How to test XCOM “dice rolls” for fairness

XCOM: Enemy Unknown is a turn based video game where the player choses among actions (for example shooting an alien) that are labeled with a declared probability of success.


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Image copyright Firaxis Games

A lot of gamers, after missing a 80% chance of success shot, start asking if the game’s pseudo random number generator is fair. Is the game really rolling the dice as stated, or is it cheating? Of course the matching question is: are player memories at all fair; would they remember the other 4 out of 5 times they made such a shot?

This article is intended as an introduction to the methods you would use to test such a question (be it in a video game, in science, or in a business application such as measuring advertisement conversion). There are already some interesting articles on collecting and analyzing XCOM data and finding and characterizing the actual pseudo random generator code in the game, and discussing the importance of repeatable pseudo-random results. But we want to add a discussion pointed a bit more at analysis technique in general. We emphasize methods that are efficient in their use of data. This is a statistical term meaning that a maximal amount of learning is gained from the data. In particular we do not recommend data binning as a first choice for analysis as it cuts down on sample size and thus is not the most efficient estimation technique.

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Please stop using Excel-like formats to exchange data

I know “officially” data scientists all always work in “big data” environments with data in a remote database, streaming store or key-value system. But in day to day work Excel files and Excel export files get used a lot and cause a disproportionate amount of pain.

I would like to make a plea to my fellow data scientists to stop using Excel-like formats for informal data exchange and become much stricter in producing and insisting on truly open machine readable files. Open files are those in an open format (not proprietary like Microsoft Excel) and machine readable in this case means readable by a very simple program (preferring simple escaping strategies to complicated quoting strategies). A lot of commonly preferred formats surprisingly do not meet these conditions: for example Microsoft Excel, XML and quoted CSV all fail the test. A few formats that do meet these conditions: SQL dumps, JSON and what I call “strong TSV.” I will illustrate some of the difficulty in using ad-hoc formats in R and suggest work-arounds. Continue reading Please stop using Excel-like formats to exchange data