## Class 32: Gambling

### For Monday

On Monday, Prof. Eldar Shafir from the psychology department will come to the class In preparation for his visit, please mad his article "Intuitions about rationality and cognition".

### Comments on Journal 5 by Laurie:

I gave 4 points for good discussions on ear of the three questions with an extra point for an occasional unusually insightful discussion. As usual I also gave up to 4 points for your chance observations beyond the assigned questions.

Sever of you enjoyed the article on Murphy's Law and a couple oven took a stab at working the sock problem This was

Murphy's law of Odd Socks is that if an odd sock can be created it will be. If you start with a drawer of 10 complete pairs and you lose just six socks at random, then it is 100 times more likely that you will be left with the worst possible outcome - six odd socked than with a drawer free of odd socks.

Suppose the 10 pairs arc different colors. Then to get six socks all of diffident color you nest fast choose 6 out of the ten possible colors and for each of these there are two possible socks you can choose. Thus the probability of this happening is:

2^6*choose(10,6)/choose(20,6) = .347

To choose 6 socks which are three pairs you only have to choose 3 out of tile 10 possible colors since you then have to choose both socks of drip color. Thus the probability that you choose three such pails and hence have a drawer free of odds socks is

choose(10,3)/choose(20,6) = .031.

Thus you arc about 100 times more likely to be left with the worst possible outcome.

One person offend an interesting new explanation for a Murphy Law. Consider the Murphy Law that says that every time you go on a picnic it rains. The explanation is that Spring is the time for picnics and also for rain.

Most of you were not too warned about doomsday coming because of too low a sperm count. Some put their faith in the principle of natural selection: those with high sperm count will have mole children and these children will have high spew count etc. Of course this assumes that sperm count is a genetic trait. One person also suggested that if it is a genetic wait, this might account for the lack of normality in the sperm count in a population of men. Others pointed out flat just because it was declining linearly now did not mean the linearity will continue right down to 0. For example, it could very well Fatten out before it gets down to a dangerous level.

It seemed that about half believed that there was such a thing as extra sensory perception and half did not. Some stated that you had to have had a comparable experience to believe in such things. For example, one person mentioned that she occasionally felt that a place new to her seemed very familiar only to realize that this was because a year or so ago she had dreamed of being in this place. Others mentioned coincidences they had experienced: for example, they were just about to Bite their grandmother to whom they had not written for five years when a telegram arrives saying Ale just died. Coincidences are an Interesting topic in their own right and we will try to talc About this in another class.

I had a chance to visit with Professor Jessica Utt at University of California Davis on my trip. Professor us is a statistician who has studied many of the asp experiments and is wowing on ways to determine when the results are significant and to explain how this happens when they are. She has recently written a paper that discusses the Pear results. Her main point is that the data does not support the force theory but rather another theory called a sampling theory. She argues that if you believe tile force theory that the subject by some force is actually effecting the individual outcomes you should believe Thai you would get a higher z value when a trial consists of 2000 coin flips rather than 200 and this does not occur. Under the sampling theory the subject is not changing the machine outcomes but rather is able to select see a favorable situation coming up by chance and start (push the button) at the right time. If anyone is writing a project on the Pear lab and would like to see her work just let me know.

Recall an the bet I made with Linda, when as a subject in the Pear experiment, l gave her ten to one odds that she would not attain a result significant at the 5% level. Most of you felt that even though I should have given 19 to 1 odds if Linda is just guessing, she still had a good bet. This was based on the fact that so many of the subjects were able to show significant results. Linda has done the trials and argues that they are significant. Like other careless experimenters we were not very precise about what constituted a significant result. We base decided to let the class arbitrate this delicate matter.