Marbar means "of killing."

The game starts with a rectangular grid of squares, all but one of which are occupied by "civilians." With two of those civilians are "hunters", one belonging to each player. The center space is occupied by the "monster:"

A turn consists of two steps, both of which are mandatory, but only one of which (usually) involves a choice:

• Move your hunter orthogonally one step to any space occupied by a civilian, and not the opponent's hunter.

• Move the monster orthogonally one step. This is always deterministic:
  • If there is only one civilian adjacent to the monster, it moves to that space and devours the civilian there.
  • If there is more than one civilian in reach, it favors them in this order:
    • Minimal straight-line distance to the hunter that just moved
    • Minimal straight-line distance to the other hunter
      • These two are sufficient for the vast majority of cases
    • Move toward the starting space of the hunter that just moved
    • Move perpendicular to the direction the hunter just moved

When the monster moves, it devours the citizen that it moves to. Any space occupied by the monster at any point in the game must remain vacant once the monster steps off of it.

To win, you must have a straight orthogonal line between your hunter and the monster, with no civilians in between, so that your hunter has a clear shot to kill the monster. This can only happen on your turn, before or after you move your hunter but before you move the monster. After you move the monster, it is no longer your turn and you cannot win the game if it is not your turn.

Black to move, but the monster has only one possible move.

White to move...

It is still White's turn, so White wins.

If your opponent's hunter gets eaten, you do not automatically win. You may take unlimited moves, but if you cannot kill the monster then the game is a draw. If the monster is immobilized and neither hunter can reach a place from which to kill it, the game is a draw.

I write poetry sometimes. I've been playing around with a new form that I call ring-terzanelle, which I quite like. This is one of my early attempts:

Click here to download:

ShownbythePhoenix.pdf (41 KB)

(download)

Click here to download:

ShownbythePhoenix.pdf (41 KB)

Yusailo is a pen-and-paper game for 2 players. The goal was to make a pen and paper game that takes less set up than Dots and Boxes, and is easier to play than Sprouts.

To start out, mark some number of spots such that you can distinguish between spots owned by one or the other player. On paper I like to mark X and O for the spots, over the internet I use these:

One player decides how many of which spots to place; the other player chooses whether to move first or second, and decides which side to play.

A basic move is drawing a line or curve that begins at one of your own spots and ends on any spot, (subject to restriction) and then placing a new spot of your own somewhere on that line:

Every spot has three "liberties": if a spot is connected to three other spots, no new lines may originate or end at that spot. If the spot that your move ends on -- regardless of owner -- becomes a dead spot as a result of your move, then you must move again beginning with the new spot that you just added.

Black is compelled to make another move, but there is nowhere to move to.

A3G is a game that came out of the same process that eventually produced Yusailo. It can be played with pen and paper, but it takes more set-up than Dots and Boxes, which was a key design goal. For this reason it is not completely finished. During that design process, I went through so many terrible ideas that I started naming them like pretentious modern art, but with the series title "Abomination." This was the third iteration in that series, Abomination #3 in Grey, which got shortened to A3G.

For two players, X and O. Begin with a rectangular grid of points.

A turn consists of drawing a rectangle around some number of points, such that:

• It may share edges or parts of edges with other rectangles, but no lines may cross.
• It may be inside of another rectangle, but must not contain another rectangle.
• It must be around 2 or more spots.
• Whatever region it is in, it must divide the spots there into at least 2 non-empty groups.

The formal definition of "region" is a bit convoluted, but in practice it is pretty intuitive: if you can legally make a rectangle around two spots, they are in the same region. There are some edge cases that this doesn't cover, but intuitively it works fine.

Formally: If a straight, orthogonal line could connect two spots without crossing another line, those spots are in the same region. This property is transitive: if spot A is in the same region as B, and B is in the same region as C, then A is in the same region as C, whether or not they have a clear straight-line path.

Regions with only one or two spots are "dead" -- no moves can be made in them by either player. When you make a move that creates new dead regions, mark those regions.

Passing is not allowed. If there are no more moves available, the game is over. Count the number of spots in regions marked by each player, that is your score. Determine a winner based on that score.

