## Saturday, August 15, 2015

### Expected value and what it means for blackjack

Expected value, or EV, can be defined as the theoretical average of a variable.  It is calculated by taking the sum of all possible values, and multiplying those by their probability of occurrence.  Take that in for a moment. Use that definition to help understand why advantage play in blackjack is a long term game.

To better understand, let's take a very simple example and calculate our EV.

10,000 lottery tickets are sold at \$1 each with a grand prize of \$4500.  If you were to purchase one ticket, what is your expected value?

In this example, we can see that there can only be two results.  You will either lose \$1 or win \$4499 (grand prize - entry fee).  But what is the probability of each of these events?

The probability of winning is 1/10,000.  One time in 10,000 we will gain \$4499.
The probability of losing is 9,999/10,000.   9,999 in 10,000 we will lose \$1.

By using the definition above we set up our formula:
EV = (\$4499 * 1/10,000) + (-\$1 * 9,999/10,000)
EV = (.4499) + (-.9999)
EV = -0.55

The expected value of our ticket says that we will lose .55 cents on average every time we buy a ticket.  But does that ever actually happen?  Of course not.  We will either completely lose our dollar, or we will win \$4499.  Blackjack works the same way.  You either win the hand, lose the hand, or push.  You are not paid in fractions of a penny, even if the play you just made earned you a fraction of a penny in expected value.  This is the reason an advantage player cannot draw conclusions off of single hands or even single sessions.

Too often I have seen casinos scramble to figure out what a player is doing after having a large winning session.  All too often I've seen players claim that counting doesn't work after a single large losing session.  I cannot stress enough that these sessions can and WILL happen to every card counter, regardless of their skill level.

Trust the math.  Trust your count.  Make the correct play that the count calls for.  Do not deviate based on hunches.  Play the long term game.  Get your expected value.