmove through (6,6) GOmove, and find them all fascinating. Maybe it's an acquired taste. But I believe it's worth pounding hell out of games to see what happens when you stress, distort, and warp them, a 'test to destruction' kind of attitude. It's not something I do all that often, since it can be time-wasting and counterproductive, but when the right inspiration strikes, I get out the hammer. For the pie rule, if you must have one, do it the way checkers does. Put every reasonable opening set of moves on a set of cards, and draw one randomly to see your game set-up, *after* you've picked sides. Doesn't that obviate the common methods of "cheating" with pie rules?

*******************EDIT:
Time has marched on and there are 2 more comments, from mocko and Russ. I believe I've answered a bit of the questions asked, but not all. Yes. the base game is changed, and I'm in favor of that. I like 2 games for the price of 1.

I will respectfully disagree with you, Russ, that you are playing the base game twice if playing the same 2-player game on both sides. The foundational premise here is that the game is unbalanced, and that one side is predator and the other is prey. You are not playing the same game twice, but rather both non-matching halves of the same game. Different experience, different strategy...

Because of my particular prejudices, I argue that the reason so many games have a first-player advantage is that the gameboard is too small and the games are some initial maneuvering moves too short. Most chess games are a good example of this. They are set up with the action just starting, after all the maneuvering involved in coming to the field of battle. There's a reason wargames take 5 - 10 times as long as chess games generally. Okay, there are a few reasons, including more pieces and more rules, but a good wargame is designed to prevent first move advantages, even if it means tweaking the victory conditions. Which I, of course, favor.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Nathan James
United States
Covington
Ohio
flag msg tools
designer
mbmbmb
joejoyce wrote:
For the pie rule, if you must have one, do it the way checkers does. Put every reasonable opening set of moves on a set of cards, and draw one randomly to see your game set-up, *after* you've picked sides. Doesn't that obviate the common methods of "cheating" with pie rules?

OK this makes me wonder what problem you think the pie rule is solving, because this doesn't make any sense at all.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Joe Joyce
United States
Yonkers
New York
flag msg tools
designer
Avatar
mbmbmbmbmb
NJames wrote:
joejoyce wrote:
For the pie rule, if you must have one, do it the way checkers does. Put every reasonable opening set of moves on a set of cards, and draw one randomly to see your game set-up, *after* you've picked sides. Doesn't that obviate the common methods of "cheating" with pie rules?

OK this makes me wonder what problem you think the pie rule is solving, because this doesn't make any sense at all.

To the best of my understanding, checkers tourneys use randomly drawn cards with the first few moves already made to start the games because the 'opening book' is too good, giving the first player a major advantage. To fix this, checkers instituted a pie rule set of starting positions to make the game more fair. This is something I read a number of years back. I don't personally know, because I don't play checkers or draughts. It seems like a reasonable idea to fix a game that is well thought of but has a demonstrated first turn advantage. The card bit is a checkers version of chess960.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Peter Ward
msg tools
mb
joejoyce wrote:

To the best of my understanding, checkers tourneys use randomly drawn cards with the first few moves already made to start the games because the 'opening book' is too good, giving the first player a major advantage. To fix this, checkers instituted a pie rule set of starting positions to make the game more fair. This is something I read a number of years back. I don't personally know, because I don't play checkers or draughts. It seems like a reasonable idea to fix a game that is well thought of but has a demonstrated first turn advantage. The card bit is a checkers version of chess960.


I'm not sure how widespread it is (not being a draughts or checkers player either) but I think this is called "Two-Move or Three-Move Restriction" Checkers. Another variant is to simply remove a piece from each side at random from the front two rows before the first turn (11 Man Ballot).
1 
 Thumb up
0.02
 tip
 Hide
  • [+] Dice rolls
christian freeling
Netherlands
flag msg tools
designer
Avatar
mbmb
joejoyce wrote:
The card bit is a checkers version of chess960.

In that it is equally clumsy?
2 
 Thumb up
0.04
 tip
 Hide
  • [+] Dice rolls
Nathan James
United States
Covington
Ohio
flag msg tools
designer
mbmbmb
Ah. As I recall it, Checkers used the cards because best play produces a draw and the best players were able to do it. So the goal of the cards was not the goal of the pie rule.

Has anyone considered how the pie rule formalizes what might occur informally among players in love with a game like Hex? First posit that they love the game. Then that they play frequently and get decently skilled at it. But the challenge is that before too long they find that the first player wins after opening with F6, which is clearly the strongest move. What do they do? By agreement they stop opening with F6, and they continue exploring the game.

Pie rule is a protocol that formalizes that sort of approach to the game. And it does it in a way that guarantees the game goes on as long as there are any openings left to explore. Its quite remarkable for that.
3 
 Thumb up
0.06
 tip
 Hide
  • [+] Dice rolls
Russ Williams
Poland
Wrocław
Dolny Śląsk
flag msg tools
designer
badge
Avatar
mbmbmb
joejoyce wrote:
I will respectfully disagree with you, Russ, that you are playing the base game twice if playing the same 2-player game on both sides. The foundational premise here is that the game is unbalanced, and that one side is predator and the other is prey. You are not playing the same game twice, but rather both non-matching halves of the same game. Different experience, different strategy...


Hmm, but where do you draw the line? Suppose we take a game considered to be pretty well balanced, e.g. Shogi or Go with komi. There's still SOME kind (very small and hard to determine with certainty) advantage for the first player or the second player. So by the same reasoning, we "should" play 2 games of Shogi or Go, with some arbitrary tie-breaker tacked on (e.g. who mated in the fewest moves or who won by the bigger point margin).

