It's not Hex or Havannah, nor do I mention it as a suggestion for LG, although someone might, eventually, but it just so happened. It's never been played - the subject of the thread at Arimaa.

Yvy

Thanks for the new game, is there a swap rule (first move can connect two bricks)?

It is not stated in the rules

Can you explain the name? (I think Ys take less part than in Havannah, but there will be super-Ys). Also do you think the play will be very different from Havannah?

Sure, a swap may be used. But the first move cannot connect two bricks - bricks are part of the playing area and must be occupied to connect. So you need 3 in a corner, 4 on a side to connect two bricks. Of course both players may occupy the same brick.

It wasn't the 'Y' connection, no pun intended, but I misspelled Ivy, and then liked 'YvY' by the shortness, the sound and the look of it :)

I took Ivy and bricks because it is slightly reminiscent of Ivy creeping along bricks. The loop is a tactical disruption tool in the general strategy. It wins regardless of the score at that point.

The scoring is similar to *Star, where each connected group is essentially worth 4 points less than the amount of perimeter territory it controls.

If all the bricks were single cells, and the sides were of length 4N+3 (which means there is room for an odd number of singleton bricks along each side), and three non-adjacent sides had an even number of singleton bricks (perhaps by placing another grey spot in the middle of those sides, or perhaps by having three sides of length 4N+1) Then draws would be (essentially) impossible. Here's an outline of a proof: Suppose we modify the scoring system so that each chain which includes at least one brick costs that player one point and benefits the opponent by one point. This should not change who wins the game. With singleton bricks, only one player can claim any brick, and there should be no unclaimed bricks at the end of the game, since at least one of the players must be able to and would benefit by such a claim. (See below.) The sum of the players' scores would be the same as the total number of bricks, which is now odd. So, the scores can never be equal.

There is a special case to consider, where one player has “walled off” a brick or bricks without necessarily claiming them. If a player has walled off two bricks, Then if he claims one he should claim the other, at no net benefit, but whether he claims both or claims neither, the sum of the remaining bricks is still odd, so this would not create an equal score. If a player has walled off more than two bricks, he should claim them all for a net benefit. So, the only case which might result in an equal score is when a player walls off a single brick without occupying it. Would this be possible between two players who are both trying to win? I don't have a clue, but it doesn't seem very likely to me.

I should add that, as I understand the rules, if a lone stone occupies a brick then that is regarded as a chain, costing that player 1 point total, or using my modified scoring, 0 points for that player and 1 for the opponent. This is why I use the phrase “walling off without claiming.” Certainly the opponent could occupy and thereby claim any of these walled off unclaimed bricks, but it would not be advantageous for that player to do so.

@ David

You are right about Star. Superstar admittedly grew out of dissatisfaction with it, but I'm not too satisfied about Superstar either.

YvY has a simple scoring system. As it is, 16 points is the maximum a player can score (by connecting all bricks).

I chose bricks to give both players access to the same unit.

I'm not sure I understand the one-stone chain on a brick “costing that player 1 point total”. You need to connect 3 bricks to get 1 point, and connecting two previously disconnected chains that each have connections to bricks, gives the new chain 2 points more than the seperate totals would.

I'm sure there are puzzles here regarding points distribution and draws and the like. I'm not opposed to a small margin of draws, by the way.

Saturday I must give a lecture of sorts about raccoon dogs for the dutch association of lovers of canidae, and I'm working on the powerpoint presentation, so I'll not be able to add much in the coming days. Should anyone care to give it a try, I hope it is fun :)

A single stone on a brick, not connected to any other stone of the same color, is worth two points less than the number of bricks connected.

# of bricks connected = 1

2 points less than that = -1

So, that single stone costs that player one point.

Or did I read it wrong?

@ David

No you didn't, not as I read it :)

I didn't mean to go into the negative, my bad.

Two connected bricks are 0 points, 3 are 1 point, 4 are 2 points and so on. Connect a 2-brick chain to a 3-brick one (seperately 0+1), then the new 5-brick one is worth 3.

A loop's worth is infinite ;)

Hi David, here's a base-9/11 board - of course any base-2n+1/2n+3 is possible.

