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Subject: Balancing protocols rss

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christian freeling
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I'm interested in which balancing protocols are used in two-player abstract strategy games, so I've made a provisional list.

1. Playing the same number of games with black and white
This would seem to be the only 100% generic protocol, applicable to all games.

2. The swap rule
This one is 'fairly generic'. It is certainly not applicable to all games, but it can sometimes be modified to suit games that show a certain reluctancy to it or have obvious means to refine it, for instance by incorporating positions in which more than one move has been made.

3. Komi
If the object implies scoring points, assigning a number of points to compensate for turn order advantage is the quick and dirty solution. Somewhat more elegant is to make the actual number of points subject to a swap.

4. The 1-2-2... move protocol
For placement games this protocol gives both players a one-placement lead after each turn. I'm not sure about the existence of movement games using it.

5. The 1-2-3-4... move protocol
Not very inviting for placement games, it would seem. Movement games have progressive Chess as a prime example. It's questionable though whether it's actually a balancing protocol.

6. Negative feedback
In some games actions may be made that are (or at least would appear) advantageous in terms of the goal, but only at the cost of a simultaneous disadvantage, thus causing a dilemma. Games that come to mind are Catchup, Yinsh and Hare & Tortoise.

7. The one-bound-one-free opening protocol
This is a placement protocol that results in an 'initial position' for a subsequent game that itself may have a placement- or a movement protocol, or a combination of both. It divides a game in two separate phases although a 'bridging factor' may be present, like capture being possible in Io in both phases. It operates equally well under c4, c6 and c8 connectivity.

The 'balancing aspect' is rooted in the opaqueness of the first phase. Although placement easily adapts to the overall object whatever it is, an attempt to be the first (or second) player to move in the second phase isn't so easy and the clouds are not really lifting till late in that first phase.

8. The Symple move protocol
The move protocol that finds its origin in Symple has an embedded balancing mechanism with a high resolution. Applicability may be limited to placement games with a territorial or a connectivity goal.

I'm pretty sure I missed one or two, that's why I post it here. Any addition or comment is welcome. I plan a more extensive coverage of the subject to get me through the winter. "Make the Netherlands skate again" isn't really my policy.
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Richard Moxham
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Christian, in my sketch-for-a-game Dreikaiserbund I proposed a device called "the amulet" - strictly speaking not a mechanism in itself but rather a marker to designate the current holder of an (exceptional) right. The point was that the right, once exercised by the holder, would pass over to his opponent, but that the 'meta-right' to refrain from exercising it would therefore be a kind of alternative advantage in its own way. Obviously the amulet would begin life in the custody of whichever player was supposedly disadvantaged by the turn order.

Refinements are possible in cases where the initial disadvantage is held to be particularly severe. An earlier draft of Dreikaiserbund featured a two-sided amulet with a double eye on one side and a single on the other. At the start of the game, the double eye was displayed, signifying the entitlement of the initial holder (but not his opponent) to exercise the special right twice on its first spell in his custody (but never again). To keep track of this the amulet was inverted after his first use of it, and thereafter the single eye was always uppermost.

There's a sense in which all this might be thought to be covered by your Negative Feedback, but I feel that would make the category broader than is ideal for optimum usefulness. A passing back and forth of the selfsame right seems to me to distinguish the mechanism from that of Catchup in a manner worth registering. I confess to not being familiar with either Yinsh or Hare & Tortoise.

 
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David Buckley
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Two more that spring to mind:

1) Komi auction. Similar to komi swap but has the advantage of not putting the onus all on one player.

2) The Unlur balancing mechanism. Only applicable to games with asymmetric forces. Players take turns playing for black until one player decides to pass. Their opponent then becomes white and makes the next move.
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christian freeling
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mocko wrote:

Christian, in my sketch-for-a-game Dreikaiserbund I proposed a device called "the amulet" - strictly speaking not a mechanism in itself but rather a marker to designate the current holder of an (exceptional) right. The point was that the right, once exercised by the holder, would pass over to his opponent, but that the 'meta-right' to refrain from exercising it would therefore be a kind of alternative advantage in its own way. Obviously the amulet would begin life in the custody of whichever player was supposedly disadvantaged by the turn order.

...

