If you have ever spent time in the company of avid video poker fans, you have probably heard them discuss expected value and expected return across different variants of the game. Gaining a proper understanding of these two concepts is key to becoming a successful video poker player. This type of casino game combines luck with strategic play, as players’ decisions can influence the outcome to a certain extent.
Sometimes, when one is dealt a good initial hand, the correct decision is quite obvious. However, one cannot expect to be dealt a made hand on every deal, and there are often strategic decisions to make in order to improve one’s chances of winning with a specific combination of cards. This is where the concepts of expected value and expected return come in handy, as they play an important role in 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 determine which course of action will yield the highest return in the long run. The term expected value denotes the average return players can anticipate when they are dealt a specific combination of cards. In other words, expected value represents the number of credits a player can expect to win back for every credit wagered.
The great thing about video poker is that players can generate steady profits in the long run, provided the decisions they make yield a positive expected value. A positive expected value is expressed as 1.0 or above, whereas a negative expected value is below 1.0 and may cost players a significant amount of money over time.
Calculating the Expected Value
One need not be a mathematician to determine the expected value in video poker, as the calculations involved are relatively easy to perform. Nevertheless, it is best to illustrate the process with an example. Imagine you are playing a full-pay game of Jacks or Better in which a full house pays 9 to 1 and a flush pays 6 to 1 per unit wagered.
The hand you have been dealt is the following [2][5][6][7][8]. You now face two viable options – you can either hold the [5][6][7][8] and try to draw to a straight, or you can keep the four suited cards and attempt to draw another spade to complete a flush.
Now let us explore which of the two decisions would be more profitable. Before we proceed, remember that the five cards were dealt at random from a shuffled deck, so the pack now contains only 47 cards that can be used to complete either your straight or your flush.
Video Poker Cards Generator
Expected Value and Expected Return
What Video Poker Games Pay Best
Tens or Better Video Poker
Jacks or Better
With the first option, where you are chasing a straight draw, you need either a 4 or a 9 (of any suit). There are four remaining 4s and four remaining 9s in the deck. Thus, eight cards out of 47 can complete your hand, which may be expressed as the ratio 8:47. 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 winning cards by the total number of cards remaining in the deck, and then multiplying the result by the hand’s payout, as follows: 8/47 × 20 = 3.40. Therefore, the expected value of the hand is positive, standing at 3.40.
In comparison, if you pursue the flush draw and hold the [2][5][7][8], you need any spade to complete your flush. There are thirteen spades in a standard deck and you are already holding four of them. Consequently, nine cards out of the 47 remaining can help you secure a payout of 30 credits. The expected value of this spade flush is therefore 9/47 × 30 = 5.74. On average, this equates to a return of about £5.74, compared with the £3.40 average return for a £5 wager that the straight offers in the long run. The smarter decision is to go for the flush and discard the [6], because the flush carries a higher expected value than the straight.
Novices should not be intimidated, because there is no need to memorise the expected value of every possible hold in video poker. There are plenty of strategy charts available online that you can use; they list the expected value of each possible hold, ranked from highest to lowest.
Expected Return in Video Poker
Expected return is the second major factor to consider when playing video poker. It is usually expressed as a percentage because it reflects a game’s overall payback. In other words, it shows what proportion of all wagers placed on a given game will be returned to players over the long run, provided they employ optimal strategy.
The good news is that players can easily determine whether a given video poker variant offers the maximum expected return simply by glancing at its paytable. This is precisely why paytables are so important when choosing which video poker game to play. Variants that offer an expected return exceeding 100% are considered positive-expectation games for the player and can be quite profitable in the long run. Those with an expected return far below 100% should be avoided at all costs.
To determine whether a particular video poker variant offers optimal return, you should check the payouts for the full house and the flush shown in the paytable. Games that pay 9 to 1 for a full house and 6 to 1 for a flush are known as 9/6 or “full-pay” machines. When optimal strategy is employed, such games generally offer a theoretical payback of about 99.54%, which is remarkably good for a casino title. This means that for every £100 wagered, the game would return approximately £99.54 to players in the long run, while the house would retain only £0.46 as profit.
Knowing the theoretical expected return also enables you to calculate a game’s house edge. You simply 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 available in a casino.