I'm not sure I understand your suggested modification:

“Suppose we modify the scoring system so that each chain which includes at least one brick costs that player one point and benefits the opponent by one point.“

The modification is based on the rule that a chain is worth 2 points less than the number of bricks - “sprouts” in this one cell version - it connects.

This is a good rule, rewarding connections between separate chains.

You rightly pointed out that a pure interpretation would make a chain connected to a single sprout worth “-1” points.

In my interpretation it would be worth “0” points.

Your new suggestion seems different from both.

Obviously your aim is to prevent draws. That's a good aim, but I'm bad at deductive thinking.

So if you can provide a simple scoring system for the above board(s), based on the “minus 2” rule and preventing draws, then this, together with the suggestion of single-cell 'bricks', would make this version of YvY very much a joint venture, and if it is better than my version, then we'll choose this one to be 'YvY' and make it a joint invention.

What do you think?

This board is perfect, but I don't really see the added value of the grey cells to separate the orange sprouts. I would prefer a uniform framed board.

Then David argument holds provided that you have an odd perimeter to ensure you get no draw :

- suppose player1 gets A border cells in K groups and player2 gets B border cells in L groups,

- the scores will be A-2K and B-2L, and as A+B is odd, A and B and hence the scores will have different parities.

This would be an equivalent of Go, for border cells, with a penalty for having many groups. Taking an isolated border cell would not change the scoring, removing one point for both players (if the penalty extends to the 1-chain), so a player would try to invade the other's territory only if he can get two sprouts(like eyes in Go?).

A 10/11 board with orange boundary would have right parameters…

I think in this game there will be an interesting trade-off between central cells to get the covering “Y” and the border cells to prevent small-trees.

Another way of stating your scoring system is: each chain which includes at least one sprout costs that player two points.

Compared to my scoring system, the difference between the players' scores remains the same. So, the outcome of the game would be the same. It could therefore be argued that these two scoring systems are interchangeable. YvY would be the same game either way. So there should be no problem with using your scoring method.

If a chain connected to one sprout is worth 0 points under your scoring, then how much is a chain connected to 2 sprouts? As far as I can tell, a 2-sprout chain should be 0 points under your scoring and a one sprout chain is -1 points. I don't understand how you arrive at this different value.

I don't have a clue if this modified YvY would really be any better than your way. I mentioned the mod mainly because of my concern to reduce or eliminate draws, as you said. But draws are probably rare anyway under your original rules. It just appealed to my sense of game aesthetics, which of course is completely subjective. So, any way you want to go would be fine with me. I appreciate the offer.

Carroll, There may not be any obvious use for forbidden cells, and this would even eliminate the strange possible “one sprout walled off” draw I mentioned, but eliminating the grey cells would bring YvY much closer to Star and *Star and Superstar. Anyway, the rules to a game do not have to make obvious sense. They just have to be consistent. The nature of game play is what matters. Is YvY an interesting game? IMO the only way to find that out is to play it.

“IMO the only way to find that out is to play it.“

That occured 2me2 :-)

My original idea to give a single-sprout chain the value zero was that it seemed odd to be able to affect a score in a negative way by occupying a brick/sprout.

I tend to favor the latest version, not because of any inconsistency in the first, but because I suspect its marging of draws may be, well … too large for comfort.

Maybe Ed can be persuaded to make an applet so we can actually try :)

Reconsidering, the “minus 2” rule seems arbitrary. “Minus 1” has certain advantages, the first one being that a single-sprout chain has value “zero” instead of becoming negative. And it allows a rephrasing of the counting criterion that is extremely elegant:

“A player's score is the number of sprouts he occupies, minus the number of chains involved”

It's immediately clear that it's all about connecting as many sprouts as possible with as little groups as possible. I like that.

I'll add the extent of my deductive powers :)

If a vacant sprout is of no interest for one player, because it is isolated and can at most give value zero, then it is of interest for the other, because he can connect it.

All sprouts being occupied, one will have an even number, and the other an odd number.

But what about the numbers of chains/groups involved?

Can the game end in a draw?

Yes. Here is a contrived example.

Black's score would be 13-2=11.

White's score would be 14-3=11.

I didn't check this closely, but let's just say neither side can form a loop and that the piece count is legal.

If each chain costs only one point, then draws are unstoppable, and you might as well revert to your original board design with two-cell bricks.

