Which do you choose?

[Aaron Mazzrillo]

Let's have a little fun and possibly learn something about ourselves:

The Green Button is a guaranteed $1M wired into your account today.

The Red Button gives you a 50/50 chance at $100M being wired into your account today.

Which do you choose?

[Wayne Igo]

It would depend on my personal circumstances but mathematically this is a no brainer.   "Expected Value" is defined as the product of the probability that something will happen times the value received if it does happen.  Probability is a number from 0 to 1 corresponding to 0% to 100% chance of occurring.  This metric is used in Game Theory, market analysis, etc and I use it to make everyday decisions if I have confidence in the numbers.

In this example, the probability of getting a  1 million if I choose the green button is 1 ( or 100%).  So the Expected Value (EV) is 1.0 x 1 million or 1 million.  On the other hand, if I choose the red button the probability is 0.5 (50%) of getting 100 million. So the expected value in this case is EV = 0.5 x 100 million or 50 million.  So clearly choosing the red button is the best choice mathematically because the expected value is 50 times greater. 

For me personally, if I were down and out and cash poor I would probably do a worst case /best case analysis.  You simply list the worst and best thing that could happen if you choose the green button and the worst and best thing that could happen if you choose the red button.  If the consequences of getting nothing were severe and I would be "OK" with taking the 1 million I would choose the green.

One last note.  Expected value works on average.  If you can quantify and get a descent probability and value, using expected value over time will make you more profitable.