To become successful investors we have to think like burglars, because we must be constantly on the lookout for windows of opportunity So today’s post is about finding those opportunities with the help of math and probability
In a recent Poll, I asked if readers would prefer to receive a guaranteed $3,000 or an 80% chance of getting $4,000. If you didn’t get a chance to vote, make a choice now, and remember your decision. You might be asked about it later Here are the poll results (^_^)
85% of you who voted chose the first outcome
*Sigh* (-_-) Folks, this is NOT okay (>_<) Dagnabbit, you guys It’s time we had a serious discussion about this. I know it’s probably my fault for not blogging about this sooner but today’s concept is uber important and may change the way you look at money forever.
In probability theory, Expected Value means the “expected” average outcome if an event were to run an infinite number of times. And the law of large numbers dictates that the average of the results obtained from a large number of trials should be close to the Expected Value.
For example, a 6-sided die produces one of 6 numbers when rolled, each with equal probability. Thus, the expected value of a single die roll is 3.5.
According to the law of large numbers, if we rolled a die a large number of times (like 1,000 times) then the average of the produced values is likely to be very close to 3.5, with the precision increasing the more times it’s rolled.
Below is a graph showing a series of 1,000 rolls of a single die. As the number of rolls increases, the average of the values of all the results will automagically approach 3.5.
The same thing would happen with a coin toss. The Expected Value that a coin will land on heads is 50%. So if we flipped a coin a gazillion times eventually the actual data that we witness will come closer and closer to the expected value of 50%.
Now that we understand what expected value and law of large numbers mean we can approach the poll again from a mathematical angle. The expected value of the first outcome is $3,000 as there is a 100% chance of receiving exactly $3,000 every single time. The expected value of the second choice is $3,200 since (80% x $4,000)+(20% x $0)
If math isn’t your strong suit allow me to sum it up for you Basically we should choose the second outcome every time because it has a higher Expected Value.