Loops are out of the loop in this context. They're more of a treat, not likely to actually materialize in a high level game. The example will probably be far from an actual game situation, but that too is irelevant: this appears to be a draw.

In the “minus 2” count, Black's score would be 13-2*2=9 and white's score would be 14-3*2=8.

So a player's score might be formulated as:

The number of sprouts he occupies, minus twice the number of groups involved”

Sacrificing a flick of elegance, but eliminating draws.

Right?

Interesting is the single white stone at the bottom: should white not occupy it, then his score would be 1 higher, but then of course black would occupy it and connect, making his score 1 higher too.

But White could take the two areas above that brick, thus blocking it, and causing a draw, right?

A Marius, you're a genius, annoyingly so, but nevertheless ;-)

And you're absolutely right.

Provisional bummer :(

Draws, though not impossible, may yet be very unlikely. What Marius describes seems a very exeptional situation: the creation of a vacant sprout the occupation of which is disadvantageous for both players.

The bottom line is: white would have to invest two stones to prevent black from getting one point - might be little more than an anomaly in endgame situations.

Looking again at the example position, there are several loop opportunities for black and at least two for white, but as contrived as these moves are, it would not be much more contrived to say that both players passed.

As I admitted in my first post to this thread, a walled off single cell brick, later termed a sprout, can lead to a draw. All this modification does not eliminate draws, but I believe it would make them more rare.

“All this modification does not eliminate draws, but I believe it would make them more rare.“

I agree, it might amount to little more than havannah's margin. And I'd like to have a go at it. I'm sure Ed is willing to make an applet based on the 9/11 board.

Here's the new YvY board - let's call this one base 4/5.

The green cells are 'sprouts' and a closed chain of like colored stones is a 'group'.

The game has a swap and players may pass without losing the right to move next turn.

Loops must surround at least one cell completely (vacant or occupied doesn't matter), and win regardless of the score.

The score for each player after two successive passes is:

The number of occupied sprouts minus twice the number of groups involved.

'Bad sprouts' are vacant sprouts the occupation of which reduces the score for either player doing so.

Close off a vacant sprout with two white stones, and close off those two stones with black ones, and you have a bad sprout.

In order to end in a draw, an odd number of bad sprouts is necessary, but not sufficient.

YvY © MindSports/David J Bush

I'm curious about the degree in which YvY fills the niche of the category “connection games with a scoring system”.

There's Star of course, which is boring, and Superstar, which has too complex a scoring system to be convenient. YvY seems to stike the right balance.

Are there any other games in this category that anyone knows of?

There is an aspect of YvY that begs playtesting. The whole point of David's suggestion to take an odd number of single-cell sprouts, was to eliminate draws.

Consider: with all sprouts occupied, one has an odd number, and one an even number. Both must subtract an even number, i.e. 'twice the number of groups involved'.

So with all sprouts occupied, a draw cannot occur.

Whether or not this was a good decision would depend on the frequency in which 'bad sprouts' occur. My guess is that they will occur occasionally. It is not likely that one would occur in the opening, or even middle game: there are other priorities at these stages. So the cradle must be in the finer points of the endgame. It is admittedly hard to make a calculated guess about the frequency of occurence of bad sprouts without a great number of games between seasoned players.

As it is, the first ideas about strategy haven't even been established.

Does one take the sprouts first, and if so, does one 'keep them close' to be able to connect?

Or does one take the center first to ensure connections and interweave loop threats?

Most likely something in between - it is reminiscent of the same dilemma in havannah: snake versus spider.

http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=other;action=display;num=1236541162;start=105#115

YvY has come together. Here's an adaption of a post at the Arimaa Forum. Can't upload it all at once it seems, so I'll try to make it two posts.

FindingYvY

Inspired by the deafening silence I'll try to show what you're looking at and how it will behave. As for playtesting: Ed and I just started our first game - you can find it in the MindSports Spectators Section at the bottom of the scroll box.

First the rules in a nutshell:

An YvY base 4/5 board

The diagram shows a base 4/5 board, with 27 cells called 'sprouts' along the edges.

There are two players, black and white. White moves first by putting one stone on the board, after which black has the option to swap.

After that players alternately put one stone on the board. Players may pass their turn without losing the right to move next turn. The game ends by sudden death or when both pass on successive turns.

