All gambling games are designed to give the casino an advantage, known as the house edge, and slots are not an exception to this rule. Yet, these constantly buzzing machines are unlike any other casino game. Card or dice players can easily calculate their odds and know exactly what they are up against but this is not the case with real spinners.
The mathematics behind slots is rather complex due to the incredibly high number of possible outcomes and combinations. On top of this, casinos prefer to keep all the parameters that go into the calculation of their slots’ odds a secret.
Despite these obstacles, a serious reel spinner always seeks to understand how the house edge works and how to calculate it. This gives them an insight as to 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 spot the games that can give you positive expected value.
Why There Is No Need for the House to Cheat Slot Players
1They already hold an advantage
Many gamblers who experience devastating short-term losses are quick to assume casinos resort to deceptive methods like rigging the slot machines. The fact of the matter is such players are simply bitter and cannot handle losses that usually result from a lack of understanding of the games, bad luck, and inadequate strategy.
In reality, there is no reason for casinos to cheat players through underhanded means. Gambling establishments already hold an advantage over their customers. This advantage is inherently built into the structure and payouts of casino games and is known as the house edge.
It results either from poor playing conditions, i.e. from disadvantageous rules, or from reductions in the payouts as winners are never paid at true odds. Often the house edge comes as a combination of both factors.
2The house always win
It is not unheard of for slot players to suffer huge losses or walk away thousands of credits richer from the casino floor. Everything is possible in the short term after a dozen spins. But the sad truth is most reel spinners will inevitably lose over the long run. This is so because the machines have been programmed to return less money than gamblers collectively wager over hundreds of thousands of rounds.
This pre-programming is perfectly legal mind you. The house is allowed to retain specific percentages from its games by its local gambling regulators. The house edge ensures the casino turns sufficient long-term returns that enable it to run its operations and collect a guaranteed profit.
3Regulations and legalities
Another equally compelling argument against casino cheating has to do with regulations and legalities. Licensing authorities are quick to react to cheating allegations. If foul play is indeed at hand, the cheating operator is heavily fined or has its license revoked.
The bottom line is slot players can have their peace of mind as long as they are gambling with licensed and properly overseen operators. It makes no sense for trusted casinos to put their reputation and licenses at stake when their built-in advantage already enables them to generate consistent long-term profits.
The House Edge
Figuring Out the House Edge in Slots
Also known as “hold”, the house edge of slot machines is set by programmers and mathematicians working for the games’ manufacturers. Casinos are only given several optional paytables for the slot to use as a reference.
Suppose, for example, Bellagio is looking to purchase the slot Game of Thrones by manufacturer Aristocrat. The manufacturer offers Game of Thrones machines with several theoretical returns like 90%, 92%, and 94%. The Bellagio chooses the machines with an average return of 94% and this is the percentage players collectively get back.
From the perspective of slot manufacturers, the process is the following. A mathematician first analyzes the slot and creates its paytable by building the so-called PARS sheet, a term which stands for “paytable and reel strip”.
This document is then sent to the programmers who use it to write the game with a computer code. The sheet gives them vital information about the hit frequencies of the symbols and the payouts for the 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 all about achieving balance.
If it is too low or around 0%, the casino will not generate sufficient long-term profits from the respective machine and will quickly ditch it from its floors. If it is too high, spinners will lose money at a faster pace and will soon lose interest in playing the slot.
The casino hold with slots can be calculated with a computer but you need to go through all possible combinations of symbols. One must gain information about the number of symbols per reel and the number of spaces in between. To complicate matters even further, modern slots use virtual instead of mechanical reels. This makes it possible to map a huge number of virtual symbols per reel.
Worst of all players have no way of knowing how many symbols are mapped on these virtual reels. Casinos keep PARS-sheet information strictly confidential and would never reveal it to the average player.
There is No Way To Reduce the House Edge in Slots
The weirdest thing about all this secrecy is that this information is almost useless from the perspective of the customer. There is a common misconception that slot games are set up to go through hot and cold cycles during given periods. In reality, each stop on the reels has equal chances of hitting as the rest. The odds are determined in advance and remain the same on each spin.
Even if a player is familiar with the reel stripping of a given slot, this knowledge gives them no advantage whatsoever. They cannot use it to develop a strategy capable of overturning the house edge built into the game. No such strategy exists with random games of independent trials like the slots.
To draw a parallel with a coin flip, most people know there are two possible outcomes, heads or tails, and both have equal chances of occurring when a fair coin is tossed. However, this knowledge alone does not allow a person to predict which of the two results will occur on the next flip.
The good news is there is a way to calculate what house edge you are fighting on a given slot, even without having information about the game’s PARS sheet. All it takes is knowing the theoretical return to player percentage or RTP.
This is information many trusted online operators are willing to share. Online and landbased casinos operating in the UK, in particular, are even required to make this percentage available under their licensing terms.
