Complexity, Dominant Strategies and Balance in Upwords

Complexity in Game Design is a heavily debated topic. In his blog, Dan Felder chooses to categorize complexity into 3 distinct categories. Comprehension complexity – the difficulty in understanding what the designer is trying to communicate; Tracking complexity – the difficulty in keeping track of, or remembering everything that the designer taught you; and Depth – the difficulty in figuring out the best possible move in strategy games.

I agree with the criteria of distinction for the first two categories. But what he describes as Depth, I find, is an emergent category instead of being distinct. Coming up with the best possible moves in a strategy game resembles coming up with a Dominant Strategy. The depth of the game depends upon how difficult it is to come up with a dominant strategy.

A snapshot of my play-through

Dan uses Chess as an example to explain these concepts. I chose to examine one of my favorite board games – Upwords. It is a word building game akin to Scrabble. The twist is that players can stack letters on top of each other to change the words that have already been placed. Examining Upwords by applying these criteria, we can easily say that the comprehension complexity is low.

The player can easily understand that he is supposed to form words using the 7 letters he picked. The tracking complexity increases steadily as the game progresses, as the number of possible places to form words using existing letters also increases. There is an additional level of tracking complexity here in the form of stacking, to change the words that are already placed on the board.

The designers of Upwords added a layer of tracking complexity to the existing one provided by Scrabble. However, they chose to reduce the size of the board to force the players to stack letters and make use of the vertical axis instead of just expanding breadthwise. They also removed the frequency-based scoring system of Scrabble which rewarded players with additional points when they used rare letters. There also aren’t any special squares on the board that provide a bonus reward. Keeping track of the number of different ways one could play their turn might be a little tricky to accomplish during the first couple of games. But soon, the player realizes that he can score the highest by using as few letters to change as many words as possible during his turn. There is a clear dominant strategy in this game. But does that make it boring as soon as you discover it? Quite the contrary.

What we see is that the discovery of the dominant strategy is still limited by two random factors – the probability of picking a letter that can be used effectively, and the (un)predictability of the other players. This is where balance comes in. The game’s fun factor can change based on the number of letter tiles for each alphabet in the bag and the placement pattern that the other players chose to follow. So even though there is a dominant strategy that can be followed to get the maximum possible points from in your game, the ability to adapt that dominant strategy to the actions of other players and the availability of letters is what ultimately decides the winner. I still didn’t discuss one vital mechanic of the game – if a player uses all the 7 letters in his hand on a single turn, he gets 20 points. This is still not necessarily the highest possible points you can get in a turn. But if played early in the game, it serves as an intimidation to the other players. The emergence of a dominant strategy can be mitigated by bringing in the behavioral aspect of the players.

By keeping the comprehension and tracking complexities low and by providing a behavioral aspect to the existing rules of Scrabble, the designers successfully made a game for players who are anxious of its complexities. Upwords keeps the players engaged by making the discovery of a dominant strategy fairly simple but adding enough tracking complexity to keep the experienced players come back for more. The complexities of design and discovery of dominant strategies influence the way the game is balanced. Hence, balance arises out of the difficulty in discovering a dominant strategy, which in turn arises out of the difficulty in comprehending the mechanics and keeping track of them to make informed decisions.

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