Groups

A 'group' is a number of connected stones of like color. A single stone is a group by definition. An 'involved group' is a group containing one or more sprouts.

Loops / Sudden Death

A 'loop' is a group that completely surrounds one or more cells. Whether or by whom such cells are occupied is irrelevant.

A player completing a loop wins immediately, regardless of the score.

The Score

If no loops are completed the game ends after the players both pass on successive turns.

Now all uninvolved groups are removed from the board and the player with the highest score wins.

A player's score is the number of sprouts he occupies minus twice the number of his groups (now all involved).

This is equivalent with an involved group having a value equal to the number of sprouts it contains minus 2.

However, if a group is located inside a group of like color (as a result of the removal of uninvolved groups), the two count as one group.

connections, loops, cutting points

If black occupies F1 he gets one point but at the same time creates a new involved group that cannot be connected anywhere, costing two points, the net result being the loss of one point.

If white occupies F1, the same applies initially. However, at the end of the game, the black group of 2 is removed and a white stone on F1 is considered connected to the surrounding white group. So for white the net result is the gain of one point.

Note: a purely theoretical consideration: suppose black has a group around the 5 white stones, including stones on D1 and H1. Now the white group is uninvolved too and situation is the reverse. Black can occupy F1 and eventually score +1, white cannot occupy it because it would render -1.

History

The twilight zone between Go and Hex

I posted a question at LG asking if anyone knew other abstract boardgames besides Craige Schensted's Star and my own Superstar where connections rendered scores.

There was no answer, so I figure there may not be all that many. However, I found the inventor formerly called Craige, himself improved on his creation. I must say I like this one better, because it shifts the counting from vacant cells adjacent to the board, to actual cells (or points rather) on the board. And what a board! A beautiful 'hexpentagonal' plane with slightly rounded edges.

Like Hex, Star is pure 'pathfinding'. But where Hex is abysmal in a life or death situation, Star is abysmal in a point scoring situation, and not a very convenient count either. There's nothing wrong with that, or Go would have the same defect, but back then I thought I'd make it a bit livelier, and created Superstar.

Superstar isn't all that bad either if you get to know it, but it doesn't exactly invite you to get to know it. Complex rules and complex counting of stars, superstars and loops, are too much of a treshold for that.

That thought occured to me a few days back, followed by “a loop should simply win”, followed by the consideration that simultaneously merging the concept of stars and superstars, would reduce counting to just one aspect instead of three. And it would keep the loop in play as monkey in the snakepit, introducing similar tactics as the ring in Havannah into the general 'pathfinding' strategies.

The merger is still visible in the 'bricks' of the first version. It's not a flawed game. What's wrong with it is that this one is so much better. The most important push was due to David's quest to eliminate draws. The final piece of the puzzle was the removal of uninvolved groups at the end and defining enclosed groups of like color as 'connected' to the enclosing group.

To speak with Michael: This is it.

Character

I don't hesitate to call Star a quintessential “Gonnection” game. Although that qualification has already been taken by Gonnect - a game that developed in the opposite direction: employing territorial mechanics for an absolute connection goal - I'll use it here for convenience.

Yet Star falls short of Go in the tactical realm. Not that it doesn't have deep tactics, but they are not all that pluriform. That's why I made Superstar in the first place, overshooting the target.

YvY, more than Havannah, will have the feel of Go, very much a game of territorial influence. It's resolution is lower because there are only 27 sprouts to be divided. The bright side is that counting is too easy to be distracting and a swap seems to remedy too much of an advantage for the first player.

After that it's a fine line: as in Havannah or Go, it can be a one point difference that makes all the difference, and at its highest level it almost certainly will be.

At its highest level, too, the loop will be a constant presence in the equation, without ever materializing. In Havannah a ring may materialize as the consequence of a simultaneous deadly threat, but in YvY you're inclined to prevent one at all cost, because it's a choice between sudden death and losing one or two points. .

Of course loops might materialize in less high level games.

The 'influence' aspect comes from the risk of occupying a sprout: unconnected it will cost a point, so taking one is a risk to begin with, and taking one under an 'umbrella' of the opponent is probably a bad idea. In consequence an umbrella, or 'influence' will be a leading strategical concept.