The RTP tells you what percentage of all money staked on a given slot is given back 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 said to be 95.10%. Therefore, the house edge it yields is equal to 100 – 95.10 = 4.90. This means the casino gets to collect nearly $0.05 out of every dollar players wagers on this slot in the long term.
The Hourly Expected Losses of a Slot Player
1How to calculate the cost
Knowing the theoretical return and the house edge of slots cannot help you devise a winning strategy to beat the game. With that in mind, this information is particularly useful when it comes to choosing what slots you play because the higher the house edge is, the faster you will lose money.
The advantage is in favor of the house which ultimately means players end up losing money in the long run. However, the knowledge of the house edge allows you to calculate the cost of playing slots for entertainment.
2Factors you need to consider
Several factors are taken into consideration for these calculations. Apart from the house edge, you must take into account the average size of your bets and the average number of spins you play per hour. The number of spins depends on your style of play but there is a general consensus that most players make between 400 and 600 spins per hour.
Let’s assume you play Microgaming’s Game of Thrones 243 Ways slot with a house edge of 4.90%. You prefer a more dynamic pace so you go through 600 spins each hour. Your average bet per spin is $1.20.
You can calculate the long-term losses you are expected to incur per hour by multiplying all of the above-mentioned factors like this 0.049 x 600 x 1.20, which corresponds to long-term hourly losses of $35.28.
You need to have enough hours under your belt to arrive at these numbers, though. Both the theoretical return percentage and the house edge are meant to represent long-term expectation. The more rounds you play, the closer you get to your average hourly expectation, which is negative for slot players as we shall explain later.
Casino Myths and Tricks
Can Casinos Manipulate the Odds to Increase Their Edge?
A recurring motif among losing players is that casinos are in the habit of manipulating the odds and the payout percentages to extract a higher edge from their slot machines. The common misconception is that this happens covertly with the switch of a button even while someone is already playing the machine.
Another misapprehension is that the floor personnel is instructed to “tighten” the machines during the busier weekends and “loosen” them for the remainder of the week.
Contrary to the assumptions of such players, gambling operators cannot reduce the payout percentages by switching any buttons. For this to happen, the machine’s current EPROM chip must be replaced with a new one.
The switch does not happen covertly, though. An important casino employee must first fill out tons of documents and send them to the local gambling regulator for approval. If such is granted, a new approved chip must be purchased, which naturally costs a lot of money.
More importantly, the chip change cannot take place while someone is already playing the machine. In the state of Nevada, for example, locally regulated casinos are prohibited from changing slot chips unless the machine has been inactive for a minimum of four minutes before the replacement.
Also, the machine has to show a message on the screen to inform players it is currently under maintenance. Chip change is a time-consuming process, especially with popular slots, because the casino has to wait until the action slows down. The bottom line is it makes no sense from a financial perspective to change slots’ payback percentages.
Online casinos, too, face roadblocks where odds alteration is concerned. The theoretical return percentages of online slots are determined by the games’ software developers. When suppliers like NetEnt and Playtech develop a given slot, they set a fixed return percentage offered to all gambling operators using their software.
Gambling sites rarely have a say when it comes to slot payback percentages although in some cases they might be granted a choice from several return options. Software supplier RealTime Gaming (RTG) provides operators with more flexibility with RTP options that range from 91% to 97.5%. Nevertheless, online casinos using this software must pick 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 are looking for ways to increase the profits they collect from the games they offer. In the context of slots, this profit boost was achieved with the introduction of multi-coin games with multiple paylines, which quickly overshadowed classic three-reel slots in terms of popularity.
Many video slots yield a higher casino hold because their payout percentages are lower at around 95% or 96%. This drop in return causes players to burn through their bankrolls at a faster rate. A bankroll of $100 that would last for an hour on classic slots would now last only half an hour on modern multi-credit games.
The arrival of the virtual reel has completely revolutionized slot play as it allowed casino operators to offer astronomical jackpots. To curb losses on machines with bigger jackpots, casinos had no other choice but to reduce the odds of winning by making the huge prizes much harder to hit.
No longer restricted by the limitations of physical space, game designers are now capable of mapping a greater number of symbols and blank spaces on the reels, collectively known as stops. The game’s Random Number Generator tells it what symbols to display on the screen at the end of an animated spinning sequence.
Each stop on the virtual reels coincides with specific random numbers but these numbers, the symbols, and the blanks are not weighted evenly. On the contrary, most of the randomly generated numbers are linked to blanks, which are non-paying positions on the virtual reels.
The opposite is true of winning symbols which result from fewer randomly generated numbers. The gist of it is slots with virtual reels ultimately give you longer odds of winning than machines that rely on physical reels.
Said odds remain hidden from the player who has no way of knowing the overall number of stops and how many random numbers are keyed to each stop. In many jurisdictions, including the state of Nevada, casino operators are not bound by law to display the winning odds on their slot machines. Some regulators even argue this would take away the element of surprise, inherent to slots.
The way the machines react when low-paying combinations hit is also deceptive to a certain extent. Modern video slots require the player to place bets on the paylines to activate them. This increases the number of credits played per spin.