There's a sense in which all this might be thought to be covered by your Negative Feedback, but I feel that would make the category broader than is ideal for optimum usefulness. A passing back and forth of the selfsame right seems to me to distinguish the mechanism from that of Catchup in a manner worth registering. I confess to not being familiar with either Yinsh or Hare & Tortoise.

I'm not sure how considering this to be covered by 'negative feedback' would make that category less useful. To me it seems yet another way to implement negative feedback, different from the other three mentioned. These also have very different implementations. It is certainly worth mentioning as another example.
 
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Craig Duncan
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A couple of comments:

Regarding swap rules: It's probably worth mentioning the possibility of multiple-move swap rules, e.g. the first player places three moves on the board (black-white-black) and the other player chooses colors. (I've never liked these but I suppose some games may require something stronger than a one-move swap rule, e.g. Projex.)

EDIT: Re-reading Christian's OP I see he has already mentioned multiple move swaps. I need to be a better reader.

Regarding 12*: For games that don't really support 2-move turns, or that become a fundamentally different game with 2-move turns (e.g. chess, I should think), I have heard of the following radical option: Play three simultaneous games of the game in question using 12*: the first player gets one move on turn 1, and thereafter each player gets to make two moves on each turn, with the restriction that the two moves can't be in the same game. The player who wins 2 of the 3 games is the overall winner.
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christian freeling
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Buckersuk wrote:
Two more that spring to mind:

1) Komi auction. Similar to komi swap but has the advantage of not putting the onus all on one player.


I can see how that works and it is certainly worth mentioning.

Buckersuk wrote:
2) The Unlur balancing mechanism. Only applicable to games with asymmetric forces. Players take turns playing for black until one player decides to pass. Their opponent then becomes white and makes the next move.

And this one too, although asymmetric games have never had much of my attention. Come to think of it, precisely because of the balancing issues involved. I think this one is about as generic as it gets in this category.
 
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David Buckley
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christianF wrote:
I'm interested in which balancing protocols are used in two-player abstract strategy games, so I've made a provisional list.

1. Playing the same number of games with black and white
This would seem to be the only 100% generic protocol, applicable to all games.



Unsatisfactory for games with a naturally large first player advantage. A variation would be that the winner is the player who scores the most points after an even number of rounds with alternating colours. The downside is that it implies playing every game out to the bitter end. I like to call this the "Cricket Method".

Quote:

2. The swap rule
This one is 'fairly generic'. It is certainly not applicable to all games, but it can sometimes be modified to suit games that show a certain reluctancy to it or have obvious means to refine it, for instance by incorporating positions in which more than one move has been made.


Overrated in my opinion, particularly in games with variable set up. The job of finding a first move which offers balanced chances seems harder than the job of judging which side the chosen move should favour.

Quote:

3. Komi
If the object implies scoring points, assigning a number of points to compensate for turn order advantage is the quick and dirty solution. Somewhat more elegant is to make the actual number of points subject to a swap.

4. The 1-2-2... move protocol
For placement games this protocol gives both players a one-placement lead after each turn. I'm not sure about the existence of movement games using it.


An interesting point. I can't think of any movement games that use this protocol either. It seems to work well in the placement games that I know of.

Quote:

5. The 1-2-3-4... move protocol
Not very inviting for placement games, it would seem. Movement games have progressive Chess as a prime example. It's questionable though whether it's actually a balancing protocol.


I strongly suspect that Progressive Chess is not a balanced game but I'm not sure which side is supposed to win.

Quote:

6. Negative feedback
In some games actions may be made that are (or at least would appear) advantageous in terms of the goal, but only at the cost of a simultaneous disadvantage, thus causing a dilemma. Games that come to mind are Catchup, Yinsh and Hare & Tortoise.


I think of this not so much as a balancing mechanism as an example of how it's possible for a game to balanced without a balancing mechanism.

Quote:

7. The one-bound-one-free opening protocol
This is a placement protocol that results in an 'initial position' for a subsequent game that itself may have a placement- or a movement protocol, or a combination of both. It divides a game in two separate phases although a 'bridging factor' may be present, like capture being possible in Io in both phases. It operates equally well under c4, c6 and c8 connectivity.

