This page was inspired by Better thinking through experiential games, and some of the comments on this post.
This page is an attempt to create a list of online games that can be used to test your rationality, your problem-solving skills, etc. Unfortunately very few of these games directly test Bayesian reasoning, and the puzzles tend to be unrealistic, which means that they test how good you are at puzzle games, rather than how good you are at real-world rationality. Still, creating this list seemed like it would be worth a try.
Most of the game links are from Kongregate.com. If you sign up for a kongregate.com account, the site will keep track of your achievements in the games. You can then link to your badges page to show off which badges you've collected.
But be warned: THIS CAN BE EXTREMELY ADDICTIVE!
Difficulty: Medium
Description: A series of duck-themed puzzles, each of which has different rules.
Skills required: Basic puzzle-solving skills.
Difficulty: Medium
Description: A series of key-themed puzzles, each of which has different rules.
Skills required: Basic puzzle-solving skills.
Difficulty: Hard!
Description: A series of puzzles, connected by other puzzles, each of which have different rules, and most of which have a counterintuitive solution. Hints about the solutions are cleverly hidden in the game.
Skills required: Advanced puzzle-solving skills, finding and interpreting cleverly hidden clues.
Hint: Gur cevagfperra ohggba vf lbhe sevraq. (rot13'd)
Difficulty: Hard
Description: A series of puzzles, each of which has a deliberately counterintuitive, and often malevolent, solution. Don't worry if you can't solve all of them, some of the solutions require specific computer hardware or software to win.
Skills required: Interpreting deliberately counterintuitive clues. Guessing what the game designer could possibly have meant. Some of the puzzles require specific computer hardware or software to solve.
Difficulty: Almost Impossible
Description: A series of quiz questions and other challenges that have deliberately counterintuitive solutions.
Skills required: Some questions require trivia knowledge. Some questions require logic skills. Some questions require "thinking outside the box". Some of the questions are solvable only by trial and error. Some of the challenges require extremely fast reflexes. Many of the puzzles are blatantly evil. Do not expect to win this. You have been warned.
Difficulty: Easy
Description: Given a plain white ball, a few tools, and a picture, change the ball to make it match the picture.
Skills required: Figuring out what the tools do, and how to use them in to achieve the goal.
Difficulty: Medium
Description: Given a few parts, figure out where to place them to connect power from the power supply to the target.
Skills required: Physics-based puzzle-solving skills.
Difficulty: Medium
Description: Given a few parts, figure out where to place them to make the metal ball go into the bucket.
Skills required: Physics-based puzzle-solving skills.
Difficulty: Medium
Description: Click the orange data ports around the edges of the level, to fire packets which interact with various objects, to eventually reach the green root node.
Skills required: Physics-based puzzle-solving skills. Some levels require quick reflexes and precise timing.
Difficulty: Medium
Description: Click on some types of objects to make them disappear. The objective is to remove all of the red objects from the screen, while keeping all of the green objects on the screen.
Skills required: Physics-based puzzle-solving skills. Some levels require quick reflexes and precise timing.
Difficulty: Medium
Description: Place the shapes so that they don't fall off the screen.
Skills required: Physics-based puzzle-solving skills. Some levels require quick reflexes and precise timing.
Difficulty: Medium
Description: Guide the ball to the destination by cutting objects.
Skills required: Physics-based puzzle-solving skills. Some levels require quick reflexes and precise timing.
Difficulty: Advanced
Description: Construct complex machines to navigate from the start area to the destination area, or accomplish other tasks.
Skills required: Physics-based puzzle-solving skills. Constructing machines with many interacting parts.
Difficulty: Advanced
Description: Anagrams + block-sliding puzzle = fun :)
Skills required: Anagrams. Block-sliding-puzzle skills. General logic skills.
Difficulty: Advanced
Description: Use a small set of instructions to program a robot to light a specific pattern of tiles.
Skills required: Programming. Optimizing code for limited computing resources. Understanding spaghetti code.
Difficulty: Advanced
Description: "Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve."
Skills required: Programming in any language.
Difficulty: Advanced
Description: Create paths between nodes of the same colour, without the paths overlapping.
Skills required: Visual-spatial logic skills. General logic skills.
Difficulty: Easy
Description: Solve easy puzzles in a dreamlike environment without any hints.
Skills required: Figuring out what various objects do, and what you're supposed to do with them. Basic platforming skills.
Difficulty: Medium
Description: There's only one level, just get to the exit. Oh, and each time you get to the exit, the rules change.
Skills required: Basic platforming skills. Figuring out the new rules each time they change, and adapting to them.
Difficulty: Medium
Description: A unique game where unless light is shining on an object, the player will pass right through it.
Skills required: Puzzles involving manipulating light and darkness. Figuring out what various objects do, and what to do with them. Intermediate platforming skills
Difficulty: Medium
Description: A slightly innovative platform puzzler. The storyline involves weird time paradoxes, but the puzzles themselves don't.
Skills required: Intermediate platform-puzzle skills.
Difficulty: Medium
Description: A slightly innovative platform puzzler. Press the shift key to turn the world upside down, switching background and foreground.
Skills required: Intermediate platform-puzzle skills.
Difficulty: Medium
Description: An innovative platform puzzler. The objective is to find a way to kill your character. Harder than it sounds.
Skills required: Intermediate platform-puzzle skills. Outside-the-box thinking.
Difficulty: Hard
Description: Create portals to solve puzzles and reach the exit. Based on the original game by Valve.
Skills required: Advanced platform-puzzle skills. Understanding how portals work and using them effectively.