| Updated: All gambling games are designed to give the casino an advantage, known as the house edge, and slots are no exception. Card and dice players can easily calculate their odds and know exactly what they are up against. This is not the case for slot players.
The mathematics behind slots is complex because of the extremely high number of possible outcomes and combinations. In addition, casinos prefer to keep the parameters used to calculate their slot odds secret.
Despite these obstacles, dedicated slot players may want to understand how the house edge works and how to calculate it. This can provide insight into which machines to play and which ones to avoid. This article explains how the house obtains an edge in slots, how to calculate it, and how to identify games that may offer a positive expected value.
The House Edge
Figuring Out the House Edge in Slots
There is No Way To Reduce the House Edge in SlotsFiguring Out the House Edge in Slots
Also known as “hold,” the house edge of slot machines is set by programmers and mathematicians working for game manufacturers. Casinos are offered several optional paytables for a slot.
Suppose, for example, that Bellagio is looking to purchase the Game of Thrones slot from manufacturer Aristocrat. The manufacturer offers Game of Thrones machines with several theoretical returns, such as 90%, 92%, and 94%. Bellagio chooses the machines with an average return of 94%, which is the percentage collectively returned to players.
From the slot manufacturer’s perspective, the process works as follows. A mathematician first analyzes the slot and creates its paytable by building the so-called PARS sheet, a term that stands for “paytable and reel strip.”
This document is then sent to programmers, who use it to write the game’s code. The sheet provides vital information about symbol hit frequencies and payouts for winning combinations.
The house edge of slots varies from as little as 0.5% to as high as 25%. Slots that yield a casino advantage of under 4% are considered loose, while those with an edge over 8% are deemed tight. The house edge is ultimately about achieving a balance.
If it is too low or close to 0%, the casino will not generate sufficient long-term profit from the machine and may quickly remove it from the casino floor. If it is too high, players will lose money faster and may soon lose interest in the slot.
The casino hold for slots can be calculated with a computer, but this requires analyzing every possible combination of symbols. You need information about the number of symbols on each reel and the spaces between them. To complicate matters further, modern slots use virtual rather than mechanical reels, making it possible to map a huge number of virtual symbols to each reel.
Players have no way of knowing how many symbols are mapped to these virtual reels. Casinos keep PARS-sheet information strictly confidential and do not reveal it to the average player.
There is No Way To Reduce the House Edge in Slots
The peculiar thing about all this secrecy is that the information is almost useless from the player’s perspective. There is a common misconception that slot games are programmed to go through hot and cold cycles during specific periods. In reality, each spin is independent. The odds are determined in advance and remain the same on each spin.
Even if a player is familiar with the reel-strip configuration of a particular slot, this knowledge provides no advantage. It cannot be used to develop a strategy capable of overcoming the house edge built into the game. No such strategy exists for random games consisting of independent trials, such as slots.
Consider a coin flip. Most people know there are two possible outcomes, heads or tails, and that both have an equal chance of occurring when a fair coin is tossed. However, this knowledge alone does not allow anyone to predict which result will occur on the next flip.
The good news is that there is a way to calculate the house edge you face on a particular slot without knowing the details of the game’s PARS sheet. All you need is the theoretical return-to-player percentage, or RTP.
Many reputable online operators willingly share this information. Online and land-based casinos operating in the UK, in particular, are even required to make this percentage available under their licensing terms.
The RTP indicates the percentage of all money wagered on a slot that is returned to players. The remainder represents the casino’s advantage. Therefore, all you have to do is subtract the RTP from 100%.
Let’s use Microgaming’s Game of Thrones slot (the 243-ways version) as an example. The RTP of this game is listed as 95.10%. Therefore, its house edge is 100% – 95.10% = 4.90%. This means the casino collects nearly $0.05 from every dollar players wager on this slot over the long term.
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Casino Myths and Tricks
Can Casinos Manipulate the Odds to Increase Their Edge? Casino Tricks to Boost Slot ProfitsCan Casinos Manipulate the Odds to Increase Their Edge?
A recurring complaint among losing players is that casinos routinely manipulate odds and payout percentages to extract a higher edge from their slot machines. The common misconception is that this happens covertly at the press of a button, even while someone is playing the machine.
