Inversion

Inversion is my first abstract board game, invented in 2010 and played with two people. This PDF is a convenient one-page rule sheet, which is reproduced below in a blog-friendly format.

Board

Inversion is played on a hexagonal board with five cells per side.

Inversion board

Objective

The objective of Inversion is to occupy more cells with your own stones than your opponent when there are no legal moves remaining. This occurs when all cells have been occupied.

No draws are possible in Inversion.

Play

Players move alternatingly, starting with White.

The player must first place a stone of his or her color in any empty cell.

hex is any set of seven cells consisting of one center cell and its six surrounding cells. The dominant color of a hex is the color occupying four or more of the seven cells. If the player’s stone occupies the last empty cell in a hex, then the stones of the dominant color in that hex are replaced by stones of the non-dominant color. This is called an inversion.

Inversion example 1

The placement of a stone often completes multiple hexes simultaneously. In this case, the player may choose the order in which to invert the hexes. Each of the completed hexes must be inverted once and only once.

Inversion example 2

Inversion example 2a

Inversion example 2b

Commentary

Inversion is probably not as good a game as Annelids, but that might just be the result of insufficient play testing. Specifically, it isn’t obvious to me what rule for dealing with multiple hexes is most robust against strategic abuse. Maybe players should alternate choosing which hex to invert when a stone completes several hexes (in this case, you would probably let the player who placed the stone choose who starts inverting hexes). Or maybe no more than one hex should be inverted per turn. And so on.

The biggest problem with the game in its current form is that whoever goes last generally has a big advantage since the last hex flip can make rack up quite a few stones all at once. The player who goes last is also the player who goes first because there are 61 cells on the board. This could easily be compensated for by awarding automatic points to the second player, a practice known in Go as komi. However, it’s hard to say what the value of the komi should be without data on scores equal-skill players end up with. It is also popular to fix first-move bias with a “pie rule,” where one player goes first (cuts the pie) and the second player chooses which color to play afterward (picks their slice). However, the pie rule probably doesn’t help here because the advantage of having the last move might outweigh the strategic impact of any first move selection.

The coolest thing about Inversion is that players have conflicting motivations about when to start dominating the board. If you start out by just trying to fill the board with as much of your color as possible, then you’ll probably lose miserably because this makes it easier for your opponent to invert a lot of the board later on (since a hex inverts to the minority color). In my experience, this adds a pretty interesting element to the strategy.

Short version: I think Inversion is promising, but am looking for people to play test it with me, probably using a variety of “house rules” to see what works best in practice.

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