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Subject: Quick thought: 2* bi-color turn rule for connection games rss

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Nick Bentley
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A thought just floated into my head, and since I don't have time to test stuff these days, I thought I'd just share it here instead.

For most connection games, different parts of the board have dramatically different values. The center of the board is usually much more valuable than edges and corners. This often curtails the "meaningful branch factor" of connection games.

For placement-only games, it occurs to me you might be able to somewhat equalize board areas using a turn rule where, on your turn, you place an opponent stone in addition to your own stone.

Naturally, you'd start by stuffing opponent stones in weak areas, but by doing so, you'd make those areas stronger, which would give the opponent a wider set of things to think about in deciding where to place her own stones.

(I assume pie rules would still be required)

Thoughts? Is there something dumb about this idea I haven't thought of?

If it's not dumb, I'd like to try this for The Game of Y, for example.

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Russ Williams
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FWIW if you use the (IMHO too broad) broad definition of "connection game" that involve connected groups in any way whatsoever (as opposed to connecting different sides/parts of the board), then this is used in Nestor's OMEGA (similar multiplicative scoring goal to your Produto).
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Nick Bentley
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russ wrote:
FWIW if you use the (IMHO too broad) broad definition of "connection game" that involve connected groups in any way whatsoever (as opposed to "connecting different sides/parts of the board), then this is used in Nestor's OMEGA (similar multiplicative scoring goal to your Produto).

Indeed! I've never seen it used for traditional connection games though.
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Nick Bentley
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I also like the idea that the board would fill up more before the game is decided, something that bothers me about hex and Y. I'd expect this to happen because half the stones of a given color would be placed to avoid establishing connection in that color.
 
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FWIW, I believe Mark Steere’s game Fractal attacks this issue of central vs edge space value by creating a different number of (and different sizes for) the central, middle, and edge spaces. I have not tried it but it certainly looks interesting. Also, I believe the Hex variant Nex (for neutral Hex) gives you options for playing stones other than your own. I have played that before (on IGGC, I think) and it is really quite intriguing. So this may not be directly helpful for what you’re looking for, but these were the games I thought to refer you to for some additional ideas.
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Matteo Perlini
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Hi Nick,
this idea applied to Hex was proposed, if I remember correctly, many years ago in rec.games.abstract.

But I personally don't like to place an opponent stone in these kind of games: most of the time the choice of the move is trivial. It is like to play Hex and Misere Hex at the same time on the same board; the problem is that Hex is a great game but Misere Hex is not (at least for me).

In general, I think it would be more productive and fun to use the Ecalper protocol instead.

 
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christian freeling
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milomilo122 wrote:

A thought just floated into my head, and since I don't have time to test stuff these days, I thought I'd just share it here instead.
Turning one's passion into work is considered a great goal in life by many!

milomilo122 wrote:
For most connection games, different parts of the board have dramatically different values. The center of the board is usually much more valuable than edges and corners. This often curtails the "meaningful branch factor" of connection games.

For placement-only games, it occurs to me you might be able to somewhat equalize board areas using a turn rule where, on your turn, you place an opponent stone in addition to your own stone.

Naturally, you'd start by stuffing opponent stones in weak areas, but by doing so, you'd make those areas stronger, which would give the opponent a wider set of things to think about in deciding where to place her own stones.

(I assume pie rules would still be required)

Thoughts? Is there something dumb about this idea I haven't thought of?

If it's not dumb, I'd like to try this for The Game of Y, for example.

It's not dumb as a general idea but I doubt whether it's an improvement on say Hex. It's loaded with negative feedback so you'd need a concept that's decisive to begin with. And too much negative feedback has its own drawbacks. I this case lack of clarity may be such a drawback, meaning that you will arrive at a decision more by the inherent decisiveness than by careful planning.
 
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Craig Duncan
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Something a bit like Nick's idea is built into my game Chromatix, FWIW.

