The Math Of Slot Machines

The Math Of Slot Machines Jackpots
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Someone hit a jackpot on the machine you just left - so you would have won that jackpot if you kept. Understanding the mathematics behind online slot games is invaluable in helping players choose the best machine. So let’s start by explaining how mathematics is used to operate slot machines. Slots mathematics. The outcome of each spin on a slot machine is determined by a Random Number Generator (RNG). Classic Slot Games: For the nostalgic veterans who enjoy the traditional casino-style games, we supply over 400 3-reel free slots no download games and two-dimensional machines. They are usually not abundant with bonuses, but they are easy to use as they consist of a few lines and rows.

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Some people might look at slot machines as a crap shoot, but the reality is a slot machine operates just like any other casino game. A random result is obtained with every bet wagered, and it doesn’t matter if the bet comes from a ball falling into a slot on the wheel, the dealing of cards, the throwing of dice, or the spinning of reels. While the result is random, the house achieves an edge in the games it offers through the math, and that is how the casinos make their money.

When a slot machine player is searching for a machine, they are attracted to the machines they 'feel' will hit. They might look for patterns in the time of day, how much money has been fed into the machine, and even the location of a machine. Patterns help justify the choice of the machine they have selected. Whether they win or lose, they attribute it to their selection process, but the reality is it is all random.

The math behind slot machines dictates that it be random. It doesn’t matter when the last jackpot hit or how much money was wagered; you have the same chance of hitting a jackpot on a 'cold' machine as a 'hot' one. And because it’s random, it’s impossible to predict when or where a payout will happen.

What you need to know is the game starts and is over when you place your bet. A random number generator determines the outcome of each of the reels the second the reels start turning.

Random outcomes are the whole premise of casino games, not just slot machines. In fact, for regulated casinos, these random outcomes are rigorously protected by the official government bodies who provide the license. Every regulated casino reports to a gaming authority like the United Kingdom Gambling Commission(UKGC) or the Malta Gambling Authority (MGA) that requires random results and dictates that the payouts account for a certain percentage of the money wagered.

The Math Behind the Slots

It’s important to understand odds to understand the math behind slots. Let’s take the simple example of heads and tails. The odds of getting heads or tails with the flip of a coin is 50/50; it’s an even-sum game. Meaning if you wagered money over the long term you would expect to be even.

For a casino to make money on this game, they would use the math to create terms that benefit them. If you lose the bet, you lose the full bet, but if you win, your payout will be 90 percent of the full bet. In this scenario, over the long term you will end up losing 10 percent of the amount wagered. The casino took a break-even game and created an edge to give the house an advantage.

Simply put, that is how the math behind slot machines works. The payouts are calculated to be less than the odds of hitting a payout. In the long run, you can’t beat an even-sum game or a slot machine when they are designed to pay you a percentage on the dollar.

Strategies for Managing Bankroll with Slot Machines

Now that you know why casinos and slot machines are the winners, let’s look at some ways to manage your bankroll responsibly while we’re playing.

Play Small

It’s true that lower-stakes machines usually have worse odds than higher-stakes ones. However, when you do the math using an average bet amount per hour and the payout percentages, you’ll find it’s easier to control your spending by playing the machines that have smaller jackpots. Keep this in mind when you choose one of the casinos listed on our casino A-Z directory

Stay Away from Huge Progressive Jackpots

The appeal of winning a big jackpot is undeniable, but you should know a portion of each bet goes towards making the progressive jackpot higher. Your payout percentages on all of the other ways to win are less because you are technically wagering less money. If you can’t stay away from the enticement of the huge jackpots that some slot machines offer, then at least choose a lower-stakes machine.

Choose a Real-Reel over a Video-Reel Machine

Video-reel slots are fun to watch because of the bells and whistles. They add to the entertainment value of the machine. The problem with all the lights and sounds is it takes longer to display the chosen symbols than a traditional slot machine does. The casino isn’t earning money when the machine is entertaining you. Although it is true to say that slot machines all over the world draw on the most popular references from celebrity culture and that there are countless slots games inspired by popular TV shows and movies, one should always remember that video-reel slots often pay out at a smaller percentage compared to a physical slot machine to compensate for the extra time needed to display the results.

Capitalize on Loyalty Reward Programs

Casinos want to keep slot machine players playing, and they do that by offering coupons, discounts, cash back, and other prizes. While the program has no relevance on whether you win or not, offsetting your expenses with their offers can help you save money. We have published a page about all the best free cash bonuses available in the industry to help you choose the best casino room to play at. Have a look at it and don’t forget we update it every week.

