Statistics and Probability

I’m sure that most of you have encountered statistics at some point in the course of your life, and some of you will have recoiled in horror. Most of statistics is basically involved in making sure you don’t believe the obvious answers taht feel right, because they rarely are.

It’s important to have at least a feeling for statistics when creating games, especially card
games. Understanding how decks of cards work is important, and can save a lot of headaches with your design. Using stats you can get an idea of how likely you are to draw a certain card, or hand of cards, how different hands of cards will be, and how these values will change over the course of the game.

The two most important concepts to consider are the expected value, or mean, and the variance. The expected value will tell you what result to expect, and the variance will give you an idea of how widely spaced the observations will be.

As an example, let’s consider a standard deck of cards, and determine the expected number of red cards in a three card hand. This is simple to calculate, and is equal to 1.5. If we have two decks of cards together, then we still expect to draw 1.5 red cards.

If we look at the distribution of cards drawn, we see that the probability of drawing all red cards is 0.1176 with one deck, and 0.1214 with two. So, the distribution of hands is less
concentrated to the middle with two decks, we see more extreme hands, and have a greater variance.

This is important because it means you can’t simply add cards to your deck and assume that the game will play as before.

You can make other uses of stats and probability to help you in designing you games, I hope that my writing has got you to consider how. If you want to learn more about statistics, you could do far worse than Mathworld.


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