So where does YvY fit in? Thematically it's in the “Gonnection” class that as far as I know holds four games, two of which are more or less redundant.

For the 'feel' of it, it resembles Havannah as 'something in between Hex and Go', but YvY leans more to the Go side in that a player can accumulate, whereas Havannah is all about one winning structure. Stripped from the 'loop' YvY would be a Star variant. The loop provides what is lacking in Star: pluriformity of tactics. A pluriformity that strongly resembles Havannah's.

Let's have a look at the diagram again.

connections, loops, cutting points

In Star a black stone at “X” would be a rock solid connection in the vast majority of cases, and the white groups would have no escape. In YvY however, white A and B cannot be defended both, because then C would mean sudden death.

The loop is the basic tool to gain tempo, force cuts an draw defensive stones in the process, which are the primary source of 'uninvolved' groups.

There'll be no end to YvY's inticacies. Thirty years after its invention, Mirko Rahn (current rating at LG: 2102) taught me a new 'basic tactic' in Havannah, by making me its victim three times in a row. I'm a slow learner. The thing is called a “blockbuster” and requires the preparation of a second stone at some distance, but then it makes a block impossible. So I can still learn in Havannah, and YvY will not be different in this respect.

That's my prediction about its general behaviour at high level play, should it ever come to that. There's no need to take my word for it however, as far as I'm concerned YvY should be able to care for itself.

I don't know about David, but I guess he feels the same.

We hope you enjoy the game :)

YvY © MindSports / David J Bush

In Go, if it is said that a certain group is dead, it doesn't mean that the group is a group, nor that dead is dead in the formal sense. The 'group' may consist of several smaller groups or loose stones, and all of them may have liberties, or they wouldn't be on the board in the first place.

In YvY (and other games) a similar semantic freedom is used. Formally a group must be connected, but when I say that in the endposition both players have two groups, it is said in this semantic freedom.

Also, vacant sprouts under a player's control simply count as belonging to the enclosing group. Of course they could be formally occupied, like one could formally enclose dead groups in Go. It just isn't done because experienced players know and agree on the situation, or both wouldn't have passed.

Here we're halfway

Here both have passed

Here the uninvolved groups have been removed

The single white stone bottomleft formally is an 'uninvolved group' - of course it isn't within the semantic freedom between experienced players. Likewise the bottomleft red 'group' fomally consists of three groups.

The count

Both have two groups, so that evens out. White occupies two sprouts and controls five, red occupies three and controls five.

Red wins by one point.

Note: In this example the situation didn't arise, but if the final position has groups that include precisely one sprout, without contolling others, then such groups may be removed since doing so doesn't alter the score difference: both gain a point.

The upper right white group does initially block a sprout for red. Removing that gives red an extra point. Is that your intention?

It's impicitely for red. White cannot take the sprout, because it would cost him a point. Red can take it, because the white group is 'uninvolved' and will disappear. Formally the stone on the sprout, then, is considered connected to the enclosing group.

Because of this outcome, Red doesn't actually have to occupy is, just as the owner of all other vacant sprouts is clear.

I think this removal of groups is unneccesary, and makes the game more confusing and less “pure” - and in my opinion less interresting. I definitely would prefer to just let all groups stay and count the score like you suggested earlier.

Actually I indulged a bit too much in 'semantic freedom'.

If white takes the sprout, he creates a new 'involved group' worth “-1”. At the same time he snatches one point from Red, so the move doesn't bring him anything.

If Red takes the point he proves beyond doubt that it is his: the white group disappears and the red stone is formally connected to the enclosing group.

Therefore both passed at a right moment. They might have made a couple of more moves, but nothing that would have altered the outcome.

As for your suggestion to return to the old count: it makes draws possible because of 'bad sprouts' - sprouts the occupation of which is disadvantageous to both.

The removal of uninvolved ('dead') groups makes that bad sprouts cease to exist, and that ownership of vacant sprouts is clear. It's not a 'fix' rule but a key rule in the whole concept.

I'm probably bound to be contradicted here, but this is a very 'organic' game with, by the feel of it, a fair resemblance to Havannah, but more 'fluid' because the target is all around.

In terms of programming, it appears to be in the same league too.

I'm very glad we found this game, and very thankful for David's key suggestions and his quest to eliminate draws, a quest that now has succeeded.