The 'balancing aspect' is rooted in the opaqueness of the first phase. Although placement easily adapts to the overall object whatever it is, an attempt to be the first (or second) player to move in the second phase isn't so easy and the clouds are not really lifting till late in that first phase.


As a matter of personal preference I'm not too keen on the existence of a "setting up" phase, perhaps because of the implied opacity. However it's hard to argue against its effectiveness as a balancing tool.

Quote:

8. The Symple move protocol
The move protocol that finds its origin in Symple has an embedded balancing mechanism with a high resolution. Applicability may be limited to placement games with a territorial or a connectivity goal.


A neat protocol but I do have a niggle with it. If White grows first she will be left with n groups of two stones versus n singletons Black to move. If Black grows first she will be left with n-1 groups of two stones + 1 singleton versus n singletons. White to move. Why does Black's prerogative allow her to grow and then place rather than to place and then grow?

Quote:

I'm pretty sure I missed one or two, that's why I post it here. Any addition or comment is welcome. I plan a more extensive coverage of the subject to get me through the winter. "Make the Netherlands skate again" isn't really my policy.
 
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christian freeling
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cdunc123 wrote:
A couple of comments:

Regarding swap rules: It's probably worth mentioning the possibility of multiple-move swap rules, e.g. the first player places three moves on the board (black-white-black) and the other player chooses colors. (I've never liked these but I suppose some games may require something stronger than a one-move swap rule, e.g. Projex.)


I had realised the multiple move swap and did actually refer to it. But your post made me realise I'd left out the "Marquisian Method" used in for instance Swish & Squeeze.

cdunc123 wrote:
Regarding 12*: For games that don't really support 2-move turns, or that become a fundamentally different game with 2-move turns (e.g. chess, I should think), I have heard of the following radical option: Play three simultaneous games of the game in question using 12*: the first player gets one move on turn 1, and thereafter each player gets to make two moves on each turn, with the restriction that the two moves can't be in the same game. The player who wins 2 of the 3 games is the overall winner.

My plan is to more or less indicate the area of 'natural applicability' for each balancing protocol, and for 12* that indeed wouldn't include Chess or Draughts. The question "what are we balancing?" may be somewhat deeper than the obvious answer would suggest as it is, but in the above sketch makes it a real brainteaser.
 
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Rex Moore
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This will be of limited use to you because it only works for games in which (up to) three turns in a row would be fine, but for the sake of completeness…

Andy Looney has an interesting mechanic in his pyramid game Petal Battle that he calls “sequencing.”

The players each have a trio of pyramids (sizes 1, 2, and 3) they use specifically for this sequencing process. Before each round, they secretly stack their trios in whatever order they wish, then reveal the stacks simultaneously.

***Whoever has the smallest piece at the top of their stack will be the first player for the next three turns (until the next round of sequencing).*

***During the next three turns, each player will take the number of actions equal to the number of pips on the top-most pyramid in their stack (setting aside each pyramid as it’s used).

***Repeat every three rounds.

I find sequencing interesting because it eliminates first-player advantage and adds an element of “bidding" for turn order and number of actions taken.

Other than choosing the order in your stack secretly (and the tiebreaker aspect mentioned in the footnote below), I think Petal Battle is a pure combinatorial abstract as we generally think about it here.

*He breaks ties by looking at the next piece in the stack, and if the stacks are identical whoever finished their sequencing stack first goes first. I can imagine this speed mechanic would be frowned on here, so an alternate tiebreaker could be used, e.g., whoever went second last round goes first this round.
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Richard Moxham
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christianF wrote:
mocko wrote:

Christian, in my sketch-for-a-game Dreikaiserbund I proposed a device called "the amulet" - strictly speaking not a mechanism in itself but rather a marker to designate the current holder of an (exceptional) right. The point was that the right, once exercised by the holder, would pass over to his opponent, but that the 'meta-right' to refrain from exercising it would therefore be a kind of alternative advantage in its own way. Obviously the amulet would begin life in the custody of whichever player was supposedly disadvantaged by the turn order.

...

There's a sense in which all this might be thought to be covered by your Negative Feedback, but I feel that would make the category broader than is ideal for optimum usefulness. A passing back and forth of the selfsame right seems to me to distinguish the mechanism from that of Catchup in a manner worth registering. I confess to not being familiar with either Yinsh or Hare & Tortoise.

