November 5th, 2009|12:26pm.
So being in a Psych (Cognitive Science) class this semester along with having a casual interest in math got me thinking about the real expected value of simple gambling (yes, this is honestly what I was thinking about right before I fell asleep last night). Earlier in my Psych class we touched on the concept of perceived diminishing returns, how the more of something we have, the less "valuable" each increment seems. Basically, if you have $100 and receive $100 dollars this is perceived as a more positive gain than if you have $1000000 and receive $100. This can be extrapolated down to say that if you have $100 and receive $100 it is perceived as better than if you have $101 and receive $100 (technically).
Now, take simple .5 probability gambling (a coin flip). You flip a coin; heads you win a dollar, tails you loose a dollar. Mathematically the expected value of this action is 0 [ (.5 * 1) + ( .5 * -1) ]. So, based on probability you will break even financially from this gamble.
But you might not break even psychologically. Based on diminishing returns, the $1 you would loose by flipping tails, is psychologically worth more than the $1 you gain by landing on heads.
Let's say you have $50 to your name. If you flip a coin and win $1 you'll have $51. If you loose, you'll have $49. The $1 between $49 and $50 is perceived as more than the $1 between $50 and $51. A more obvious example (values increased to make the point more clear) would be that you have $50000 to your name, and if you win you get $50000, if you lose you lose $50000. The benefit of having $100000 compared to $50000 does not outway the benefit of having $50000 compared to have having nothing.
So my point is that from a psychological point of view the expected value of a coin flip gamble is negative. What's more interesting is that if 2 people are playing this game, it would still be perceived as negative for both people, as both have an equal chance of losing (though it would be less negative for the person who currently has the most money). Obviously this is just a little thought experiment in a closed system, but I still think it's interesting that an act that is probabilistically neutral seems to be psychologically negative.
Hmm... I guess this was kind of a weird and random blog entry, huh?