Monday, 10 March 2008

Game Theory Applied to Random Games

Game Theory (or Decision Theory) is a branch of applied mathematics which is used in the social sciences (most notably economics), biology, computer science and philosophy. Game theory attempts to mathematically capture behavior in strategic situations, where an individual's success in making choices depends on the choices of others. While initially developed to analyze competitions where one individual does better at another's expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria.

Traditional applications of game theory attempt to find equilibria in these games—sets of strategies where individuals are unlikely to change their behavior. Many equilibrium concepts have been developed (most famously the Nash equilibrium) in an attempt to capture this idea. These equilibrium concepts are motivated differently depending on the field of application, although they often overlap or coincide. This methodology is not without criticism, and debates continue over the appropriateness of particular equilibrium concepts, the appropriateness of equilibria altogether, and the usefulness of mathematical models more generally.

Usually Random Games like Video Slots are analized mathematically from the point of view of Probability Theory. Our hypothesis is players act with a mix of strategies depending of his personality to extend time or gain. From this point of view the behavior of the player psicologically it's like playing against some kind of rational machine, not random. For that reason we think Game Theory will be applicable.

I give you an example. One of the main theorem of the theory is Minimax (a method for minimizing the maximum possible loss) and the reverse, Maximin, maximizing the minimum gain. When a player plays maximum lines at minimum credits is playing a maximin strategy. There are more examples and variations. Also if the best players know the main features of the game (volatility, payout, hit frequency) can't predict in which point of random number cycle they are. So they make decisions based on the results of the lastest spins, in the same way as a interaction with other supposed player and also obviously depending of the kind of player they are.

In the future, data mining of tracking player can allow pattern recognition of relevant game strategy behavior. New slots can change par-sheet on the fly and will adapt to player expectations. Fuzzy Logic and Artificial Intelligence algorithms can help on that process.

The Network Centric Games (like Server Based Games) no more machine centric, will open huge possibilities for customer satisfaction and entertaining.

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posted by Rais @ 00:27   2 Comments

2 Comments:

At 10 March 2008 23:14 , Anonymous John R. said...

Brilliant! There is any article about that. I want to know.

 
At 28 March 2008 16:39 , Blogger Axel said...

As someone working in the gaming industry and looking at this group it's very interesting to see it's focus. Which is primarily US/North American.

Gaming is, and is increasingly becoming more of, a worldwide industry, blurring borders and growing international communities.

Perhaps the most creative, competitive and inspirational areas at the moment remain the far east.

Europe remains a powerhouse of creative minds, industry leaders and top professional players.

Key subjects such as the exploitation of persistent virtual worlds, the importance of community engagment and management, the gradual merger of technologies etc etc.

Keys markets such as China, India not to mention the poor use of ads and general game marketting. These are all things I'd like to see addressed.

Failure to understand your market, the demands of your potential customers and the variety of cultural differences is the difference between making money and making a fortune in this business.

 

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