As a result, losing spins are often disguised as winning ones deceiving patrons to continue playing. How is this possible? The payouts on some multi-line wagers are smaller than the overall amount the player has bet.
Suppose, for instance, you are playing Betsoft’s Fruit Zen slot, which is a five-reel game with 10 adjustable paylines and bets of up to 10 credits per active win line.
You are betting 1 coin of $0.10 on each of the 10 paylines. This ultimately means you are risking $1 on each spin. A combination of three raspberries hits on line 2 and rewards you with 5 credits.
You are $0.50 down on this spin, yet the machine still reacts as if you have turned a profit. Your “win” is accompanied with exciting sound effects and flashy animations. This approach is intended to keep reel spinners on the machines for longer periods.
And as we explained already, the longer you play, the more spins you go through. The more spins you go through, the more the house edge begins to manifest itself.
Slots and Positive Expected Value
All casino games, including slots, are based on mathematics, which makes it possible for players to calculate how much a given bet is worth. Players face two options on the casino floor – they can either play a game with positive expected value or one with a negative expected value. The term expected value, or EV, refers to the average amount a given bet is worth. Let's see how slots perform in terms of EV.
Defining Positive Expected Value
Expected value is easier to explain with a coin-flip example. If you use a fair coin, the chances of it landing on tails are the same as those for heads. In the short term, the coin may produce more heads than tails but if you flip it repeatedly thousands of times, the odds will start to even out so that each outcome occurs roughly 50% of the time.
Now, suppose you wager a dollar per flip and win a dollar each time your prediction is correct. You are paid at true odds so your expected value is nil. If you go through 100,000 flips, there is a good chance you will not register much of a net profit, if any.
This is not how things work in the context of gambling where games rarely 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 few games can yield positive expectation for the player.
Such is the case with blackjack and some video poker variations where you can turn a net profit over the long haul through advantage play and strategy. The long-term expected value of a bet is calculated by multiplying your edge by your average bet. If you are looking to arrive at your hourly expected value, you also need to factor in the average number of wagers you make per hour.
Let’s suppose you find a full-pay version of Double Double Bonus Poker where you get 10 credits for a full house and 6 credits for a flush on the first betting level. One such machine offers a long-term return of 1.000670 for every dollar you wager which corresponds to 100.067%.
It yields a positive expectation with optimal strategy since the player has an edge of 0.067% over the casino. The long-term expected value of a $25 bet, for example, is equal to 0.00067 x 25, or 0.01675. In other words, you will win a little over a cent from every $25 you stake in the long run. Not much but at least the game is still giving you positive value over the long haul.
But what about slots? The vast majority of slot machines offer return percentages under 100%. Let’s see how Playtech’s Goblin’s Cave measures against the full-pay video poker variation from the previous example. This is one of the top payers in Playtech’s gaming library, with an RTP of 99.32%.
Here the player advantage (or shall we say disadvantage) of -0.0068 or 0.68%. Therefore, the expected value a $25 bet would generate is 25 x -0.0068, or -0.17, causing you to lose $0.17 with this wager in the long run. 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 the player whenever the top prize exceeds a specific value. The main trouble here stems from the fact it is difficult for the player to determine at what point this theoretical edge manifests itself because game developers are reluctant to reveal the details you need to figure the odds out.
This is not the case with video poker and other card games where it is easy to calculate the odds by knowing the number of cards in play and the hand that pays 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 about slots because their developers choose to keep this information confidential.
Slots with Mystery Jackpots
An exception can be made about slots with mystery jackpots where the top prize is paid when the pot meter reaches a specific value. You can figure out when one such slot gives you an advantage by using the following formula: t = m x (h + r) / (h + 2 x r).
- t stands for target point
- m stands for maximum jackpot
- c corresponds to the percentage contribution toward the jackpot
- h represents the house edge
- r stands for the rate at which the jackpot meter is rising
Of course, you need to know the values of all variables to use the formula. Figuring out the house edge is easy when you play online slots. We already explained how to calculate this when you know the games’ theoretical return percentages.
Uncovering the jackpot contribution is more difficult as few suppliers share this information. Here is an example with a fictitious slot so you can see the formula in action. Let’s assume the mystery jackpot of the game drops around the $1,500 mark and the slot has a house edge of 7% (the RTP is 93%).
The jackpot contribution of each bet is 3%. When we add these variables to the formula, it looks like this: t = 1,500 x (0.07 + 0.03) / (0.07 + 0.03 x 2). The result we arrive at indicates that this slot starts offering positive expectation when the jackpot meter escalates to around $1,153.
Slots with mystery progressive jackpots are a good bet because they allow players to identify positive EV situations. Of course, players themselves need to do their homework by tracking the jackpots of the progressive slots available at different casinos and digging out all the information necessary for the calculations.
If the house edge and the jackpot contribution are unknown, you can try making an educated guess on these two variables. When playing at landbased casinos, you can use state gaming reports as a guideline since they contain information about the machines’ average payouts with each coin denomination.