Expected Value & Understand Your Downside Risk

Human Brain the more you work for it the smarter it will become. We will learn & understand a few mathematical calculations out of Probability that we studied in our school books and will see how this will improve our thought process while taking a decision in our life.

Decisions should be taken by knowing the Expected Value that you will get from that decision. In business, life, betting, or investing everywhere the expected value can be calculated and this will help you to make the right decisions – Decisions that will always be in your favor.

Expected Value

Let’s understand the practical applicability of Expected Value through this interesting video by Professor Arthur Benjamin who used the example of Roulette to help us understand the expected value. Do watch this video before reading further…

As in the above video, the one who bets $1 in the casino each time loses 5.3 cents means that if you bet when the expected value is negative you are losing for your every bet no matter how many bets you make.

Let’s understand more about the expected value with an example of the Coin Toss.

As you can see in this video that though at the start for a normal person who is not aware of this Expected Value concept of Probability will choose the 2nd option where he pays Game Fee of $6 for every game thinking he will lose less, is actually losing every time he bet through the second option because the expected value is (-$1) 

Therefore, always bet or take a decision where the expected value is positive or putting something in your pocket instead of taking out of your pocket.

But wait, it is not just about the Expected Value being positive it is also about understanding the Downside Risk.

Downside Risk with the example of Russian Roulette.

In Russian Roulette, there are 6 equally possible outcomes – 5 Empty and 1 with Bullet.

If you survive you win INR 5 Lakhs. You can play this game for FREE.

So, should you play this game or not? Let’s calculate the expected value of this too as we understood in the above videos.

EV of Surviving

= 5/6 * 5 Lakhs + (1/6) * 0

= 4.16 Lakhs

So the expected value is positive INR 4.16 Lakhs which is in your favor.

But what is the downside risk? It’s DEATH. Why should you risk your life?

Before taking any decision or bet in your life, look at the downside risk and make sure that the downside risk is acceptable. Never play any game or take any decision where the downside risk is not acceptable to you even if the expected value is in your favor.