I agree that draws are eliminated this way. However, I don't see any REASON to eliminate draws. To me, a game is just as good if there are possibilities for draws. Making extra rules and redusing the “purity” and clearity of a game might be necessary to make it more balanced, but in my opinion, it is a very bad idea to do so just to eliminate the possibilities of draws.

If one fears that draws might occur too often, then usually (although I guess there are exceptions) that means the game is simply unbalanced, and removing draws will just give one side a large advantage.

But these are, of course, just my opinions :-)

_“Opinions are difficult because they're too damn easy”

mindsports_ ;-)

Seriously, I politely disagree. The rule was found while contemplating 'bad sprouts', and yes, it does eliminate draws. But that's a side-effect as far as I'm concerned. If I made a mistake, it was in the semantics: I should have called involved and uninvolved groups 'live' and 'dead' to begin with. And I will. Not only is the removal of dead groups logical, but the killing of groups is a strategic goal that emphazises YvY's inclination towards Go, as far as connection games Go ;-)

That is: you can kill a group not only by preventing its access to a sprout, but also by making this access worthless. It isn't an 'extra rule', nor a 'fix rule', its the heart of the organism.

That presents a thoroughly different take on the game. I think you're right, it's a better game. But you're right, you have to present it that way to begin with.

Suppose from the halfway diagram, Red's group on the right failed to connect to a sprout on the bottom. Then Red's right group and White's upper right group are each alive only if the other is dead. I see nothing in the rules that will resolve the situation.

Haha, seki :)

Well, seki in Go is rare, because ordinarily stones that are not unequivocally alive can be captured. With no in-game capturing, unresolvable life and death positions in YvY may be all too common and ruin the game, especially on larger boards.

I hope I'm missing something.

@ DvdAvins

Red's group has a sprout at the top and thus lives. If for the rest it were surrounded completely by white, the situation around the vacant sprout would not change.

You may refer to a situation I described in my post from nov. 2:

Note: a purely theoretical consideration: suppose black has a group around the 5 white stones, including stones on D1 and H1. Now the white group is uninvolved too and situation is the reverse. Black can occupy F1 and eventually score +1, white cannot occupy it because it would render -1.

FWIW I approve of Christian's final tweak which eliminates those terrible terrible draws, as if there were any doubt. Nicely done! I just hope it will be easy to program the server to recognize the special case described, so it will remove the correct color group at the end.

There may be an issue regarding players who both pass in a position which is not yet fully resolved. Perhaps they both became bored with the game or something. So, for example, it may not be clear which groups should be removed as dead. How should this be dealt with?

Formally yes. It happens in Go. If in doubt, play on.

And if bored … well, maybe we're missing something :)

As for the server, that would depend on Richard. I can imagine YvY's not the first in line by a long shot.

Just because Go has this problem does not imply that YvY should have it, too. As I understand the rules, when both players pass, game play ends. Is this correct? Or is this qualified depending on whether the game has been “sufficiently played out” or not?

There are two ways to go. Forbid a player from passing if the opponent just passed and the position does not yet meet specific criteria, or allow game play to end whenever both players pass, and precisely define what groups are dead and how the position should be scored regardless of the position.

Sorry for being a stickler, but I believe the rules should cover every possible situation.

How about, if your opponent has just passed and you wish to pass as well, first your opponent must agree with you regarding who has control of which sprouts, and which groups are dead. If there is disagreement, you must play on.

@David and generally

Isn't that the way it is solved in Go too?

Seki doesn't exist in YvY, and barring situations I've not yet been able to envision, the control over any specific sprout should always be clear.

An interesting aspect is that 'giving a group life' - connecting its first sprout - always costs a point. So isolating groups is implicitly good. This means that the game, like Go but quite unlike Havannah, generally evolves at some distance of the edges.

As I write, Ed and I got 63 stones on the board (mindsports spectators/players section, scroll down the 'list selected games' box - http://mindsports.nl/index.php/players-section) but only 4 sprouts have actually been occupied. So you're right: the center is where it all comes together.

Your switch from bricks, where both had access to the same unit (and where draws were implicitly present) to sprouts, where there are two access cells but only one unit, was absolutely crucial, and eventually it was the key to eliminating draws.