I'm not sure how considering this to be covered by 'negative feedback' would make that category less useful. To me it seems yet another way to implement negative feedback, different from the other three mentioned. These also have very different implementations. It is certainly worth mentioning as another example.

Well, supposing someone says "I'm envisaging a mechanism where the two players get to enjoy a specific advantage in alternation, but we give first turn to the second mover." Full stop. Put like that, I don't think you'd call it negative feedback at all, would you? Yet it's an exact, if slightly incomplete, description of the amulet mechanism. The difference as against, say, Catchup, is that the advantage surrendered is identical to the one enjoyed. It's not easy to argue this in satisfactorily rigorous terms, but I do feel that it's a difference which makes a difference. What about the reductio ad absurdum that by playing a move at chess (or any other game) you concede to your opponent the right to make the next one? Would that qualify as negative feedback? And a propos breadth of categories, could your 4. and 5. cases be combined under a more general heading of moves consisting of variable numbers of actions? Or do you think it's more useful to register the distinction?

Just askin'
 
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Carlos Luna
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mocko wrote:
Christian, in my sketch-for-a-game Dreikaiserbund I proposed a device called "the amulet" - strictly speaking not a mechanism in itself but rather a marker to designate the current holder of an (exceptional) right. The point was that the right, once exercised by the holder, would pass over to his opponent, but that the 'meta-right' to refrain from exercising it would therefore be a kind of alternative advantage in its own way. Obviously the amulet would begin life in the custody of whichever player was supposedly disadvantaged by the turn order.


A simple version of this "token passing" mechanism can also be found in Yellow.

A sophisticated version of the "1-2-2-..." mechanism is the "Thue-Morse turn order sequence" discussed here.

Finally, some non-necessarily-abstract balancing mechanism are discussed here.

So far, my favorite balancing mechanism are the Token-Passing protocol (because adds a whole new dimension to the game and it's very flexible) and the 1-2-2-... moving protocol (because it just feels right and tends to speed up a bit games that will be rather lengthy otherwise).
 
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cdunc123 wrote:
Regarding 12*: For games that don't really support 2-move turns, or that become a fundamentally different game with 2-move turns (e.g. chess, I should think), I have heard of the following radical option: Play three simultaneous games of the game in question using 12*: the first player gets one move on turn 1, and thereafter each player gets to make two moves on each turn, with the restriction that the two moves can't be in the same game. The player who wins 2 of the 3 games is the overall winner.

I'd not heard that idea before: it sounds like wacky appealing fun!
 
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Russ Williams
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Is it worth geekily (or pedantically) noting for completeness the "no-op"/idempotent balancing protocol?

I.e. nothing additional being added to the rules, because there is already naturally no evident disparity in advantage between the first and second players (e.g. Shogi)?
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christian freeling
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russ wrote:
Is it worth geekily (or pedantically) noting for completeness the "no-op"/idempotent balancing protocol?

I.e. nothing additional being added to the rules, because there is already naturally no evident disparity in advantage between the first and second players (e.g. Shogi)?


It's at least worth noting that such games exist. It touches on the very thing I'm interested in: what makes a balancing mechanism 'just and fair'. The very acknowledgement of games that have 'no evident disparity' in terms of turn order advantage shows that we should think in human terms.

I say this because occasionally it has been pointed out that in a game theoretical sense all games in question are completely determined and every legal position can (again theoretically) be labeled win or lose or, if applicable, draw. That of course includes Shogi's initial position. At the same time this means absolutely nothing in human terms.
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christian freeling
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CarlosLuna wrote:
A simple version of this "token passing" mechanism can also be found in Yellow.

A sophisticated version of the "1-2-2-..." mechanism is the "Thue-Morse turn order sequence" discussed here.

Finally, some non-necessarily-abstract balancing mechanism are discussed here.

So far, my favorite balancing mechanism are the Token-Passing protocol (because adds a whole new dimension to the game and it's very flexible) and the 1-2-2-... moving protocol (because it just feels right and tends to speed up a bit games that will be rather lengthy otherwise).