Ok what I mean is, I have not done enough testing to know if a high score or a low score makes more sense for the win condition. My gamer intuition is that low-score is a better goal, because the high-score game seems like it could degenerate into just making little boxes and then somebody wins. I could be wrong about that though, and if there was a way of crushing that strategy, then the game could be very interesting.

After some more investigation, I figured out that I was playing Yusailo all wrong. I think for a new game, this is a good thing.

I stripped it down to the smallest possible sub-games, and discovered some interesting things. A game with one spot per player is a first player loss, but two spots per player is a first player win -- if that first move is to connect two of your own spots. It turns out that having a lot of liberties isn't always a good thing, if your opponent can exploit them.

Adding just one spot can totally change the strategy of the game, and it looks like there are diminishing returns pretty early on -- a similar problem to Kitaran. I found that with a lot of spots, it becomes too easy for one or the other player to split the opponent's spots up and create lots of free moves.

Securing free moves is still important, but the game is by its nature non-local. It's entirely possible to win one region, secure a free-move there, but then leave the rest of the board in a position such that you will lose. There is some drama, it does appear to be possible to recover if your opponent gets a free move before you do. However, it is impossible right now to say whether or not this drama holds even with (as they say in bridge) "correct defense."

For this shallow examination, Yusailo has proven a fascinating game. It often seems like it is on the brink of collapse, about to show a dominant strategy for one side or the other, but I keep finding new ways of turning it around. I keep changing my mind about which player has the advantage.

For the future, I do not seriously expect that it will hold up -- it's just too fragile, and showing too many weaknesses. There is a chance that it could hold up under some amount of serious play, enough of a chance that I would like to pursue this avenue, but my quest to design a great game is not over.

So far Yusailo does in fact seem less obscure than either Sprouts or Dots and Boxes. Still, there are some interesting dynamics in the ways you can create free-moves for yourself while taking them away from your opponent. A powerful tactic is illustrated below:

After

1. 1(15)2
2. 4(16)15,16(18)3
3. 1(17)18,17(19)4[1,2]

the following position was reached:

This move must be answered immediately. As it stands, Odd has created a hot game, and Even wants to immediately make some move that ends on 2. Otherwise Odd will kill 4, leaving an extra move for Odd and no move in the region that Even can make -- 2 would be the only place to start a move, but it is also the only place a move can end.

The move 4(20)19,20(22)2 wins the region and deprives odd of liberties, but after

4. 4(20)19,20(22)2

5. 5. 3(21)3[5,6], 21(23)5

It looks like Odd has gained a genuine free move. It took a while to find the correct response in this situation:

6. 6(24)23, 24(26)6

And now Odd's clever move has turned into a bad mistake: Even has the free move.

5. ...21(23)8

Is even worse, as it allows Even to start splitting up Odds spots, and create a free move as well:

6. 8(24)23[7], 24(26)8[9], 26(28)9

The correct move 5 is probably

5. 3(21)3[6], 21(23)6

Now Odd has the free move they were looking for, and Even has been split up. Further, Odd has material superiority in the remaining region.

For a very long time, I have been trying to design my ideal pen-and-paper game. I am very fond of Dots and Boxes, but it takes just a bit too much set-up, and the tactics are somewhat obscure. Recently the game Sprouts captured my imagination; it is an even more elegant game, but also another wide leap more obtuse. I got caught up in the possibilities of a continuous-space game, and eventually worked out the rules to Yusailo. It is a combinatorial game that in practice does not play like a combinatorial, which has been a theme in some other recent abstract games (most recently Ayu, but the idea stretches at least as far back as Amazons.)

These are the rules as I have most recently played it:

• The start position is not necessarily defined. 5-7 each of X and O spots seems fine.
• On your turn, draw a line from a live spot that you own to any live spot, and place a spot of your own somewhere on that line.
  • A spot is "live" if it is connected to fewer than three other spots, and dead if it is connected to exactly three other spots.
  • The spot that you start from must be your own, and is the "source spot" of the move. The other spot is the "target spot".
• If a move causes the target spot to become a dead spot, then you must move again, starting from the newly created spot.
• If you cannot complete a move (that is, move to a target spot with 2 or 3 liberties) then you lose the game.

