# Expected Value and Expected Return

If you have ever spent some time in the company of avid video poker fans, you probably have heard them discuss the expected value and the expected return of different variations of the game. Gaining a proper understanding of these two concepts is key to being a successful video poker player. This type of casino game combines luck and strategic play since players’ decisions can influence the outcome to a certain extent.

Sometimes when one is dealt a good initial hand, the right decision is pretty much obvious. However, one cannot expect to get made hands on each deal and often there are strategy decisions to be made in order to improve your chances of winning with a specific combination of cards. This is where the concepts of expected value and expected return can come in handy as they play an important role when it comes to analysing such situations and determining the most advantageous course of action.

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## Expected Value in Video Poker

The expected value is important because it helps video poker players to determine which course of action will give them the highest value in the long run. The term expected value is used to denote the average return players can expect when they are dealt a specific combination of cards in a hand. In other words, the expected value represents the number of credits a given player can expect to win back per every credit they have wagered.

The great thing about video poker is that players can generate steady profits in the long run as long as the decisions they make yield positive expected value. The positive expected value is expressed as 1.0 or above while the negative expected value is below 1.0 and may cost players a good amount of money in the long term.

### Calculating the Expected Value

One is not required to be a mathematician to determine what the expected value in video poker is since the calculations involved are relatively simple to perform but it would be best to demonstrate it with an example for clarity. Imagine you are playing a full-pay game of Jacks or Better where the full house pays 9 to 1 and the flush pays 6 to 1 per unit wagered.

The hand you have received on the deal is the following [2][5][6][7][8], in which there are two suitable options for you – you can either hold the [5][6][7][8] and attempt to draw to a straight or you can opt for holding the four suited cards and try to draw one more card of the same suit in an attempt to form a flush with the spades.

Now let us explore which of the two decisions will be more profitable for you. But before we proceed with this, we would remind that the five cards were dealt randomly from the shuffled deck for your original hand, which is to say the deck now contains only 47 cards you can use to complete your straight or potentially your flush.

With hand number 1 where you are attempting a straight draw, you will need either a 4 or a 9 (of any suit) as a replacement. There are four cards with a value of 4 and four cards with a value of 9 in the remaining deck. From this, it follows that there are eight cards that can help you win out of 47, which can be expressed like this 8:47 in a ratio form. In Jacks or Better, straights typically pay 20 units for five-credit bets. The expected value of this hand is calculated by dividing the number of cards you can win with by the overall number of remaining cards in the deck and then multiplying the result by the hand’s payout like this: 8/47 x 20 = 3.40. Therefore, the expected value of your hand is positive and stands at 3.40.

In comparison, if you attempt the flush draw and hold the [2][5][7][8], you will need any spades-suited card to complete your flush. There are thirteen spades-suited cards in a standard deck and you are already holding four of them. This means that there are 9 cards out of the 47 remaining in the deck that can possibly help you collect a payout of 30 credits. It follows that the expected value of your flush of spades would be 9/47 x 30 = 5.74. This translates into an average return of about £5.74 as opposed to the £3.40 average return for a £5 wager the straight can give you in the long run. The smarter decision to make would be to go for the flush and discard the [6] because the flush offers you a higher expected value than the straight.

Novices should not be intimidated by this because there is no need to remember the expected value of all possible holds in video poker. There are plenty of strategy charts available online, which you can use since they include the expected value of the card holds, ranked from the highest to the lowest.

## Expected Return in Video Poker

The expected return is the second major factor one needs to consider when playing a game of video poker. The expected return is usually expressed in terms of percentages because it reflects the game’s overall payback percentage. Thus, it is used to express what amount of all wagers made on a given game will be returned back to the players over the long run, provided they have adopted an optimal strategy.

The good news is players can easily determine whether a given video poker variation offers them the maximum expected return simply by taking a quick look at the game’s paytable. This is precisely the reason why paytables are so important when selecting which video poker game to play. Video poker variations which offer expected return that exceeds 100% are considered positive expectation games for the player and will be quite profitable over the long run. Those that offer expected return way below 100% should be avoided at all costs.

In order to determine whether a given video poker variation offers you optimal return, you need to check the game’s payouts for the full house and the flush, listed in the paytable. Video poker variations which offer payouts of 9 to 1 for a full house and 6 to 1 for a flush are called 9/6 or “full-pay” machines. When optimal strategy is at hand, such games generally offer theoretical payback percentage of around 99.54%, which is rather satisfactory for a casino game. This means that for every £100 wagered, the game would return to players £99.55 in the long run while the house will keep only £0.46 in profits.

It makes sense that you can also calculate the house edge of video poker games when you know their theoretical expected return. As you can see, you simply need to subtract the expected return from 100%, so in this case, the house edge for a full-pay 9/6 game would be only 0.46% – one of the lowest you can benefit from in a casino.

Then again, players will come across video poker variations which offer them lower payouts for the full house and the flush, for instance, 8/5, 7/5 or even 6/5. These variations are frequently referred to as “short payback” games and for a good reason. The adjustments in the paytable may appear minor but they have huge effect on the theoretical expected return of the games. An example would be a 8/5 Jacks or Better game where the long-term expected return drops to 97.30%. The reduction of a single unit in the payouts for full house and flush leads to an overall drop of 1.10% in the payback for each of the two bets.

Sometimes software developers may try to compensate players for the reduced payouts of the flush and the full house by boosting the payouts on other hands but this happens on rare occasions only and such games are hard to find. Some casinos may offer increased payouts for Royal Flushes when players bet five credits. Yet, this would lead only to a slight improvement in the overall theoretical return of the game, so players are highly recommended to check the rest of the paytable to make sure no adjustments have been made to the payouts of other bets.