This game was designed for 3 players, ORANGE, GREEN, and PURPLE, who each own a pair of opposite sides on a hexhex board. Each player owns two colors of stones, namely, the primary colors that make his/her board-side-color (thus, PURPLE owns blue and red stones, ORANGE owns red and yellow, GREEN owns blue and yellow). On his/her turn, a player chooses a single stone in an owned color and plays it to the board. The winner is the first player to connect his/her sides in a chain consisting of owned-color stones (e.g. PURPLE wins by connecting the purple sides with a chain consisting exclusively of red and blue stones).


A win for orange


Anyway, in this game, each stone you play can be used by one other player, so you have to be sure that any stone you place helps you more than it helps the relevant opponent.

But that's not really Nick's idea in the OP. HOWEVER, I did like the game enough that I thought it should have a 2p version. The best I came up with is the following.

2p Chromatix: ORANGE lines up a series of stones off-board in the following color order: RYBRYBRYB... Meanwhile, PURPLE lines up stones BRYBRYBRY... Each player on his/her turn takes the stone from the front of his/her off-board line of stones and plays that single stone to the board. (Thus, in the aggregate, the stones are played in the RBYRBYRBY... order.)

This means that on every third turn a player must play a stone that helps only his/her opponent. And in play-testing, it was just as you described: a player buries such a stone in the most obscure region of the board still available.

It worked fine! That said, the game seemed a bit of kludge compared to the more natural, original 3p version. But it is viable game, as I recall.
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David Bush
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milomilo122 wrote:

For most connection games, different parts of the board have dramatically different values. The center of the board is usually much more valuable than edges and corners. This often curtails the "meaningful branch factor" of connection games.

Not trying to be argumentative, but compared to what? Compared to your two-stones-per-move suggestion?
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I also like the idea that the board would fill up more before the game is decided, something that bothers me about hex and Y. I'd expect this to happen because half the stones of a given color would be placed to avoid establishing connection in that color.

So a Hex game is decided sooner than you would prefer? Here's a recent battle of the bots game, which is more interesting than a mere human game.

There is no move labeled 1, since white swapped black's first stone, changed its color and moved it to the location labeled 2. So there are 53 stones at (black's) resignation on a 13x13 board, which is about 31%. Not dense enough for you? To each his own I guess. Note the stones are fairly evenly distributed despite the difference in importance of different regions of the blank initial board. This is because regions of the board can change value during the game.

Your idea is interesting, but I'm not sure this is a problem that needs fixing in the first place.
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Russ Williams
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twixter wrote:
Your idea is interesting, but I'm not sure this is a problem that needs fixing in the first place.

A fair point indeed; I too don't see it as a problem that most of a Hex board doesn't get filled up in play or that typically many cells are clearly bad moves.
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twixter wrote:
Here's a recent battle of the bots game, which is more interesting than a mere human game.

Not to derail the thread, but just a thought on this board. I presume Black resigned, since 54-white was the final stone played, as far as I can see.

If so, then those bots can see more than I can see, because I have to admit, as Black I'd have played on rather than resigning. I see that the 34-white stone will connect to the white edge, and given that connection, I also see that Black cannot stop White from connecting the right-hand white side to stones 20 and stones 6.

If I'd been Black, I'd likely have played my next stone (i.e. 54-black) right below 21-black, since that seems the area where White is the greatest threat. That seems to me like an effective defensive play in that area for Black, so White will shift his attention to 20-white, and will likely play in a cell between 5-black and the black edge. But that 5-black as some power, I think. At least, I'm not seeing a trivial win for White.

What am I missing? Have I got this all wrong somehow?
 
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cdunc123 wrote:
twixter wrote:
Here's a recent battle of the bots game, which is more interesting than a mere human game.

Not to derail the thread, but just a thought on this board. I presume Black resigned, since 54-white was the final stone played, as far as I can see.