Another misconception is that floor personnel are instructed to “tighten” the machines during busy weekends and “loosen” them for the rest of the week.
Contrary to these assumptions, gambling operators cannot reduce payout percentages simply by pressing a button. To do so, the machine’s current EPROM chip must be replaced with a new one.
The replacement does not happen covertly. A senior casino employee must first complete extensive paperwork and submit it to the local gambling regulator for approval. If approval is granted, the casino must purchase a new approved chip, which can be expensive.
More importantly, the chip cannot be replaced while someone is playing the machine. In Nevada, for example, locally regulated casinos are prohibited from changing slot chips unless the machine has been inactive for at least four minutes.
The machine must also display a message informing players that it is under maintenance. Changing a chip is a time-consuming process, especially with popular slots, because the casino must wait until activity slows. The bottom line is that changing a slot’s payback percentage rarely makes financial sense.
Online casinos also face obstacles when it comes to altering odds. The theoretical return percentages of online slots are determined by the games’ software developers. When suppliers such as NetEnt and Playtech develop a slot, they set one or more predefined return percentages for operators using their software.
Gambling sites rarely have control over slot payback percentages, although in some cases they may be allowed to choose from several return options. Software supplier RealTime Gaming (RTG) provides operators with more flexibility through RTP options ranging from 91% to 97.5%. Nevertheless, online casinos using this software must select a specific percentage and stick with it. They cannot alter the odds back and forth on a daily basis.
Casino Tricks to Boost Slot Profits
Like most businesses, casinos look for ways to increase the profits they earn from their games. In the context of slots, this goal was advanced by the introduction of multi-coin games with multiple paylines, which quickly surpassed classic three-reel slots in popularity.
Many video slots produce a higher casino hold because their payout percentages are lower, at around 95% or 96%. This lower return causes players to use their bankrolls faster. A $100 bankroll that might last an hour on classic slots could last only 30 minutes on modern multi-credit games.
The arrival of virtual reels revolutionized slot play by allowing casino operators to offer astronomical jackpots. To offset potential losses on machines with larger jackpots, casinos reduced the odds of winning by making the largest prizes much harder to hit.
No longer limited by physical space, game designers can map a greater number of symbols and blank spaces onto the reels, collectively known as stops. The game’s random number generator determines which symbols appear on the screen at the end of each animated spin.
Each stop on the virtual reels corresponds to specific random numbers, but these numbers, symbols, and blanks are not weighted evenly. Most randomly generated numbers are linked to blanks, which are non-paying positions on the virtual reels.
The opposite is true of winning symbols, which correspond to fewer randomly generated numbers. As a result, slots with virtual reels can give players longer odds of winning than machines that rely on physical reels.
These odds remain hidden from players, who have no way of knowing the total number of stops or how many random numbers are assigned to each stop. In many jurisdictions, including Nevada, casino operators are not bound by law to display the winning odds on their slot machines. Some regulators even argue that doing so would diminish the element of surprise inherent in slots.
The way machines respond when low-paying combinations appear can also be misleading. Modern video slots require players to place bets on the paylines to activate them. This increases the number of credits wagered per spin.
As a result, losing spins are often disguised as winning ones, encouraging players to continue. How is this possible? The payouts on some multi-line wagers are smaller than the total amount the player has bet.
Suppose, for example, that you are playing Betsoft’s Fruit Zen slot, a five-reel game with 10 adjustable paylines and bets of up to 10 credits per active line.
You bet one $0.10 coin on each of the 10 paylines, risking $1 per spin. A combination of three raspberries appears on line 2 and awards you 5 credits.
You are $0.50 down on this spin, yet the machine still reacts as if you have made a profit. Your “win” is accompanied by exciting sound effects and flashy animations. This approach is intended to keep slot players at the machines for longer periods.
As explained above, the longer you play, the more spins you complete. The more spins you complete, the more the house edge begins to affect your results.
Slots and Positive Expected Value
All casino games, including slots, are rooted in mathematics, allowing players to estimate how much a given bet is worth. On the casino floor, you have two choices: play a game with a positive expected value or one with a negative expected value. Expected value, or EV, represents the average amount a specific bet is worth. Let’s examine how slots stack up in terms of EV.