I'll have to look deeper into those applications. Thue-Morse touches on the human side again: is balancing ad infinitum a rational goal or does a balancing protocol 'merely' have to provide a high enough resolution to make any 'advantage' indiscernible for humans?
 
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Cool topic, the 1-2-3-4-5.. protocol seems very interesting to me, but I do not know any games that use it.

The card game Impulse uses 1-2-3-4-4-4, but it feels like it could keep growing.
 
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christian freeling
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Buckersuk wrote:

christianF wrote:
1. Playing the same number of games with black and white
This would seem to be the only 100% generic protocol, applicable to all games.


Unsatisfactory for games with a naturally large first player advantage. A variation would be that the winner is the player who scores the most points after an even number of rounds with alternating colours. The downside is that it implies playing every game out to the bitter end. I like to call this the "Cricket Method".

At the moment I'm more interested in the list than in the relative qualities. Alternating black and white does have those disadvantages for unbalanced games. But Chess still survives on it and in Draughts it hardly matters.

Buckersuk wrote:
Quote:

2. The swap rule


Overrated in my opinion, particularly in games with variable set up. The job of finding a first move which offers balanced chances seems harder than the job of judging which side the chosen move should favour.

Both can be hard, depending on the game. And as said: not all games can be thus balanced.


Buckersuk wrote:
Quote:

5. The 1-2-3-4... move protocol


I strongly suspect that Progressive Chess is not a balanced game but I'm not sure which side is supposed to win.

Well put .

Buckersuk wrote:
Quote:

6. Negative feedback


I think of this not so much as a balancing mechanism as an example of how it's possible for a game to balanced without a balancing mechanism.

I think it can certainly be labeled a 'protocol' in the games mentioned.

Buckersuk wrote:
Quote:

7. The one-bound-one-free opening protocol


As a matter of personal preference I'm not too keen on the existence of a "setting up" phase, perhaps because of the implied opacity. However it's hard to argue against its effectiveness as a balancing tool.


You actually make a new 'initial position' in each game. That at least eliminates possible disadvantages of a fixed one.

Buckersuk wrote:
Quote:

8. The Symple move protocol


A neat protocol but I do have a niggle with it. If White grows first she will be left with n groups of two stones versus n singletons Black to move. If Black grows first she will be left with n-1 groups of two stones + 1 singleton versus n singletons. White to move. Why does Black's prerogative allow her to grow and then place rather than to place and then grow?


An interesting thought that somehow managed to escape me.
I'll have to sleep on it, just to make sure nothing more escapes me .
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russ wrote:
cdunc123 wrote:
Regarding 12*: For games that don't really support 2-move turns, or that become a fundamentally different game with 2-move turns (e.g. chess, I should think), I have heard of the following radical option: Play three simultaneous games of the game in question using 12*: the first player gets one move on turn 1, and thereafter each player gets to make two moves on each turn, with the restriction that the two moves can't be in the same game. The player who wins 2 of the 3 games is the overall winner.

I'd not heard that idea before: it sounds like wacky appealing fun!


I've not tried this myself, though I agree it sounds fun. One question I have is what happens in a case where player A wins one of the games, and player B wins another, and thus the overall winner comes to hinge on the outcome of the remaining third game. Do players play two moves per turn in the remaining game, or just one move per turn? I'd go with that latter option, though either option I presume would be fine so long as the players agree in advance how to handle such a case.
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Buckersuk wrote:

Quote:

2. The swap rule
This one is 'fairly generic'. It is certainly not applicable to all games, but it can sometimes be modified to suit games that show a certain reluctancy to it or have obvious means to refine it, for instance by incorporating positions in which more than one move has been made.


Overrated in my opinion, particularly in games with variable set up. The job of finding a first move which offers balanced chances seems harder than the job of judging which side the chosen move should favour.

If the player who sets up has "done homework" and knows particular tricks and traps associated with that setup, perhaps the chooser will have more difficulty during the game, even if they correctly choose which side to play. So I agree this method is not perfect.

Quote:

6. Negative feedback
In some games actions may be made that are (or at least would appear) advantageous in terms of the goal, but only at the cost of a simultaneous disadvantage, thus causing a dilemma. Games that come to mind are Catchup, Yinsh and Hare & Tortoise.

