Game thinking from Adam Clare

Tag: math

Board Games Keep Evolving In Form And Function

Board games have seen a resurgence in the past few years for a variety of reasons, and as a result we have seen an evolution in the style of games, critiques of their design, and the technology the games use.

Over the past few months I’ve come across some cool new developments and analysis on the world of board games.

The beauty of hex grids
If you’re using square or rectangle tiles then you’re living the past. Step up your game by getting with the greatest of grids: the hex.

The 13am team knows my love for hex grids and brought my attention to this great article at Gamasutra: 20 Fun Grid Facts (Hex Grids). Here’s one of those fun facts:

Fun grid fact #6: There is only one magic hexagon with more than one cell

There are magic squares possible for any order, where all the numbers run from one to however many cells there are. But, except for the single cell, there is only one such magic hexagon possible (ignoring reflections and rotations).

Magic shapes that have all the integers in sequence starting from 1 are called normal. Abnormal magic shapes have numbers in sequence that start at a different integer. If we allow abnormal magic hexagons, then there are more possibilities.

If that doesn’t convince you, take a look how hex grids are influencing architecture! Here you can see that hex grids can be used almost anywhere.

Dealing with chance

For board game design exercises I purposefully don’t let people use dice (for reasons that would require their own post); but that doesn’t mean dice are not a good thing for games. Indeed, there are some great games out there which use dice as the primary mechanic. That being said, in my experience new game designers of table top games of all forms tend to use dice as a crutch.

If you’re thinking of using dice in your game you should give this article on to use dice effectively a read. The article looks at Alien Frontiers creator and his goals to make dice games better and more engaging.

Any given turn of Castles of Burgundy, for example, can give players an almost paralyzing number of options. When a player’s roll doesn’t match the actions he wants to take, he may spend workers to make it match. Or he may spend a die to get workers and ensure that he can take the action most important to him. Or he may conserve his workers, ignore the actions he planned to take, and hope he can do them more cheaply on the next turn.

In the 5,000-year scale of dice history, that’s an incredibly new dynamic, but it may be an idea whose time has come. Feld and Niemann arrived at their designs independently. At the time that he created Alien Frontiers in 2010, Niemann had never heard of Feld’s work — despite the fact four of his dice games had reached publication. Instead, Niemann said he drew his inspiration from a game called Kingsburg.

Cultural analysis of games

Not only is there better analysis of how to make and design games every year, we also get better critiques of games.

Bruno Faidutti has an excellent piece titled Postcolonial Catan in which he explores the current aesthetics in popular board games. He looks at the games he’s created and others in a way many designers never do.

There is something old-fashioned, charming and romantic, not only in the themes and settings of boardgames, but also in their graphic style. See the covers of Ticket to Ride and Settlers of Catan, probably the two most influential typical board game designs of these last twenty years. Playing games has become a powerful anxiolytic in a western society which probably feels less secure than it did a few decades ago. This might explain why board game sales are countercyclical, why game designers are mostly old white males (I’m one), and why game themes and looks sound so old-fashioned.

He goes on to other important issues in the world of board games in both player and desirgern terms. Indeed, he has a great take on the use of other cultures in the games we play and make. This is also the first time I’ve seen Edward Said’s Orientalism used in an analysis of board games.


Lastly, here’s a fun article looking at the history of how electronic board game have changed over 100 years. That’s right 100 years. To be honest, I didn’t know that electricity was being used that long ago – it seems downright dangerous.

The first electronic game (pictured above) was Electra in 1910!

Parrondo’s Paradox

When I tell people that I teach game design theory usually they just hear game theory and admittedly there are some connections. Take a look at Parrondo’s paradox, it does comes up in game design although it isn’t often referred to directly.

The basic idea of Parrondo’s paradox is that one can “win” by losing at two separate games, as long as those games being lost are different. Playing either game on their own will result in a loss, but playing the games together in a certain way can mean winning.


These images from Wikipedia may help visual thinkers understand what’s up:

io9 has an OK example of Parrondo’s paradox:

This isn’t just a mathematical abstraction that Parrondo came up with. It’s based on a physics concept. If people placed water at the bottom of a long, gentle slope, the water would just stay there. If they placed it at the bottom of a spiky slope, like the one simulated by the second game, it would also just sit there. Any water placed at the top of either slope would roll down it. But if the slope flashed back and forth between its smooth and spiky counterpart, the water would actually travel uphill. Parrondo considered this physical finding, and translated it into a game to come up with his paradox. The paradox is now being studied by investors and financial analysts, eager to see how they, too can juggle losing assets to make the “slide uphill.”

For another interpretation on how this paradox can work in the real world for tangible benefits, check this out:

Since the Paradox has been reported a couple of years ago, many real world and abstract examples has been thought up that make it more palatable. Indeed, monetary rewards apart, a combination of negative trends may lead to a positive outcome.

Brooke Buckley, an undergraduate student from Eastern Kentucky University, mentions in her honors thesis that it’s a well known fact in agriculture, “that both sparrows and insects can eat all the crops. However, by having a combination of sparrows and insects, a healthy crop is harvested.”(*)

This is taken from a good introduction to the Parrondo paradox, which has some more examples.

How does this relate to game design you ask? In many different settings it can have impacts that you may not have predicted.

Keep the sparrow example in mind as you think of ways that people can (and do) exploit MMOs. A single person may die consistently in one area, but if the player is put in that area with other competitors (who the original player would lose to) the chances of the player passing that are may increase. Essentially, you can get ahead by combining two losing opportunities.

Another example could include ammo or health replenishment. If a player needs to acquire both but can only do so by playing two separate mini-games they can, in essence, still progress even if they lose at both. Go to one mini game, get health and lose ammo, then go to the other mini game and get ammo, but lose health. It’s all about finding the pattern that permits a net-gain in both.

A simulator that explores this paradox can be found here.

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