The Tetris Effect
Tetris was a hit videogame and I’m sure that anyone reading this article knows it intimately - but what Tetris did was really imprint a certain knowledge of tetrominoes on an entire generation of players.
There are 7 Tetrominoes - I, L and J, Z and S, O, and T. At least - for Tetris there are 7. 2 of these pairs have mirror symmetry, so in a boardgame scenario where tiles are often double sided and as such can be flipped as well as rotated you actually only have 5 - J disappears as a mirror image of L and Z disappears as a mirror image of S.
The 7 tetrominoes that exist if mirror images are considered to be different.
Pentominoes take you to 12 different shapes, and they have names too.
As an aside, as well as a huge boardgaming enthusiast I am also a big puzzle nerd. It’s amazing how much easier it became to reason about shapes when I realised they had names1! My point about these shapes is how familiar you are with them can impact how well you perform at certain boardgames.
For example, when I first played Bear Park, I recognised that the pieces had been partitioned by size and shape. There being 12 larger pieces had my spider sense tingling - indeed they are one full set of the 12 pentominoes. Straight away I could see that meant that the pentomino tiles were unique, and I was going to have to avoid being left with the difficult-to-fit pentominoes like the X, well known for cutting your remaining free space into multiple small areas, which is absolutely not conducive to an efficient covering tile layout.
Here’s an example from Patchwork, which mixes polyominoes of many different sizes, and allows you to choose from the next available 3. I need to take one of the upcoming 3 tiles and place them on my board. The first available tile is a long Z piece, does it have a good home on my board? Answer in the footnotes2. Of course, in the game you could pick up the piece and try it out - but you can’t pick up future pieces without at least alerting your opponent to what you’re thinking about. Even just picking up the piece could make your opponent realise you’re dependent on that shape and do what they can to thwart you!
Another thing worth pondering about this position. The bottom-left area has 10 empty spaces. How is this going to be filled? It seems difficult to fill it with 2 pentominoes, as it doesn’t divide in half neatly without trying to be 2 P shapes where Patchwork only contains one P, or needing a T and a V shape, only T is already on my board! So my best bet is probably a 4-3-3 split of the 10 remaining spaces, or a 5-4-1 if I can expect to pick up one of the special bonus patches. But if you’ve never thought to look at the empty space you have, count the cells, and work out what size pieces you need to fill it, that thought alone can level up your spatial game across the whole genre3.
If you enjoy this kind of spatial reasoning then be sure to check out Bear Park, Blokus Duo, Patchwork, Cottage Garden, Ubongo (which adds a speed element), or even A Feast For Odin, which puts shape placement around a crunchy worker placement core.
Connectivity
Shape isn’t all about polyominoes fitting into holes however, sometimes it’s about joining lines. Here’s an example from the tile-laying game Tantrix, in which each player is a particular colour and you are trying to make your longest line longer than the longest of your opponent’s4.
First, a quick primer on the Tantrix tileset. Every tile is hexagonal, and consists of 3 differently coloured lines, each joining 2 of the sides. There are 4 colours in the game, so each tile is missing one of the colours. Every combination of colours and connections exists except one - they shun the shape that would be made from 3 straight lines going across the hexagon, leaving a set of 56 tiles instead of the ‘full’ 64.
For example, and this is relevant to the puzzle I’m about to pose, here are the tiles that have a short Red corner (i.e. two adjacent edges are connected by a red line) and that have a yellow edge immediately after the red corner, clockwise. (I would call this a RRY tile, as reading clockwise, 3 of the tile edges are RRY.)
Logically, I think you can see that the Yellow edge must join to one of the 3 remaining edges, and that leaves 2 unjoined edges which must be joined, but either in Green or Blue. That’s a total of 6 possible RRY tiles, and here they are:
The 6 RRY tiles in the Tantrix set.
So here’s the puzzle. It’s your move, and the position is as below
We are playing red5 have two choices of tile to play here (this is of course a simplified version of events. In a true Tantrix position you would have a hand of 6 tiles and also be able to see your opponent’s hand of 6 tiles). Your first visualisation challenge is to see what each tile does to your red line - the red curve extends your line but curves it away from the other endpoint. The straight threatens to loop red into an 18-tile loop for 36 points which we will assume is a game-winning score, but it will leave a RRY gap.
The question then - is there a RRY tile remaining to fill that gap? Answer in the footnotes again.6
Tournament level play of a game like Tantrix involves the ability to track and count various different tile combinations, do it under time pressure, all whilst accounting for edge cases like realising there is exactly 1 RRY tile left, and also 1 YYG tile left, and realising that it’s the same tile.
If you like the sound of this kind of connectivity game, have a look out for Tantrix, but also check out Metro, Tsuro, and Flow: Untamed Rivers. These are the purest connection-making games I can think of, but I do absolutely adore Age of Steam, a game about making connections to deliver goods but with a vicious auction-based financial aspect to it.
Incidentally, does anyone think this tile is actually a grumpy face as might be found on a totem pole, or that mask from Crash Bandicoot?
How do you like your skills tested?
My point here is this - If you did or did not like a particular boardgame, maybe the root of this feeling lies in which skills are being tested by the game. Judge a fish by its ability to ride a bicycle and you might think the fish is stupid, but let a fish judge your hobby by showing them a bicycle and they might write off gaming as a concept and never come back for water week.
The same goes for designing games - you must consider what skills you are asking your players to exercise to do well at your game, and whether the combination of skills you’re asking for match your target audience’s idea of fun.
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1 I definitely have the GAPP series to thank for this - Generally Approachable Pencil Puzzles posted daily on the Fan Discord for Cracking the Cryptic, a YouTube channel that introduced me to variant sudoku puzzles amongst other things and really got me mentally through the pandemic. If you pop along to the #daily-pencil-puzzles channel, tell them I said hi!
2 Yes it does! It might not fit well in the bottom left or bottom right areas, but on the top left it works beautifully well with the remaining shapes to fill the area - marked up image below!
3 I think I really learned this lesson when trying to solve the pencil puzzle Pentominous. As every piece in a Pentominous puzzle takes 5 cells, every time you divide your remaining empty space up, it needs to be 5, 10, 15 spaces, in order to neatly sub-divide into pentominoes. Cordon off an area of 9 spaces or 11 and you’re never going to be able to fill it no matter how many pieces you try out.
4 There’s another interesting quirk in the scoring - a closed loop counts double, so a loop of 12 tiles will score 24 and therefore beat a line of 23 tiles. There’s an interesting skill-test in deciding whether to force your opponent into a loop to limit their score, or to add to their line in the hope of preventing it from looping. The question is - if you force them into a loop, can you beat the target score you’ve now set for yourself?
5 The best colour, and yes, I have a problem.
6 Yes! 5 of the RRYYGG tiles are accounted for, but RRYYGG is unaccounted for. The gap will be filled and red is well on their way to winning this game.
Brain by Wes Breazell from Noun Project (CC BY 3.0) used under license