This makes a balance against the common "runaway positive feedback" that can occur when one player gets an advantage, but not specifically against the advantage of the first move. Renju, which combines several balancing protocols into one big mess, places specific restrictions throughout the game on the first player that are not applied to the second player. This could be called a different sort of negative feedback. It also has a stage early in the game where one player places two stones instead of the usual one, and the opponent decides which of those two will be allowed in the game. I'm not sure if that can be categorized as a swap rule or not. Renju uses all this in addition to 3-move equalization swap.
 
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twixter wrote:
Buckersuk wrote:

Quote:

2. The swap rule
This one is 'fairly generic'. It is certainly not applicable to all games, but it can sometimes be modified to suit games that show a certain reluctancy to it or have obvious means to refine it, for instance by incorporating positions in which more than one move has been made.


Overrated in my opinion, particularly in games with variable set up. The job of finding a first move which offers balanced chances seems harder than the job of judging which side the chosen move should favour.

If the player who sets up has "done homework" and knows particular tricks and traps associated with that setup, perhaps the chooser will have more difficulty during the game, even if they correctly choose which side to play. So I agree this method is not perfect.



I get this, but isn't that in essence saying that the person who studies a game more, and thus has more insight into a game, will have an advantage over a player who knows less about a game? That would be true too, of a game so inherently balanced no swap rule, no 12*, is needed. With such a game, the more insightful player has an advantage. So I don't see this to be a problem for the swap rule. Am I missing something?
 
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cdunc123 wrote:
... With such a game, the more insightful player has an advantage. So I don't see this to be a problem for the swap rule. Am I missing something?

Not so much missing something as being less fussy. The swap rule requires extra work for both players. It initiates an ever escalating war of preparedness. The time sponge threatens to devour your waking life, your family, your dog. Civilization could come to a screeching halt. Only a proper sense of balance can save us.
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Let me first thank you all for contributing. Initially I went for a more or less complete list and in that respect I hope the quest has succeeded. Although I of course don't know what's not or not yet in it, I feel I have a good basis for an article, essay, whatever on the subject.

I'd appreciate further opinions on any or all protocols. This is a subject where many aspects may or rather must be taken into account, so all viewpoints are welcome.

I've slept on Buckersuk's suggestion regarding Symple. I admire it if posters think things through to the core (because I keep finding that difficult myself). Anyway it was an interesting sleep and I even reached a conclusion. I'll post it later, I must be off now.

 
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christian freeling
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Buckersuk wrote:

christianF wrote:
8. The Symple move protocol
The move protocol that finds its origin in Symple has an embedded balancing mechanism with a high resolution. Applicability may be limited to placement games with a territorial or a connectivity goal.


A neat protocol but I do have a niggle with it. If White grows first she will be left with n groups of two stones versus n singletons Black to move. If Black grows first she will be left with n-1 groups of two stones + 1 singleton versus n singletons. White to move. Why does Black's prerogative allow her to grow and then place rather than to place and then grow?


I've slept over it. It's a small change with implications that do not really seem to matter. Of course it may just tip the scales in a particular position between taking the growing option or leaving it. But the underlying dilemma remains the same.

The lure about it is symmetry: why not make the outset exactly the same for both players? I like symmetry but I have a reservation: sometimes there's something boring about it. More importantly, it serves no purpose here in terms of improving the protocol. The source of the balance is a dilemma in which the relative value of a couple of extra stones and their future 'influence' must be measured against the relative value of having 'the move', that is having the turn when the number of groups is equal.
These 'relative values' are implicitly opaque, and a lot of experience is needed to get to a more or less reliable estimate, regardless of the game (because they behave slightly differently in say Symple, Sygo and Scware).
Whether this dilemma centered around a strictly symmetric starting point or one that is slightly off center doesn't really affect its nature.

What I don't like about the idea is the fact that it implies a group that emerges and grows in the same turn. I feel an ever so slight imbalance there that is in fact exactly as inconsequential as the one you noted. But it is one that I like less than the current one.
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Rey Alicea
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Forgive my ignorance, but how would you balance a game with a second player advantage?
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christian freeling
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reyalicea wrote:
Forgive my ignorance, but how would you balance a game with a second player advantage?

Are there protocols in which it matters?
 
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