EV, as in ‘victory’

Feb 6, 2006 5:02 AM

Generally speaking, most casino games do not require that a player be able to calculate the expected value while sitting at the table or machine. In fact, the player doesn’t even really have to know the specific expected value of any play.

However, he does need to know which of the potential plays in front of him has the highest expected value, so that he knows what is the best way to proceed.

For many, the methodology of playing the highest expected value, what we call expert strategy, is fairly obvious.

For others, it may take a deeper explanation of how expected value is calculated to better understand why it is the right option.

First, let’s start with a basic definition of what expected value, or EV for short, is. EV is the number of units that a player can expect to be returned to him for each unit wagered for any given situation over the long run.

Thus, an expected value of exactly 1.0 means that the play will result as a push in the long run. If the expected value is below 1.0, it means a losing proposition in the long run. If the expected value is greater than 1.0, it means that the proposition will result in the player theoretically winning money in the long run.

These numbers do not refer to how often the player will win, but rather takes into account every possible outcome and the number of units that will be returned to the player. A ”˜unit’ is whatever denomination the player is wagering. It can be nickels, quarters, dollars or Euros. The math is still the same.

Let’s look at an example using video poker. If you are dealt the following:


J¨   J©   Jª   Q«   Kª


Certainly not a hand you’d mind having! But do you play the three of a kind or go for the royal flush? To answer this question, we simply look at every possible result of holding each hand.

There are 1081 possible draws to each of these hands. If you hold the three of a kind, you will draw 46 quads, 66 full houses and the rest will stay as trips.

We multiply the occurrence of each resulting hand by the payback of that hand (25/9/3 on a full pay jacks or better machine) and we get a total of 4651 coins. We divide this by the number of possible draws and get 4.30. So, we now know that in the long run we will get a bit more than four coins returned for every one wagered. Since the only possible outcomes will result in a return of 25, 9 or 3, we will never actually have a return of 4.3, but this is the long-term average units returned when we’re dealt a three of a kind.

If we decide to hold the 3-card royal flush, the number of draws is the same, 1081. The possible outcomes are one royal, one straight flush, 43 flushes, 30 straights, 6 trips, 15 two pairs and 286 high pairs.

When we use the full pay jacks or better paytable, we find that the total units returned are 1562. We again divide this by 1081 and find the expected value to be 1.44. In the long run, it is still a winner for the player, but you’d be sacrificing almost three units won every time you were dealt a hand like this if you choose to go for the royal jJackpot.

It should be noted that no part of this decision is based on the fact that the three of a kind is a sure winner (you will win coins every time) while the 3-card royal will result in a winner only about 35% of the time.

There are many situations in video poker where the right play is to play the hand in a manner that would result in a lower win frequency but a higher expected value. The proper play is to play the highest expected value if you want to maximize your chances of winning the most money.

Is there ever a time when you would want to abandon playing the play with the highest expected value? Technically, yes. There are times when you are in a tournament when you would want to take higher risk in order to catch up to those ahead of you.

Or perhaps, you are trying to reduce risk to maintain a lead and thus you would, in certain cases, take the sure winner over the more risky option. If you are playing with a ”˜short’ bankroll you may want to alter your strategy slightly in order to decrease your chances of going bankrupt. Lastly, there may be times when two options are very close in expected value and one is a sure winner and the other involves a higher degree of risk. Because the sure winner is ”˜money in your pocket’, you may not be willing to risk that much money for an option with a slightly higher expected value. In the long run, you will cost yourself some money, but you will be buying a little piece of mind for this money and only you can decide if it’s worth it.