But wouldn't that seem like clearly playing Shogi or Go twice for no good reason, with some arbitrary strategy-changing incentives unnecessarily bolted onto the base game?

So at what point does it became a great enjoyable feature (in your view) instead of unnecessary redundant nonsense to require "play it twice, switching sides, and then apply this new tie-breaker method"? 51-49 advantage for one player? 55-45? 60-40? Something else?
1 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Joe Joyce
United States
Yonkers
New York
flag msg tools
designer
Avatar
mbmbmbmbmb
russ wrote:
joejoyce wrote:
I will respectfully disagree with you, Russ, that you are playing the base game twice if playing the same 2-player game on both sides. The foundational premise here is that the game is unbalanced, and that one side is predator and the other is prey. You are not playing the same game twice, but rather both non-matching halves of the same game. Different experience, different strategy...


Hmm, but where do you draw the line? Suppose we take a game considered to be pretty well balanced, e.g. Shogi or Go with komi. There's still SOME kind (very small and hard to determine with certainty) advantage for the first player or the second player. So by the same reasoning, we "should" play 2 games of Shogi or Go, with some arbitrary tie-breaker tacked on (e.g. who mated in the fewest moves or who won by the bigger point margin).

But wouldn't that seem like clearly playing Shogi or Go twice for no good reason, with some arbitrary strategy-changing incentives unnecessarily bolted onto the base game?

So at what point does it became a great enjoyable feature (in your view) instead of unnecessary redundant nonsense to require "play it twice, switching sides, and then apply this new tie-breaker method"? 51-49 advantage for one player? 55-45? 60-40? Something else?

How often does the prey eat the predator? ;)

That's actually a reasonably serious question, and it contains the outline of the answer to your question. Of course, like all greatly debatable answers, it lies in a gray area that I don't see could start any higher than roughly 99:1, and drop from there. You may see it at 90:10, but I think that sort of idea requires 2 orders of magnitude anyhow, and maybe more than 2, smaller.

And I would point out that the recent chess championship featured 12 games, 6 with each color for each player, all draws. The pressure there seems to be to not lose, rather than to win. In the game I'm talking of, the pressure is purely on winning, for both halves of the game, because the pressure to not lose is incorporated into the game structure. As predator you will be attacking as fast, hard, and often as you can, and as prey you will be ducking, dodging, running and when necessary fighting for your life as hard as you can... what's not to like?
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Joe Joyce
United States
Yonkers
New York
flag msg tools
designer
Avatar
mbmbmbmbmb
NJames wrote:
Ah. As I recall it, Checkers used the cards because best play produces a draw and the best players were able to do it. So the goal of the cards was not the goal of the pie rule.

Has anyone considered how the pie rule formalizes what might occur informally among players in love with a game like Hex? First posit that they love the game. Then that they play frequently and get decently skilled at it. But the challenge is that before too long they find that the first player wins after opening with F6, which is clearly the strongest move. What do they do? By agreement they stop opening with F6, and they continue exploring the game.

Pie rule is a protocol that formalizes that sort of approach to the game. And it does it in a way that guarantees the game goes on as long as there are any openings left to explore. Its quite remarkable for that.

Grin, what you're saying is that best play in checkers led to a draw, and to fix this, the game had to be slightly broken, just enough to put the issue in doubt until analysis solves those variant games of checkers, each of which will be win/lose or draw. And while the argument is similar with your Hex example, it leads me to ask what happens if you remove the F6 hex from the gameboard? Does that solve the 'problem'? (Or is your example just a convenient fiction for illustrative purposes?)

 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Nathan James
United States
Covington
Ohio
flag msg tools
designer
mbmbmb
joejoyce wrote:
what happens if you remove the F6 hex from the gameboard?

Well, if the hex was unplayable the game would probably end in a draw.

Actually, maybe this is Nick's dream game. You know, the one that draws with perfect play, but in practice never draws. Except F6 would be too easy. Have to try A1 or something.
2 
 Thumb up
0.02
 tip
 Hide
  • [+] Dice rolls
David Bush
United States
Lexington
Virginia
flag msg tools
designer
badge
Avatar
mbmbmbmbmb
joejoyce wrote:
NJames wrote:
Ah. As I recall it, Checkers used the cards because best play produces a draw and the best players were able to do it. So the goal of the cards was not the goal of the pie rule.

Has anyone considered how the pie rule formalizes what might occur informally among players in love with a game like Hex? First posit that they love the game. Then that they play frequently and get decently skilled at it. But the challenge is that before too long they find that the first player wins after opening with F6, which is clearly the strongest move. What do they do? By agreement they stop opening with F6, and they continue exploring the game.

Pie rule is a protocol that formalizes that sort of approach to the game. And it does it in a way that guarantees the game goes on as long as there are any openings left to explore. Its quite remarkable for that.

Grin, what you're saying is that best play in checkers led to a draw, and to fix this, the game had to be slightly broken, just enough to put the issue in doubt until analysis solves those variant games of checkers, each of which will be win/lose or draw. And while the argument is similar with your Hex example, it leads me to ask what happens if you remove the F6 hex from the gameboard? Does that solve the 'problem'? (Or is your example just a convenient fiction for illustrative purposes?)


Removing F6 from playable cells for the entire game is very different from removing it from the possible first move cells. It does nothing about first player imbalance, which is the problem we are talking about in this thread. I'm not trying to be rude, but are you talking about some other problem?
1 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Prev «  1 , 2 , 3 , 4  Next »   |