During development, there were a few tactics that seemed to threaten balance and gameplay. The worst of these was splitting the board early on into two regions, with only spots of a single color in one region. As it turns out, this is a losing strategy: the move seems always to creat a hot position. I have toyed with the idea of forbidding moves that have the same spot as both source and target, but so far that has not seemed necessary.

Sprouts notation is mostly applicable to Yusailo: use odd numbers for X spots and even numbers for O spots. The chain moves do not create ambiguity, since a player may not begin a move from an opponent's spot.

The principle objective is securing more territory in the form of free moves -- legal moves that are available to you, and cannot be taken away by your opponent. In this way it is somewhat similar to Amazons, though the different topology changes the character of the game entirely. I will post some illustrations and examples soon.

In the last post on Neighbors, I suggested a new extension of the limit on playing the highest number available: Whatever the largest number played so far, it may not be played more than twice; whenever a number becomes forbidden in this way, the restriction is passed to the next lower number. The intent was to offer the possibility of a larger space, but one in which the walls begin closing in.

To make the rule clearer, an example on 0-7:

2,5*

> 1,6* > 2,7* > 3,6 > 4,7** > 5,6* > 4,5 > 3,6** > 2,5* > 3,4 > 2,5 > 3,6*** O 0-1/2

So call the restricted number "poisoned": when the next higher number becomes poisoned, the lower number loses its poison entirely. Only once the higher number is removed does the lower number become poisoned again, and it starts back at zero. Thus causing the walls to close in gives your opponent control of the corner, but you have an escape: if you get caught in a corner loop, you can play the forbidden number and lose only 1/2 point instead of a full point.

Well, I'm not super happy about that, it comes dangerously close to breaking the game. But I don't think it does, I think that it may even improve balance, by making the corner loop worth strictly less than a mid-range win. It's one case where violating the intended spirit of the rules might actually be better than sticking to them: 1/2 points may work better as a fully-integrated part of the game, rather than as a sort of penalty, as I had first imagined them. Having multiple goals of different values is one thing that usually makes games more interesting.

With my experience in change ringing, I'm convinced that this is not, in fact, too much to hold in your mind at once. It's a lot, I expect it to be difficult, but I'm pleased to see just how flexible and powerful the human brain really is. I actually think this could be a game where even a referee has some fun, since they would have to keep track of as much information as the players, possibly more information. Just waiting to pounce on a fault, yeah, I could get into that.

On whatever range of numbers you choose, the top and bottom of that range will contain a trap, a guaranteed win for one or the other player. On a range of odd size, like 1-7, one player (in this case Odd) controls both traps, which makes Even's chances of winning very slim. On an even size, the player who controls the top trap does have some advantage, since the top trap controls more space (see the previous post on the subject) but this is made up for slightly because of the restriction on using the upper trap more than twice. Also, there is a way to "crash the trap" -- on 0-5 for instance, if the game starts 4,5 then the Even player still has a fighting chance.

So what does the game look like on larger ranges? It doesn't look good, run-away becomes a much bigger problem. Unless the starts are fairly close together, either player can grief and force a draw.

On 1-8:

2,5

If E wants to grief, and O wants to play:

2,5 > 3,6 > 2,5

If O wants to grief and E wants to play:

2,5 > 1,4 > 2,5

Similar problems arise at 3,6 and 1,4 obviously, and also at wider intervals. The problem is made worse because if both players are determined to engage, one or the other will have to give away an undercut just to get things rolling:

2,5 > 3,4 and the game can begin in earnest, but...

2,5 > 3,6 > 4,5 and O makes the sacrifice instead

Of course, neither player wants to be the one to make the sacrifice, so the dominant strategy in this case is for both players to engage in that oscillating run-away, since to engage is to be at a disadvantage.

There are some patch-rules that might fix the problem. Requiring that the opening moves be within some narrow range, or restricting how many times a player may move away from the center. In fact, that might make a good generalization of the "only play the highest number twice" rule, something like "the highest or lowest number yet reached may only be played twice, the count re-sets when a higher or lower number is played, and once a number at either extreme is forbidden, then the count is reset for the highest or lowest number still in play"

That doesn't make the game any easier or more elegant, but it may open up enough strategic interest to be worthwhile. It certainly adds a great deal more to keep track of in your head as you play, which is the principle source of fun (in my opinion, at least.) The principle questions to answer are "is it drawish?" and "is it balanced?"