Even so, players will encounter video poker variants that offer lower payouts for the full house and flush, for instance 8/5, 7/5 or even 6/5. These versions are commonly referred to as “short-pay” games, and with good reason. The adjustments in the paytable may seem minor, but they have a significant effect on the theoretical expected return. For example, in an 8/5 Jacks or Better game the long-term expected return falls to 97.30%. Reducing the payout by a single unit on both the full house and the flush results in an overall drop of 1.10 percentage points in payback for each of the two hands.
Sometimes, software developers attempt to compensate for reduced payouts on the flush and full house by boosting the payouts on other hands, but this happens only rarely and such games are difficult to find. Some casinos may offer increased payouts for royal flushes when players wager five credits. However, this leads to only a slight improvement in the game’s overall theoretical return, so players are strongly advised to examine the rest of the paytable to ensure no other payouts have been reduced.
Calculating the Expected Return via Calculators
If calculations are not your strong suit, there is no need to worry. Back in the day, it might have been difficult to determine the expected return of a particular video poker variant. Nowadays, however, players can easily find calculators online and quickly work out the expected return of any type of video poker game.
To calculate the expected return of a specific video poker variant, you simply need to enter the payouts for each hand offered by the game. The calculator will then do the maths and display the estimated expected return you can enjoy in the long run.
If you are comparing different video poker variants, online calculators can prove invaluable. You can check the expected return of several versions of a game or compare two or more variants of video poker side by side. The calculator will show you which option is the most advantageous to play and which offers the best return.
Video Poker Trainers
Online players have things especially easy thanks to the calculators they can utilise when comparing video poker variants. In addition, they can turn to so-called trainer software, which allows 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 variants among video poker fans, it is the default game configured in most trainers. That said, you can easily adjust the payouts for certain hands if you wish, and you can also select other video poker variants.
Trainers allow players to choose between Random Mode and Hard Mode when they run a video poker game through the software. In Random Mode, you are dealt five randomly selected cards, after which you must decide which cards to hold and which to discard.
After you have made your choice, the trainer will indicate the optimal move and whether your decision was correct. In addition, it will display the expected return for the hand you selected and the expected return for the hand you were advised to keep instead.
In Hard Mode, the trainer presents hands that are somewhat trickier, and even seasoned players might struggle to choose the right cards to keep. After you have made your decision, the trainer will reveal the correct hold that guarantees the best possible return.
Video Poker Expected Values When Playing with a Bonus
One of the greatest perks of playing online is the ability to take advantage of promotions. Many interactive casinos offer their new members generous welcome bonuses that can genuinely enhance the gaming experience. If you enjoy video poker, you should give casino bonuses a try, as they can have a positive impact on your session.
Before you redeem any bonus, however, make sure that you have thoroughly read the terms and conditions attached to the offer. Some interactive casinos exclude video poker from promotions or, if there are wagering requirements, allow video poker to contribute only a small percentage towards the turnover.
Let us take as an example a scenario in which you use your casino bonus on a game of 9/6 Jacks or Better. If you deposit 20 units and the play-through requirement is 40×, the probability of completing it is 19.93%. Even if the wagering requirement is much higher and you must turn over the bonus 100 times, your probability of success is still respectable, at 9.80%. These percentages assume that players are using optimal strategy.
The expected return for a 20-unit bonus play on 9/6 Jacks or Better is 18.49 bets after a play-through of 40× has been completed or the player has gone bust. The expected return falls to 17.76 bets after a 100× turnover has been satisfied or the player has busted beforehand.
If you switch to 8/5 Bonus Poker and deposit 20 units, the probability of completing a 40× play-through is 16.63%. When the turnover requirement rises to 100×, the probability falls to 8.15%. For this variant, the expected return after a 40× play-through (or after going bust) is 17.52 bets, while a 100× turnover leads to an expected return of 16.41 bets.
If you decide to use your casino bonus on a 16/10 Deuces Wild variant and deposit 20 units, your probability of success after a 40× play-through is 13.50%. If the wagering requirement is increased to 100×, the probability drops to 7.32%. The expected return after meeting the 40× requirement (or busting before that) is 19.27 bets, while a 100× turnover yields an expected return of 18.97 bets.
As you can see, provided that you secure a decent casino bonus, you can enjoy a rewarding video poker experience online. Of course, some games are better than others, and you should bear in mind that video poker generally contributes less towards bonus wagering. Even so, you should not shy away from using bonuses when playing video poker online.