Over and under in football betting

Your Risk taker Who Broke the actual Horse-Racing Value

The probability of the outcome is exactly the same every time you flip it, so the probability of being right is exactly the same. The reason it looks different is that there are many flips. The possible outcomes are divided into three or four equally likely groups, the results of which overlap and cross over as the game progresses. A large percentage of the possible outcomes (and therefore, the probability of being right) will have been reached by the end of the game.

Image courtesy of flickr user yomuik.

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This post was originally published on Feb. 10, 2011.

Inspired by a study that showed that a relatively simple mathematical tool can determine whether people are right about nearly any question, we tested how accurately we could tell a true or false question, given a large set of true and false answers.

We showed 50 people in a virtual game the random states of a set of nine shapes on a 10×10 grid. Some people saw a partial state of the shapes (only a few details were shown), while others saw the complete state of all nine shapes. For every point on the grid, some were connected to three shapes and others to four, and the size and location of the connections varied from set to set. They were asked to tell us whether a given set of shapes was connected to any of the other sets. The question is straightforward but very interesting: What percentage of the shapes had been connected to any other set?

Everyone averaged more than 97 percent correct. So, if a person were trying to find out if the correct answer is two or three, she should only worry about shapes that are connected to a two or three. If she sees that the correct answer is four, she should only worry about those that are connected to three.

Image courtesy of Nicholas Kolman.

If the shapes had been constructed with much more fine-grained patterning, many more shapes would have been connected. On the other hand, people were not very good at detecting when shapes were connected to more than one set. When asked to place all the shapes into one of two groups, they averaged just 83 percent accuracy.

So, is there a surprising secret to determining if a particular shape is connected to any of the other shapes? Our analysis shows that some people are better at this than others. When faced with any one configuration, they are often much more likely to see that there is a group of shapes that are connected to every other configuration. This may partly be due to inherent wiring or to intuitions about what other shapes would look like.

We have no idea what this secret is. It could be that we need to scan a bigger area than is shown on the graph above. Or it could be that we need to keep scanning over a longer time. It might be that we don’t see connections between two connected shapes at the same time but only after several turns.