If so, then those bots can see more than I can see, because I have to admit, as Black I'd have played on rather than resigning. I see that the 34-white stone will connect to the white edge, and given that connection, I also see that Black cannot stop White from connecting the right-hand white side to stones 20 and stones 6.

If I'd been Black, I'd likely have played my next stone (i.e. 54-black) right below 21-black, since that seems the area where White is the greatest threat. That seems to me like an effective defensive play in that area for Black, so White will shift his attention to 20-white, and will likely play in a cell between 5-black and the black edge. But that 5-black as some power, I think. At least, I'm not seeing a trivial win for White.

What am I missing? Have I got this all wrong somehow?

A1 is the leftmost cell, M1 is the top cell.
The move you are asking about it 55.G9 for black. The correct response for white is 56.E10. You can see my answer at the interactive board HERE, click the Prev button 10 times and then play it out forward.

More generally, you can look at the main game and examine variations HERE.
The key idea to recognize is that the vacant cell at F8 is not needed by white to secure a connection between stone 6 and stone 8. So, white can use that cell to secure the connection between stone 36 and (either 6 or 12 or the left border.)
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Nick Bentley
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russ wrote:
twixter wrote:
Your idea is interesting, but I'm not sure this is a problem that needs fixing in the first place.

A fair point indeed; I too don't see it as a problem that most of a Hex board doesn't get filled up in play or that typically many cells are clearly bad moves.

There's no REAL problem. Just a "taste" niggle I have with some connection games. I have this use-the-whole-buffalo aesthetic: I want all the potential state space in view to be used. There's nothing rational about this, as far as I can tell. Just my own idiosyncratic desire.
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David Bush
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milomilo122 wrote:
russ wrote:
twixter wrote:
Your idea is interesting, but I'm not sure this is a problem that needs fixing in the first place.

A fair point indeed; I too don't see it as a problem that most of a Hex board doesn't get filled up in play or that typically many cells are clearly bad moves.

There's no REAL problem. Just a "taste" niggle I have with some connection games. I have this use-the-whole-buffalo aesthetic: I want all the potential state space in view to be used. There's nothing rational about this, as far as I can tell. Just my own idiosyncratic desire.

Fair enough, but I'm not sure that your rules mod would result in a denser board at resignation time between two future bots. Do you like my rhetorical trick there? I say "I'm not suuuuuure" and "We'll just have to wait and seeeeeeee" and come off sounding all smug and superior.
 
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Nick Bentley
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twixter wrote:
milomilo122 wrote:
russ wrote:
twixter wrote:
Your idea is interesting, but I'm not sure this is a problem that needs fixing in the first place.

A fair point indeed; I too don't see it as a problem that most of a Hex board doesn't get filled up in play or that typically many cells are clearly bad moves.

There's no REAL problem. Just a "taste" niggle I have with some connection games. I have this use-the-whole-buffalo aesthetic: I want all the potential state space in view to be used. There's nothing rational about this, as far as I can tell. Just my own idiosyncratic desire.

Fair enough, but I'm not sure that your rules mod would result in a denser board at resignation time between two future bots. Do you like my rhetorical trick there? I say "I'm not suuuuuure" and "We'll just have to wait and seeeeeeee" and come off sounding all smug and superior.

An excellent rhetorical move! (and also a legitimate question)
 
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christianF wrote:

In this case lack of clarity may be such a drawback, meaning that you will arrive at a decision more by the inherent decisiveness than by careful planning.

I see how that could be. I'm not certain it will, but I see it as a possibility too.
 
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Craig Duncan
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twixter wrote:
A1 is the leftmost cell, M1 is the top cell.
The move you are asking about it 55.G9 for black. The correct response for white is 56.E10. You can see my answer at the interactive board HERE, click the Prev button 10 times and then play it out forward.

Thank you, David. I see from your play-out that -- from my perspective, at least! -- there is a fair bit of game left to play before it's screamingly obvious that White has the game in the bag. In my initial look at the board you posted above, I'd been thinking, given Black's resignation, that there must be a way for White to achieve an invulnerable position with just a few more white stones.

