Trike

Move a shared pawn on a triangle board, dropping your checker on each destination. When the pawn cannot move, score checkers under and next to it.

Inventor: Alek Erickson
Year: 2020

Published listing: BoardGameGeek: Trike.

Rules: Play on an equilateral triangular hexagon-tessellated grid. Use a neutral pawn and black/white checkers. Players take turns moving a neutral pawn around on the board (passing is not allowed). The neutral pawn can move any number of empty points, in any direction in a straight line, but cannot move onto, or jump over occupied points. When a player moves the pawn, first they place a checker of their own color, onto the destination point. Then they move the pawn on top of it. When the pawn is trapped, the game is over. At the end of the game, each player gets a point for each checker of their own color adjacent to, or underneath, the pawn. The person with the highest score wins.

Implement pie rule. This means, at the beginning of the game, the first player chooses a color and puts a checker on any point of the board, with the pawn on top of it. At this time only, the second player has a one-time chance to swap sides instead of making a regular move.

Learning, casual (default 11), competitive, and large boards.

Trike is a game of traps. But…is there a precise definition of a trap? In one sense, the term trap refers to a space where the winner is pre-determined, should the neutral piece be trapped there. But more broadly, the term can be used in an extended sense, where the “chain” of empty spaces leading to such a “dead end” is also called “a trap”. Less specifically, we can call it any “corridor or bending but non-branching path” that if the neutral piece is forced down that path then the game is solved.

1. Traps are the currency of Trike. In case of doubt, set a trap or extend a trap. Larger traps catch more fish. A bridge is two half traps, while a triangle is four half traps. Conversely, avoid creating enemy traps with your own moves.

2. Play inside a trap to defuse it. The more enemy pieces you touch now, the less you will touch later. Don't try to defuse a trap from the wrong angle, or you risk improving it. Because the opponent can defuse a trap, making two traps gives you one, while one gives none.

3. Make the adversary defuse their own trap. The reason is simply because buried stones are useless.

4. Curvy paths must be traveled one step at a time. That is why curvy traps are better than straight traps.

5. Do not partition the board. Instead, force the opponent to make the inevitable board-dividing “clogging” moves, by playing moves such that all follow-ups partition the board (finishing the corner of triangular structures can have this effect, as can 2-wide corridors with even spaces left after your move). When this occurs you will have the option of choosing which side of the board to play on. When given the choice, stay on the better half of the board (where you have more traps), but take care to avoid playing in and around your own traps until the enemy falls in.

6. Trading a trap for influence is an acceptable exchange. Defusing enemy traps is good, but if you only play defensively, you won't be able to make traps of your own. Deciding when to prioritize building over defusing is the tricky part.

7. Don't swap pie offers in the corner. Instead, swap pie offers just next to the corner. The reason is because a lone stone one space away from the corner is, by itself, a trap.

8. Do not play in line of sight of where you want to go. This is because the adversary will take you away from there.

9. Both the last AND the second to last move count as points (not just the last move). Along these lines, there are partisan traps (majority exists before the final three moves) and parity traps (majority depends on the third to last move)

Puzzle #1: Red to win in 27 moves. You do not need to brute-force calculate to understand the principle behind the winning move.

This puzzle follows the principle of “Do not partition the board. Instead, force the opponent to make the inevitable board-dividing “clogging” moves, by playing moves such that all follow-ups partition the board (finishing the corner of triangular structures can have this effect, as can 2-wide corridors with even spaces left after your move). When this occurs you will have the option of choosing which side of the board to play on. When given the choice, stay on the better half of the board (where you have more traps), but take care to avoid playing in and around your own traps until the enemy falls in.” The only non-partitioning move is i1! In Blue's replies, all possible ways forward are partitioning, which allows Red to choose the side that is winning. Since Blue owns a trap in the North, and Red owns a trap in the South, the correct answer is to then steer the pawn Southward.

Example #1

This move illustrates the principle of: “Because the opponent can defuse a trap, making two traps gives you one, while one gives none. ”

In this game, one can anticipate the way the pawn moves many turns in advance, precisely because traps get avoided. Generally, traps get avoided because falling into an opponent's trap would lead to a loss. Also, cells in line of sight of traps get avoided by trap owners in order to maximise a trap's utility. This naturally leads to the board getting carved into corridors with natural endpoints left behind. These corridors have a kind of exclusivity, in which occupation of one corridor eliminates the other from the game tree. The identity of traps terminating the often branching structure of corridors can be used to calculate which 'side' of a clogging move is favorable. In the image below, I drew lines to illustrate the corridors, and star the traps. What is amazing is that brute force calculation is not required at all to predict very accurately that the game is likely a win for Red due to their excess of traps in this position.

• Current engine version: 20240118 (2024-01-18). On Abstract Play since 2023-12-26.

• https://boardgamegeek.com/boardgame/307379/trike
• https://ericksonlaboratory.neocities.org/Abstracts/Trike/