Play Other Machine Games

You are more likely to find better odds and better payout percentages on other machine games like video poker, video roulette, and video blackjack. Even better odds can be found if you graduate from slot machines to table games. If you are more comfortable with a machine, then try your hand at video poker.

Know the Casinos

Casinos are required to payout at an agreed upon payout percentage. Some casinos advertise their percentages while others don’t, and it makes sense to choose casinos and machines that advertise a high payout percentage.

Realize that high-traffic casinos tend to have lower payout percentages while casinos with lower traffic are trying to lure new players with better percentages. Avoid advertising claims that do not speak to specific numbers because they usually do not have the data to support the claims.

If you are one of the many players that play slot machines for entertainment, then it’s your job to get the most value for your money. Do your homework, do the math, and read as many independent reviews as you can before you choose to play at the casino that offers the best experience, customer loyalty program, and where you feel most comfortable, safe and welcome.

Although most casino table games feature a relatively small, fixed number of possible outcomes, slot machines offer a huge number of possible combinations on their reels. Even classic 3-reel slots can feature tens of thousands of line combinations, which makes the process of calculating odds exceeding difficult. What’s more, bonuses, multiple paylines, nudges and other special aspects of individual games only complicate the math.

The Simplest Example

A basic 3-reel slot machine with a single payline will usually have at least 20 “stops” per reel where various symbols can come to rest. On each reel, only one of the stops is allocated for the jackpot symbol, which makes the odds of seeing it appear on the first reel payline 1-in-20, or 1/20 = 0.05 = 5%. The same is true for the jackpot symbols on the second and third reels.

A quick calculation shows the likelihood of jackpots coming up on the payline for all three reels. It is the probability of each of the three independent events multiplied together, or exactly 0.05 x 0.05 x 0.05 = 0.000125. In other words, the top prize combination can be expected to show up in 1 ÷ 0.000125 = 8,000 spins.

Suppose, then, that a player bets a dollar on each spin, with the expectation of catching at least one jackpot. The cost would be $1 x 8,000 spins = $8,000 in order to get a jackpot. A quick look at the machine’s pay table will show how much can be won for the winning combination. No doubt it will be less than 8,000X, else the slot owner would have no advantage. Quite likely is much, much less, so whatever the difference is, it must be made up by smaller wins on less rewarding combinations.

Of course, slot manufacturers re well aware of where to set the payout ratios so that slot operators can make a promise. Payback percentages on the order of 95.0% to 97.5% are not uncommon, which means out of $8,000 wagered, the player will get a return of $7,600~$7,800.

Even Greater Complexity

Of course, modern slot machines are not nearly that simple. Most of the newer games feature five reels, not three, and the number of stops associated with each symbol is not one. In fact, thanks to computerization and the use of Random Number Generators, the number of stops per reel can be several dozen or even several hundred. That means rather than odds of 1-in-20 for each reel’s jackpot symbol, the actual probability could be 1-in-100 or more.

Using a process called “mapping,” slot machine programmers assign some symbols a higher probability of appearing than others. The only method of calculating odds for such machines with accuracy is to know the ratio of virtual stops to actual stops for each symbol. Although an unlimited number of “virtual” stops are technically possible, most machines are set up to have no more than 256 or 512 of them per reel.

Unfortunately, information regarding virtual stops and mapping is not easy to come by. Slot makers rarely, if ever reveal it to the public. Only among the few machines for which the “paytable and reel” (PAR) sheets are available can accurate calculations be made.

Red, White & Blue

One slot for which PAR sheets have been released is the popular game called “Red, White and Blue.” It features three reels and a single payline, offering a top payout of 10,000 credits for a jackpot win on a maximum three-credit bet. That makes the actual payout ratio 3,333-to-1, which is awarded only when the Red 7, White 7 and Blue 7 appear on the payline in that specific order.

From the PAR sheets, it is clear that there are exactly 11 symbols and 11 blanks on each reel. Without additional information, one might calculate the odds of a jackpot to be 1/22 x 1/22 x 1/22 = 1/10,648 = 0.0000939, which is a little more than 10,000 spins required. However, that is not the case at all.

In fact, each reel has 64 virtual stops, not 22 actual stops, and those stops are unequally mapped to the 22 symbols. The true probability of catching the jackpot is 1/64 x 1/64 x 1/64 = 0.0000038, or once every 262,144 spins—which is nowhere near the 3,333-to-1 odds that the paytable might suggest or 10,648-to-1 odds based on guessing at the number of stops. What’s more, any wager less than the maximum does not payout the full jackpot when hit. China shore slot machine 1.90 big hit. With a single credit played, the top prize is just 2,400 credits—not a very good bet at all.

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