Defining Positive Expected Value What Slots Offer Positive Expectation to the Player and When Slots with Mystery JackpotsDefining Positive Expected Value
Expected value is easier to explain with a coin-flip example. If you use a fair coin, the chance of it landing on tails is the same as the chance of it landing on heads. In the short term, the coin may produce more heads than tails, but if you flip it thousands of times, the outcomes should begin to even out so that each occurs roughly 50% of the time.
Now suppose you wager one dollar per flip and win one dollar each time your prediction is correct. You are paid at true odds, so your expected value is zero. If you complete 100,000 flips, you are unlikely to record much net profit, if any.
Gambling rarely works this way because games seldom pay at true odds, and one of the parties involved, normally the house, holds the advantage. The house retains a consistent edge over players, although a few games can yield a positive expectation for the player.
This is the case with blackjack and some video poker variations, where advantage play and strategy can produce a net profit over the long term. The long-term expected value of a bet is calculated by multiplying your edge by your average bet. To determine your hourly expected value, you must also account for the average number of wagers you make per hour.
Suppose you find a full-pay version of Double Double Bonus Poker where a full house pays 10 credits and a flush pays 6 credits on the first betting level. Such a machine offers a long-term return of 1.000670 for every dollar wagered, which corresponds to 100.067%.
It yields a positive expectation with optimal strategy because the player has an edge of 0.067% over the casino. The long-term expected value of a $25 bet, for example, is 0.00067 x 25, or 0.01675. In other words, you would win a little over one cent for every $25 wagered over the long term. This is not much, but the game still provides positive value.
What about slots? The vast majority of slot machines offer return percentages below 100%. Let’s compare Playtech’s Goblin’s Cave with the full-pay video poker variation from the previous example. It is one of the highest-paying games in Playtech’s library, with an RTP of 99.32%.
Here, the player’s disadvantage is 0.0068, or 0.68%. Therefore, the expected value of a $25 bet is 25 x -0.0068, or -0.17, meaning you would lose $0.17 on this wager over the long term. Unfortunately, most slots, with very rare exceptions, are negative-expectation games.
What Slots Offer Positive Expectation to the Player and When
Some progressive jackpot slots become advantageous for players whenever the top prize exceeds a specific value. The main difficulty is determining when this theoretical edge appears because game developers are reluctant to reveal the details needed to calculate the odds.
This is not the case with video poker and other card games, where the odds can be calculated from the number of cards in play and the hand that awards the progressive jackpot.
A progressive slot becomes a positive-value bet for the player when it exceeds its break-even point. The break-even points of progressive blackjack and video poker games are readily available online. The same cannot be said for slots because their developers choose to keep this information confidential.
Slots with Mystery Jackpots
An exception involves slots with mystery jackpots, where the top prize is awarded when the meter reaches a specific value. You can determine when such a slot gives you an advantage by using the following formula: t = m x (h + r) / (h + 2 x r).
- t stands for the target point
- m stands for the maximum jackpot
- c is an alternative symbol for the contribution rate represented by r in this formula
- h represents the house edge
- r stands for the rate at which the jackpot meter rises
You must know the values of all the variables used in the formula. Determining the house edge is straightforward when you play online slots. As explained above, you can calculate it when you know the game’s theoretical return percentage.
Determining the jackpot contribution is more difficult because few suppliers share this information. Here is an example using a fictitious slot. Assume the mystery jackpot is awarded at around $1,500 and the slot has a house edge of 7% (an RTP of 93%).
The jackpot contribution from each bet is 3%. When these variables are added to the formula, it becomes t = 1,500 x (0.07 + 0.03) / (0.07 + 0.03 x 2). The result indicates that this slot begins offering a positive expectation when the jackpot meter reaches approximately $1,153.
Slots with mystery progressive jackpots can present positive-EV opportunities because they allow players to identify situations with a theoretical advantage. However, players must track progressive jackpots at different casinos and gather all the information needed for the calculations.
If the house edge and jackpot contribution are unknown, you can try to make an educated estimate of these variables. When playing at land-based casinos, you can use state gaming reports as a guide because they contain information about machines’ average payouts for each coin denomination.