I'm an Italian high-school teacher.
Every year, many students often ask me ( THE HUGE QUESTION ):
" How could I use Math in real life ? "
I think we use math for many reasons in real life, but, in some situations, a good management of your savings is also related to Math.
WHAT IS THE EXPECTED VALUE ?
It's simply the money you expect to earn or lose in the long run (due to a choice in a game, or an investment).
ROULETTE : AN INTERESTING EXAMPLE
You decide to go to Las Vegas, what's your EV when you play this game ?
To simplify, you always bet 100$ in chips on the RED and see what happens.
If you win, the dealer will give you 200$ in chips. Of course, NO returns if you lose.
How many times will you win ?
There are 37 numbers ( 18 RED numbers, 18 BLACK numbers, and 1 GREEN number) so you will
double your cash roughly 48,6% of the times.
The EV is the mathematical rappresentation of the risk/reward ratio.
Using EV you can easily understand if you are running into a big loss in the long run.
It's time to find out the EV of your strategy. In this case, you can calculate your EV using the following:
(when you bet on red/black, there are only 2 outcomes)
EV = (% RED)*(W/L if RED) + (% BLACK or GREEN)*(W/L if BLACK or GREEN)
EV = (0.486)*(100$) + (0.514)*(-100$) = 48.6$ - 51.4$ = -2.8$
Every time you bet 100$, your expected value is NEGATIVE.
In particular, if you bet x$ n times, your expected value will reach n(-2.8%x)$.
This is NOT in contrast with the possibility of win of each player, but
the calculation of the EV shows us that our odds are bad.
IN THE END...
The main purpose of this article is to state that Maths suggests how to avoid bad investments.