Understanding 'expected value' in video poker

30 January 2016

By Henry Tamburin

I often use the term expected value (or EV) when I’m writing about the best video poker playing strategies. Even though EV is foreign to most players, smart players know what that term means and how it is determined.

EV is a mathematically precise term that represents the average return that you can expect when holding a group of cards in a hand. You’ll always do better playing video poker (meaning win more or lose less money) if you choose the holding that has the highest EV.

The math used to calculate EV is not very complicated, and I’ll show in the following example how it’s done.

Suppose you are playing 9/6 Jacks or Better and you are dealt the following hand. How would you play it?

2 Diamonds, 5 Diamonds, 6 Clubs, 7 Diamonds, 8 Diamonds

There are two possible holds:

Hold #1: Hold the grouping 5-6-7-8 and draw one card, hoping for a straight or
Hold #2: Hold the grouping 2-5-7-8 and draw one card, hoping for a flush.

Assuming you bet five coins, here’s how to calculate the EVs for the two holds.

(Note: Remember that the hand began with a virtual 52 deck of cards, five cards were randomly selected from this shuffled deck for your initial hand, leaving 47 unplayed cards for the subsequent draw.)

Hold #1

We hold the four-card straight 5-6-7-8 and draw one card.

We are hoping to draw either a 4 or a 9 that would give us a straight. In the 47 unplayed cards, there are four 4s and four 9s. Therefore, the probability of drawing a 4 or 9 is the ratio 8 over 47 (8/47). The payoff for a straight is 20 coins.

The EV is the product of the probability of getting the cards you need (8/47) times the payoff (20 coins). When you do the multiplication, you arrive at an EV of 3.40, which means, on average, you will get back 3.40 coins from the 5 coins you wagered. Therefore, eight times out of every 47 times on average that you draw to this hand, you stand to win 20 coins each time, whereas 39 times you will win nothing (meaning your draw card won’t be a 4 or 9).

Therefore, think of the 3.40 EV for this hold as an average payback you can expect after an infinite number of trials.

Hold #2

This time we are going to hold the four-card flush (2-5-7-8) and draw one card from the 47 unplayed cards. We need any diamond-suited card to give us a flush, and there are nine left in the 47 cards.

(There are 13 cards diamond-suited cards per deck minus the four diamond cards in our initial hand leaving nine diamond-suited cards).

Therefore, the EV for this one card draw is the probability of drawing a diamond-suited card (9/47) times the payoff for the flush (30 coins), yielding an EV of 5.74, meaning, on average, you can expect to win 5.74 coins after many trials.

If you are a dollar player, the above EVs mean you can expect a return of $5.74 on average for your $5 bet when you hold the four-card flush, and only $3.40 for holding the four-card straight.

Clearly, holding the four-card flush is a more profitable play in the long run because it has a higher EV than holding the four-card straight.

It’s not necessary to memorize the EVs for different holds. Strategy tables and strategy cards rank the card holdings from highest EV to lowest. All you have to do is to select the holding that is highest in the table (or strategy card) for any hand and you’ll always be making the correct play. It’s that easy.


Henry Tamburin is the editor of the Blackjack Insider e-Newsletter (www.bjinsider.com)and host of smartgaming.com.