Expected Value and Expected Return

Video Poker Machine PhotoIf 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.

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.

Video Poker Machines Photo

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.

Calculating the Expected Return via Calculators

If calculations are not your strongest point, you do not have to worry about it. Back in the days, it may have been difficult to determine the expected return of a certain video poker variation. Nowadays, however, players can easily find calculators online and quickly get the expected return of any type of video poker game.

To be able to calculate the expected return of a specific video poker option, you will simply need to enter the payouts for each hand that the game is offering. This will allow the calculator to do the right math and show you the estimated expected return you can enjoy in the long run.

If you are comparing different video poker variations, online calculators can come in handy. You can check the expected return of different versions of a game, or juxtapose two or more variations of video poker. The calculator will allow you to see which option is the best one to play and will offer the best return at the end of the day.

Calculating the Expected Return

Video Poker Trainers

Online players have it extremely easy due to the online calculators they can utilize when comparing video poker variations. In addition to that, they can resort to the use of the so-called trainer software. It will allow you to recreate any video poker game and see the outcome of every possible draw.

As 9/6 Jacks or Better is one of the most popular variations among video poker fans, it is the default game set up with most trainers. That said, you can easily adjust the payouts for certain hands if they and you can also pick other video poker variations.

Trainers allow players to choose between a Random Mode and a Hard Mode when they are running a video poker game through the software. When you have set up the trainer in Random Mode, you will be dealt 5 cards that are selected randomly. Then, you will need to make a decision about which cards to hold and which ones to discard.

Once you are done with your move, the trainer will show you which was the optimal move and whether you have made the right decision. In addition to that, you will be shown the expected return for the hand you are holding and the expected return for the hand you are advised to keep instead.

In Hard Mode, the trainer will offer hands that are a bit trickier and even seasoned players might have a difficult time choosing the right cards to keep. Once you are done with your decision, you will be shown the correct hand that guarantees the best possible return.

Video Poker Expected Values When Playing with a Bonus

One of the best perks of playing online is making use of promotions. Many interactive casinos offer their new members very generous Welcome Bonuses that can truly change one’s gaming experience. If you enjoy playing video poker, you should give casino bonuses a try as they can positively affect your gaming adventure.

Before you redeem any bonus, however, make sure that you have thoroughly checked the terms and conditions that apply to the specific offer. Some interactive casinos exclude video poker games from promotions or, if there are wagering requirements, video poker games have a low contribution to the bonus turnover.

Playing with a Bonus

Let us take for an example a scenario where you wish to use your casino bonus on a game of 9/6 Jacks or Better. If you decide to deposit 20 units and the playthrough requirements are 40x, the probability of surviving the playthrough is 19.93%. Even if the wagering requirements are much higher and you need to turn over the bonus 100 times, your probability of surviving is still pretty good with an average of 9.80%. Of course, these percentages are true if players use an optimal strategy.

The expected return for a bonus play with 20 units on 9/6 Jacks or Better is 18.49 bets after a playthrough of x40 has been met or the player has gone bust. Meanwhile, the expected return will be 17.76 bets after a 100x turnover has been completed or the player has busted before that.

If you change the game to 8/5 Bonus Poker, when you deposit 20 units and you need to meet the requirements of 40x, your probability of surviving is 16.63%. When the turnover conditions are increased to 100x, the probability drops to 8.15%. In the case of this video poker variation, the expected return after you have met the wagering requirements of 40x or you have gone bust is 17.52 bets, while a playthrough of 100x will lead to an expected return of 16.41 bets.

If you decide to use your casino bonus on a 16/10 Deuces Wild variation and you deposit 20 units, your probability of success after a playthrough of 40x is going to be 13.50%. Let us boost the wagering requirements all the way to 100x and the probability of success will decrease to 7.32%. The expected return after you meet the wagering requirements or go bust before that is 19.27 bets for a 40x playthrough and 18.97 bets for wagering requirements of 100x.

As you can see, as long as you find a decent casino bonus, you can enjoy a fruitful video poker experience online. Of course, some games are better than others and you can often take into account that video poker games tend to have a lower contribution to bonus wagering. That said, you should not be afraid of using bonuses while playing video poker online.