Tuesday, September 22, 2009

Responding to Things We Think About Games -- Gaming Expectations: Playing Optimally

Last week, Cinerati featured the first in a series of responses to the book Things We Think About Games. In the post, I discussed how the interaction between a game's narrative and its mechanics might affect the player's experience. In particular, I praised Robotron 2084 and criticized the Dawn of War real time strategy game. Both games are highly enjoyable, but when Dawn of War is played in Campaign mode the ending leaves the player feeling less than satisfied with their achievements.

But specifically narrative expectations aren't the only kinds of expectation players can have when approaching a particular game. Some gamers look at the game system itself as a kind of puzzle to be solved. Many games, particularly war games and games like chess, tic-tac-toe, and checkers, have a finite number of "good moves." In fact, some games can be "solved." There is a perfect way to play checkers and chess -- thankfully the "solutions" to these games are so monumentally complex that there are currently no players who play these games "perfectly." One of the lessons of tic-tac-toe is that solving a game can make future play less fun than "imperfect" play. For these players, the examination of the system itself is a wonderful experience -- one that I will touch upon more fully in a later post -- but their mindset, that games are puzzles to be "solved," can be a useful one to those who are more competitive in their gaming habits.

Which brings us to the passage in Things We Think About Games that I'd like to talk about today:

If doing well matters to you, learn the optimal methods for the games you like.

I'll be honest, I'm not one of those people for whom doing well at a game matters. I blame Candyland for this, but for me the most important thing is that everyone is enjoying themselves. One can only submit themselves to the whims of fate, unalterable fate, as manifest in Candyland so many times before they begin to care less about winning than most game players. But I also happen to be one of those people who likes to break game systems into their respective parts and put them back together, so I do tend to play "more" optimally than someone who doesn't care at all. I just have a different motivation for finding the optimal methods for the games I like. This also means that I don't mind being totally "owned" by an opponent at Blood Bowl, as long as I can see why I was getting so easily destroyed.

But for those who do care whether or not they do well, which might be different than winning, the analytical tools that those who treat games like puzzles use are one of the first places a player should look to find out what the optimal methods of playing a particular game are.

Take for example this brief analysis of die probabilities over at the Giant Battling Robots blog. Take a moment to read Kit's article and come back to this page. We'll still be here, I promise.

The post is expressly about how modifications (bonuses and penalties) to a bell shaped probability curve have disproportionate effects on the player depending on where along the bell curve a particular target number is. That is to say that a penalty punishes the player more, with regard to a positive outcome, the closer to the middle of the distribution the initial target number was. A -1 penalty when the target number needed for success is 11 or greater, on 2 ten-sided die added together, is about 10%. The -1 penalty effectively changes the target number from 11 to 12. Whereas the same -1 penalty on a target number of 19 is only a 2% penalty.

This means that any player participating in a game that uses die rolls that have bell shaped probability distributions -- games like Feng Shui, Dream Park, and Battletech (notice I am counting "opposed" d6 rolls as the same as a 2d6 roll as they are the same for probabilistic purposes) -- one should examine what significance the individual penalty or bonus will have when making a decision. The human mind typically inducts all +1 or -1 modifiers to be the same, but this isn't the case when the die rolls have a bell shaped distribution. This means you might take a risk you might otherwise ignore if it only has a moderate affect on your probability of success. You need to know when +1 means +10% and when -1 means -2%. This lets you take more rational risks, ones that are more optimal.

Kit uses this analysis to come up with a quick equation that can be used "on the fly" to determine whether you should take a particular action. All you need to know is your initial target number, your opponent's initial target number, and how much your action will affect each of these. This is a powerful tool that can be used in a number of games and will help the player play more efficiently.

One doesn't need to be a mathematician or statistician to utilize these tools either. Thankfully, there are plenty of mathematicians and statisticians who are willing to write their discoveries regarding a particular method, and put it in layman's terms. Perhaps Kit will follow up his article with one including specific examples of how his quick equation is used. Besides this, the massive number of Chess and Poker books available at bookstores is testimony to the fact that there are those willing to share optimal play. Likely because they like to play with others who care about playing well as much as they do. Take some time to find these resources, if only to find out more about how a game works.

There are many games, Dream Park I'm looking at you, that could have benefited a great deal if they told the players a little bit about the mathematics behind their opposed roll systems. Many a GM running Feng Shui has misinterpreted the significance of adding as little as 3 points to a villain's skill/statistic. It can change the dynamic from a fun night gaming, to one where the villain is impossible to defeat. In role playing games, GMing optimally, means understanding how changes in one part of the game affect the probabilities of success. In Candyland, playing optimally means not minding that the results are predetermined the moment the cards are shuffled -- though you don't know the result -- unless you shuffle the full deck after each move in order to intentionally create a Markov-chain.
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