Good games for learning statistical thinking? Are there any games that get the player "think like a statistician"?
For example, lightbot gets you to "think like a programmer" (in a very basic way). Are there any games - designed for entertainment or teaching - that can help get one comfortable with basic concepts like correlation, p-values, least squares, variance, different kinds of probability distributions, regression to the mean ...
One example would be this correlation-guessing game.
(I'm asking because I'm thinking about developing such an application, and am trying to get a broad view of what prior work exists)
 A: Democracy by Positech is mostly a web model of all the statistical and political interactions that get news coverage. It includes polling and bias as a game mechanic but pretty much nothing else requested in the opening post. However having to conduct those studies to reveal interactions would gel very well with the game as it is now. There exist far better programing games like Hack n Slash, Quadrilateral Cowboy and Cosmic Supremacy. My Get Smarter Games playlist.
A: How about the game show "Deal or No Deal".  Though not emphasized the banker is checking the probability given the number of remaining suitcases what the probability is that the  1,000,000 dollar prize is in your suitcase.  Based on the odds he makes an offer that favors him.  Whenever I watch this I am hoping the contestant understands expected gain and expected loss so as to not go for the bankers offer unless it is close to fair and a lot of money.  As the game progresses an instructor can explain the odds and show the student how to compute what a fair offer would be.
The famous game show "Let's Make a Deal" had that flavor in it for the deal of the day at the end of the show.  A slight modification led to the famous Monty Hall problem that baffled even some famous mathematicians.
Other games have aspects of probability in their decision making.  With the spinning of the big wheel, there is the decision to hold with the first spin result or gamble to add to a higher total with the risk of going over $1.  Even if you don't have a good prior distribution for the price of an item, bidding strategy can be partially based on an idea of a bet that is going to be reasonable and have a better chance of winning than the competitors.  The best example is when you bid in the last position and the highest bid so far has a good chance in your mind to be below the actual price.  Then bidding 1 dollar over it (the minimum that you can bid over) is a very good strategy.  Many people actually use that strategy and very often are successful.
In addition I think Jeopardy with a statistics board of categories might be a fun way to reinforce concepts through competition.  I have seen this work well and be fun for medical topics and once played it on categories for nutrition to teach good eating habits.
A: Fantasy sports incentivize players to think with statistical intuition. For example, every week in fantasy football you must choose which players to start based on, e.g.: 


*

*that player's career stats,

*the trend in the time series of that player's stats,

*the team he is going up against,

*weather,

*injuries,


and many more. According to http://www.fsta.org/, 32 million people in the US and Canada now play some type of fantasy sport! I know that it was one of the major reasons I developed an interest in statistics. 
A: Poker is a good game for learning probabilistic thinking.  The game has been dominated at the highest level in recent years by "math nerds" who have spent a lot of time studying the odds and spend very little time trying to read their opponents.  Check out the Time article World Series of Poker: Attack of the Math Brats for some details.
Also, I can't find any specific examples yet, but NPR's "Math Guy" Keith Devlin has spent a lot of time in the past few years promoting video gaming as the future of math education.  Some of the links in that article might be a good starting point, or you might want to check out his book on the subject, Mathematics Education for a New Era: Video Games as a Medium for Learning.
A: I have made some statistics games for teaching. They deal with confidence intervals, hypothesis tests (Neyman-Pearson) and significance tests (Fisherian).
They are excellent tools for engaging students in lectures/workshops and a subset of the students spend quite a lot of time playing them.
I have been going to make an online high scores leader-board to make the game aspect more competitive but, well, I haven't got around to it ;-)