I'm very glad we share this game because it is a great game, holding the middle between Havannah and Go. Not everybody can immediately see what I can see. That's what my essay is about in the first place, so I hope it's understood that there's no arrogance intended.

It is also my final game - I've really come full circle with this one, and I'd rather work on improving mindsports than invent yet another one - I feel I can't beat this one anyway. My essay wil therefore have one more chapter: “A final whisper”, Thanks for whispering along :)

Technically, in Go, game play ends when the players pass. If there is disagreement about some region then that region is played out more, then when the result is agreed on, those moves are retracted to the point where both players passed. Some servers do not implement this retraction. Fortunately this is not necessary for YvY.

I'm honored to have played a role in your final abstract :-)

The honor is all mine :)

We'll implement 3 sizes at mindsports at our next update, 2/3, 3/4 and the current 4/5. You may have noticed that we've put it in the ArenA, where it belongs.

YvY is played on a special board. The image shows a 'base-9' one, with 9 sprouts - the green cells - along any two adjacent sides. MindSports also provides base-7 and base-5 applets.

• The game starts on an empty board. Players move in turn to place one stone on an empty cell. White moves first. The second player is entitled to a swap.

  The MindSports applet will shortly offer the swap under the 'choose' button. The result will be a switch of color of the stone on the board.

• A player may pass his turn, without losing the right to move on the next one.

Groups & Loops

• A 'group' consists of a number of connected like colored stones. A single stone is a group by definition.

  As in Go, a 'group' is most of the time meant in a less formal way as a group of 'cooperating' stones.

• A 'loop' is a group that completely surrounds one or more cells. Whether or not such cells are occupied, or by whom, is irrelevant.

Object

• The game ends in one of two ways:

• By sudden death: if a player completes a loop he wins, regardless of the score.

• After both players pass on successive turns: now the player with the highest score wins.

Life & Death

• A group lives if at least one of its stones occupies a sprout, otherwise it is (as yet) dead.

Territory & Scores

• If a game ends by the players passing on successive turns then dead groups are removed from the board before the counting starts.
• After the removal of dead groups, any group fenced in by a group of like color, is considered part of that same group.
• The score of each player is the number of sprouts he controls (that is: sprouts occupied or fenced in by his stones) minus twice the number of his groups.

If, for example, one player has followed a center oriented strategy, resulting in one group controlling 11 sprouts, his score would be 9. The other player controls the remaining 16 sprouts, so if he managed to do that with three groups, he has 10 points and wins, but if he needed four he has 8 points and loses. This is a game of 'divide and rule'!

Note: if one player's score is even, the other's will be odd, so the game cannot end in a draw.

Strategy & Tactics

In terms of tactics, YvY first and foremost requires reading the hexplane the same way as in games like for instance Hex and Y, but the presence of the loop as an absolute criterion to win makes its tactics much more Havannah like. In fact YvY might be considered a 'generalized Havannah' in which the concept of corners and sides has been replaced by by an odd number of evenly distributed sprouts and the goal is, roughly speaking, to connect as many of them as possible with as few groups as possible.

Not surprisingly, the strategic dilemma of Havannah - 'spider' versus 'snake' - is revisited here. The edge is important to get control of a sufficient number of sprouts, but the center is clearly the area where connections are made. One may sacrifice a couple of sprouts to connect one's own live groups, as in the example given in the rules: one group controlling eleven sprouts wins if the opponent has four groups or more, and loses if he has three groups or less. The resulting tension between moving near the edge or higher up is totally reminiscent of Havannah, as is the loop, that fulfills the same tactical role: a tool to cut and/or connect.

There are important differences nonetheless. In Havannah the fastest connection is usually very important, whether it be ring, bridge or fork. A frame doesn't mean much if the opponent has a faster one. In YvY the score is accumulative, and in terms of the absolute win, a loopframe will usually not face a faster threat (the only option being a faster loop). So basically framing is winning.

Another difference is that YvY will usually have a 'Go type' opening, with claims staked out along the edges, whereas Havannah can have many different types of opening. YvY definitely feels more Go-like than Havannah.

@ David

David, any comments on the above rules? We plan to launch YvY @ MindSports in a couple of days.

Actually it has been launched and the final chapter of “How I invented games and why not” too.