The Last Gathering

Main Match 11: The Last Gathering

Your final task is to be a shepherd, which in no way trains you for the Final Match.

Congratulations for surviving up until this Main Match. This will be the last Main Match before the Final Match. As previously announced, the winner of this Main Match goes directly to the finals; the bottom two places will fight in DM11a, and the winner of DM11a will face the runner-up of the Main Match in DM11b.

In this Main Match, your objective is to be a shepherd. Close off regions containing sheep, but make sure not to have loose ends.

ℹ Overview ℹ

You will create a board filled with some fences, sheep, and lake. A sample board looks as follows:

Fences are the thick brown borders, sheep are the little white dots, and the lake is the blue square.

A region is an area completely enclosed with fences. In the board above, the area in pink forms a region, containing 8 sheep. A loose end is an endpoint of a fence that doesn't connect to other fences. In the board above, the pink region has 2 loose ends.

A board is made up of the frame and 16 tiles in the interior. The tiles are outlined by thin gray borders, and the frame is the big O-shaped area outside the tiles. Note that the lake makes up a whole tile.

During the game, you will build your board. You will first choose your desired frame, then you will auction the right to choose which tile everyone must place in their respective boards. At the end of the game, the scores are computed to give the final results.

Throughout the game, everyone's boards are public at the start of each round.

🖼 Frame 🖼

At the beginning of the game, you are presented with 6 possible choices of frames.

You will bid for the frame you wish to take. Choose a frame, and make a bid in garnets.

If you are the only player to bid for the frame, then you get the frame for free. Otherwise, the highest bidder pays their bid and gets the frame; in case of a tie, the player with more garnets at the start of the MM wins the frame.

Players without frames will redo this auction with the remaining frames, until everyone has obtained a frame. The game then starts.

If a player doesn't submit any bid: If, after resolving the other bids, some bidder ends up not getting any frame, then these non-submitters also don't get any frame and will proceed to the next round of auction. However, if all bidders do get a frame each, all non-submitters get assigned a remaining frame randomly. (This makes sure that people that do bid will still have choices, and if all bidders have chosen, non-bidders won't block the game.)

🔄 Rounds and tiles 🔄

There are 5 kinds of tiles, named end, straight, bend, junction, cross (alternatively -, I, L, T, +):

Each tile features 1 to 4 fence segments, and also 4 quarter-sheep on its corners. When 4 tiles meet together on a corner, or tiles meet the frame on the border, the quarter-sheep match up to form a whole sheep. (The lake tile you saw on the example board is a special tile, described later.)

Fence segments on a tile divide the tile into several sections, marked with letters above. (Note: Due to symmetry, some sections are not labeled.)

The game is divided into 15 rounds, and each round is divided into 2 phases: auction and placement. Similar to the previous MM, phases from different rounds overlap: a round's placement phase runs concurrently with the next round's auction phase.

In the auction phase, you will auction for the right to choose and populate a tile. In the placement phase, you will place the tile chosen into your board. The trick is, everyone will place the same tile (the tile chosen by the auction winner); the only difference is their location and orientation on their respective boards.

🎭 Tiebreaking order 🎭

During the game, it might happen that there are ties. To resolve a tie, a tiebreaking order mechanism is used. This is the same mechanism as in MM8 (Pair Auction), so you may skip it if you already know it.

At the beginning of the game, the tiebreaking order is in order from highest garnet to lowest garnet: Jiffa, Allan, Aslyui, Athin.

Whenever there is a tie, the tiebreaking order is consulted. The player higher in the order wins the tie.

After each auction (explained below), the winner of the auction is moved to the end of the order, and everyone else is pushed to the front. Thus, for example, if Allan wins the first auction, the order after the first auction becomes Jiffa, Aslyui, Athin, Allan. This means someone that recently won an auction will have disadvantage in ties.

💸 Auction phase 💸

During the auction phase, you must submit a bid in garnets, as well as a tile from the global supply. You may optionally spend garnets to populate your tile by adding more sheep on it.

• Your bid must be a whole number, at least 0 and at most the number of garnets you have (minus those you spend for populating, see below).
• The tile chosen must still be available from the global supply. If a kind of tile runs out, you may no longer choose it.
• To populate a tile, state that you're adding an extra sheep on a section. You may only add 1 sheep; it costs 3 garnets.

For example, a valid submission is as follows: bid 3 garnets to choose a junction (T) tile with an extra sheep on section B. (This would be the following tile:)

If you win the auction, you will pay the bid you declared, plus the price for population. Your tile will be put up for everyone to place on their respective boards in the placement phase. If you don't win the auction, you don't need to pay anything, but you also can't get your desired tile.

In case of a tie, break ties with the tiebreaking order; see above.

After each auction, the winner of the auction is moved to the end of the tiebreaking order, and everyone else is pushed to the front; see above.

Each kind of tile may only be won 4 times throughout the game. If a kind of tile has been won 4 times, you may no longer choose it for all future rounds.

All bids and tiles selected will become public at the end of the round.

📥 Placement phase 📥

After the auction phase of a round, the winner will have chosen a tile. Everyone will now place the same tile onto their board, the only difference being what position and orientation the tile will be. The same tile is used for everyone, including whether it's populated.

To place a tile, simply state where on your board the tile will be placed, and in what orientation. A tile may be rotated, but not reflected.

🏆 End of the game 🏆

After all 15 rounds are over, the game ends. There will be one final spot in your board that is empty; that spot is automatically filled with a lake tile.

Scoring then commences. Each region of your board will score according to the following rules:

• If it's adjacent to the lake, then it doesn't get scored at all. (To remind you of this, a lake tile does not have quarter sheep, which means regions adjacent to the lake tile will have incomplete sheep. You don't score them because nobody wants to see butchered up sheep.)
• Otherwise, it scores 1 point per sheep and minus 2 points per loose end. Note that a region's score can be negative, if it has a bunch of loose ends.

Your final score is the product of all region scores.

For example, recall the example above:

The pink region scores 8 (sheep) - 2x2 (loose ends) = 4. The region to the top-right scores 11 - 2x6 = -1. The single-square region at the bottom-right corner scores 1 - 2x0 = 1. The two regions adjacent to the lake don't get scored at all. The final score of this example board is 4 x -1 x 1 = -4 points.

The scores are sorted from highest to lowest; that's the results for this MM. In case of a tie, the tiebreaking order at the end of the last round is used to break the tie here.

To remind you:

• The top place advances directly to the finals.
• The second place will play in DM11b, and will select the game played for DM11a.
• The third and fourth places will play in DM11a, the winner advancing to DM11b.

🕙 Timing 🕙

The first round of frame selection lasts for roughly 54 hours, until Saturday noon UTC. All future rounds of frame selection lasts for 24 hours.

Each phase lasts for 24 hours. To remind you, the placement phase of a round coincides with the auction phase of the next round.

If you miss a frame selection round, the rules are stated in the section about frames. If you miss an auction phase, you're assumed to bid 0, choosing a random tile still available, with no population. If you miss a placement phase, your tile is placed on a random empty spot in a random orientation.

In all cases, rounds/phases can end earlier, if everyone have submitted and declared they wish to end the round/phase early. Future deadlines are set so the round length is between 24 and 48 hours, with updates at the usual time (noon UTC). (This means deadlines don't change, except if a phase now lasts over 2 days, it's cut by a whole number of days to make it 1 day and a bit.)

Rule clarification: In the unlikely case none of your regions score (because they all touch the lake), your final score is 1 point.

Rule clarification: The tile placed is identical for everyone. This not only means which kind of tile, but also whether it's populated. Winning an auction only gives you the right to choose what tile everyone must place.