That's why after noting that Black should play 55.G9, I next looked to the northeast to seek White's easy win, figuring it must lie there. But no, White's eventual winning connection is from 34 to 48, ignoring the northeast. Given my level of ability, it's not obvious to me that Black's 55.G9 is destined to fail at preventing a White win.

I see NOW that with 56.E10, Black can't stop White from connecting stones 44 and 52, and I also see NOW that with 56.E10, White can either connect upwards to the 6-8 pair or push through Black's 7-3 opening. But in a face to face game, boy, I'd have to play all of that out rather than resign after 54! Those bots are smart!

I guess this means that there are now strong bots one can play with a Little Golem? Is that a new-ish development? If so, good news!
 
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Stephen Tavener
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I played around with this idea a few years back, and didn't find the extra decisions very interesting with free placement of the opponent's piece.

What did make them interesting was if you constrain the placements. I called this version Vex, though I can't find where I posted it now:

Each turn:
- place a piece of the opponent's colour. If possible, it mus be adjacent to one or more opposing stones. If several placements meet this requirement, choose a move which creates the smallest opposing group after placement (i.e. next to a single stone if possible).
- place a piece of your colour anywhere

Normal hex victory conditions apply.
The pie rule is still required.
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David Bush
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If, on your move, you are forced to complete a winning opposing path, do you lose?
 
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twixter wrote:
If, on your move, you are forced to complete a winning opposing path, do you lose?

It would seem surprising to me if not! Why wouldn't you lose?
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christian freeling
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russ wrote:
twixter wrote:
If, on your move, you are forced to complete a winning opposing path, do you lose?

It would seem surprising to me if not! Why wouldn't you lose?

Well, there's a certain irony in making your opponent's winning move. Players with a lesser sense of irony might be inclined to decline.

Here's an observation that led me to it:

It's an online AiAi game against another registered player. The score is 10-10 but Black must move, getting an extra point and an extra four-point penalty and thus losing by 3 points. My last move was February 12th.
 
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Stephen Tavener
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twixter wrote:
If, on your move, you are forced to complete a winning opposing path, do you lose?

Yes.

christianF wrote:
Well, there's a certain irony in making your opponent's winning move. Players with a lesser sense of irony might be inclined to decline.

I think that says more about the player than the game. Still, after the kids are back to school I'll add some admin functions so I can end the game in your favour.
 
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If I make a connection for the opponent, and I don't immediately lose, then on the opponent's immediately following turn, whatever they do, they have their sides connected, so they'd win on their turn anyway. Am I missing something?
 
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mrraow wrote:
I played around with this idea a few years back, and didn't find the extra decisions very interesting with free placement of the opponent's piece.

good enough for me. curiosity squelched.
 
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Nick Reymann
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I feel like this would best be implemented on Hex and Y boards that are *already* adjusted such that spaces are roughly balanced, such as the Kadon Y board or a "square" Hex board based on connectivity between spheres looking top-down on a square pyramid, like this: https://boardgamegeek.com/filepage/10382/square-hexpdf

IMO, Hex and Y on normal boards are most interesting *because* of the different and changing strategic value of spaces. The single-swap pie rule works so perfectly on them because it tends to games where under equal skill, each player usually ends up in a better position than the other after each move. Sort of like if you alternatively add one and subtract one starting from 0, you get the sequence 1,0,1,0,1,0, etc, but if you start by adding .5 first you get .5,-.5,.5,-.5, etc.

On boards with roughly equal-valued spaces in the beginning, a single-stone swap rule doesn't work because it would make sense to swap any move the first player makes, so either a multi-stone-setup swap rule must be used or a placing variant like you describe here. I imagine this game could be very interesting played on an aforementioned square hex board. Anyone know anyway to try it out online?

 
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