Expected return and how to calculate it
The term ”expected return” refers only to video poker machines that have RNGs (Random Number Generators). Respectively, it cannot be related to the majority of VLTs (video lottery terminals), as they do not have RNGs.
The expected return represents the theoretical return a player can expect to achieve from playing a particular video poker game in a longer term (after many hands). According to experts, millions of hands provide an idea of a ”longer term”.
The expected return can be evaluated by comparing the number of coins, placed as a bet to the number of coins received for every winning hand in the particular game. The result is usually expressed as a percentage.
In case the odds for a player to receive a particular winning combination were equal to the payout for the combination in the game, the expected return would be 100 percent. In case there is a 25 percent chance for a particular winning combination to occur and, at the same time, the player is to be paid 4 times the bet size for this combination, while the expected return will be 100 percent.
The expected return (payback percentage) is in a direct link to the pay table for the particular game, thus, if there is a change in the pay table, there will immediately be a change in the expected return.
In order to estimate the expected return in terms of dollars:
1. One should transform the expected return for the particular game from a percentage to a decimal. It is achieved by moving the decimal point two places to the left and removing the percent sign;
2. One should multiply the decimal by the total amount of the bet.
Let us presume that a player is willing to project how much they will be paid if they bet $350 on Full-Pay Deuces Wild, a game offering a 100.76% expected return. First, they need to move the decimal point two places to the left and remove the percent sign. This will lead them to the following result: 1.0076. Second, they need to multiply the result by the total bet, or 1.0076 x $350 = $352.66.
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How can we interpret this theoretical result?
If one is to play Full-Pay Deuces Wild with close to immaculate strategies for a sufficiently long period of time, they can expect to earn $352.66 – $350 = $2.66 for every $350 they place as a bet.
If we presume that the player is willing to play 9/6 Double Double Bonus Poker, a game with an expected return of 98.98%, their theoretical return will be estimated as follows:
First, they need to transform 98.98% into a decimal using the above mentioned method. The result will be 0.9898;
Second, they need to multiply the result by the total bet, or 0.9898 x $350 = $346.43. The interpretation, in this case, will be that for every $350 placed as a bet, the player will lose $350 – $346.43 = $3.57!
The return in reality is more likely to be close to the expected return, only if the player uses close to perfect strategies and a sufficiently large number of hands.
In a shorter term, however, there are a variety of scenarios, which can occur. The player may end up losing money on a player advantage game or earning money on a casino advantage game by using a shorter number of hands. In a longer term, if the player operates accurately, the best video poker game will be the one offering the highest expected return.
All in all, when a game offers an expected return larger than 100%, the player can expect to earn money, but when the expected return is lower than 100%, they can expect to lose money.
Those games, offering an expected return lower than 100% are known as ”casino advantage games”, while those games, offering an expected return larger than 100% are known as ”player advantage games”. It is possible for a game with an expected return below 100% to become a player advantage game through progressive jackpots, cash back offers, and other casino promotions. However, if a video poker game offers a quite low expected return, even cash back offers and progressive jackpots will not neutralize the loss of money.
Expected Value
We said earlier, that one game may come in a variety of denominations. On a single video poker machine the number of denominations may be limited, but if one takes into consideration the different types of machines, they will probably encounter: $.01, $.05, $.10, $.25, $.50, $1.00, $5.00, $10.00, $25.00, $50.00, $100.00, $500.00.
It is a practice for a casino to place machines with higher denominations ($10.00 and more) in a particular room for ”high-roller” players. After a video poker machine has been chosen, in order to estimate the actual bet, a player needs to multiply the desired denomination by the maximum coin bet (5 coins for the majority of games). Therefore, if they operate a single-hand machine with a denomination of $5.00, every bet placed will be worth $25.00 ($5.00 x 5 coins).
Video Poker RNG
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Expected Return and Value
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In addition, one should not forget that many machines provide them with the opportunity to play up to 100 hands simultaneously. If they are looking for a low-denomination machine, the penny-denominated machines should be carefully examined. In many cases, the latter are multi-hand machines and, regardless of how small the bet placed is, it will be multiplied by the number of hands played for every game.
The expected value represents the amount of money a player should be ahead after playing a ”player advantage game” for a certain period of time. The expected value is usually based on the expected return and the amount bet.
Let us evaluate the expected value for a period of, say 1 hour of play (no matter that one may play for a larger period):
1. One needs to multiply the cost of every hand by the total number of hands he/she desires to play within 1 hour. This will result in their total wager for a 1-hour play;
2. One needs to transform the expected return for the particular game into a decimal by simply moving the decimal point two places to the left and removing the percent sign;
3. One needs to multiply the result from step 2 by their total wager in order to determine what the return in cash terms is;
4. One needs to subtract the total wager in step 1 from their total return in step 3 in order to estimate their theoretical earnings (the expected value).
Now we shall estimate the expected value for two video poker games offering different expected returns and played on machines with different denominations.
Let us again take the Full-Pay Deuces Wild game, which offers an expected return of 100.76%. The player prefers a $.25 denomination and intends to bet the maximum number of coins, say 5. Thus, their total wager for each hand will be $1.25 ($0.25 x 5). The player intends to play 650 hands within a period of 1-hour.
First, the player will multiply the cost of each hand ($1.25) by the total number of hands per hour (650). $1.25 x 650 = $812.50;
Second, they will transform the expected return for Full-Pay Deuces Wild from percentage into a decimal. This way they will get 1.0076;
Third, the player will evaluate the expected return for the game in terms of cash by multiplying 1.0076 by $812.50. Or, $812.50 x 1.0076 = $818.68;
Fourth, they will subtract their total wager from his/her return. Or, $818.68 – $812.50 = $6.18. This is the expected value or the theoretical earnings for a playing period of 1 hour.
Next, let us take the 10/7 Double Bonus Poker, which offers an expected return of 100.17%. The player chooses a $5.00 denomination and intends to bet the maximum number of coins (5). Thus, their total wager for each hand will be $25.00 ($5.00 x 5). The player intends to play 650 hands within a period of 1-hour.
First, the player will multiply the cost of each hand ($25.00) by the total number of hands per hour (650). $25.00 x 650 = $16 250.00;
Second, they will transform the expected return for 10/7 Double Bonus Poker from a percentage into a decimal. This way he/she will get 1.0017;
Third, the player will evaluate the expected return for the game in terms of cash by multiplying 1.0017 by $16 250.00. Or, $16 250.00 x 1.0076 = $16 373.50;
Fourth, they will subtract their total wager from his/her return. Or, $16 373.50 – $16 250.00 = $123.50. This is the expected value or the theoretical earnings for a playing period of 1 hour.
What conclusion can be drawn?
Although Full-Pay Deuces Wild offers a higher expected return than 10/7 Double Bonus Poker, the latter will provide the player with a higher expected value. For each hour of play they can expect to earn ($123.50 – $6.18) $117.32 more if playing Double Bonus Poker than what they would earn if playing Full-Pay Deuces Wild, using the denominations pointed out above.
