Mathematics Of Slot Machines
- Mathematics Of Slot Machines Book
- Mathematics Of Slot Machines Games
- Mathematics Of Slot Machines Machine
- Mathematics Behind Slot Machines
Slot machines are the most popular form of casino gambling for many reasons. These machines are also the biggest profit center for casinos, which should tell you everything you need to know about playing them.
Slot machine math will assist in determining:. Whether a machine is performing as the vendor intended. The customers’ preferences for a machine on the floor. How much is reinvested in a customer with players club rewards. In the top row, the first set of payouts shown are those of the first slot machine (but not with the first set of reel strips used with it), as invented by Charles Fey. A photograph of the specimen of this machine which was on display at the Liberty Belle Saloon in Reno, Nevada (this business, owned by Charles Fey's grandsons Marshall Fey and Frank Fey, closed down in 2006) is shown at right. This example video unleashes to full power of SLOT-IDE by showing you how generate the mathematics of a complex slot machine game in a few seconds!
I've picked up a project from someone else who has created a spreadsheet that is meant to represent some slot machine mathematics and i'm struggling to understand the math that is used to get certain figures. The game is built on 3 sets of balls that are draw. 10 balls, 15 balls and 20 balls. Here are 5 facts based on math about the slot machines that every slots player needs to know. After you learn these 5 mathematical facts, you might decide that the slot machines aren’t the best option when you’re in the casino. 1 – Random Number Generator Math.
Casinos offer many game options that are better for you to play than slot machines, but most gamblers don’t understand why. Here are 5 facts based on math about the slot machines that every slots player needs to know.
After you learn these 5 mathematical facts, you might decide that the slot machines aren’t the best option when you’re in the casino.
1 – Random Number Generator Math
A common mistake made by many slots players is assuming that they recognize patterns and/or can time their spins to profit from the random number generator that runs the machine. The casinos actually want you to believe that you can get a edge this way, because it keeps you playing longer and this means that you lose more money.
Mathematics Of Slot Machines Book
Modern real money slot machines are complex machines that are more like computers than anything else. They use random number generators to determine the results
for the machine.
What you see on the screen when you take a spin is simply a form of entertainment, and doesn’t have anything to do with whether or not you win. The slot machine runs the random number generator program, a result is determined, and then the result is shown on the screen. The result is usually a sequence of reels spinning.
The reason why it’s impossible to see patterns or time your spins is because modern random number generators can cycle through millions of numbers every minute. This means that it’s cycling through thousands of numbers every second. The human mind and body simply can’t react fast enough to find any value in this situation.
2 – Near Miss Danger
Slot machine builders and the casinos want machines that keep gamblers spinning the reels as much as possible. Many different tricks have been developed over the years to make you play more.
One of the worst tricks for slot machine players is when the reels appear to just miss a winning combination. The result is the same as any other losing spin, but psychologically it tries to trick you into getting a little rush thinking about how close you came to winning.
When you play slots games, train yourself to ignore the reels and focus only on the results. You either win or lose, and the reels don’t have anything to do with the result. You learned in the first section that the results are determined first, and then the reels show the results.
Most slots players think the reels determine if they win or not. This makes them more susceptible to what looks like a near miss on the reels. Now that you know how slot machines really work you won’t be fooled again.
3 – Losses Disguised As Wins
Not every slot machine uses this trick, but it’s a smart psychological move from the casino’s side. This trick is commonly called losses disguised as wins. Here’s how it works.
You’re playing a slot machine that has a $2 wager amount. You take a spin and hit a small paying combination, and it pays $1.60.
Your mind registers a win and this releases chemicals that make you want to keep playing. But the problem is that you didn’t really win. You lost 40 cents on the spin.
You need to take a close look at the pay table on every slot machine before you start playing. You need to consider many different things when you choose a slot machine to play, but my personal rule is to never play a machine that ha losses disguised as wins.
Mathematics Of Slot Machines Games
Slot machine manufacturers and casinos want the machines to be as addictive as possible. Of course, you never see this published anywhere because gambling addiction is a terrible thing. But the truth is that casinos want as many gambling addicts as possible playing.
One of the min ways to keep gamblers playing longer is to give them the chemical rush when they win. The more you get this rush, the more you want to play.
This is why losses disguised as wins are so devious. They’re a tricky way to use math to make you lose more money.
4 – Progressive Slots Jackpot Math
I don’t usually play slot machines, and I don’t usually recommend playing them to beginning gamblers. But I do play some progressive jackpot slot machines. I play them for much the same reason that I buy a lottery ticket from time to time.
A big progressive jackpot slots win can be enough money to change your life. This is the same as the lottery in many ways. You need to get lucky to win a big jackpot, but it’s worth throwing a few dollars at it sometimes.
Slot machines that have progressive jackpots are the only slots games that have a possibility of offering an edge for gamblers. When a jackpot grows to a large enough amount, the edge can flip from being in the casinos favor to being in your favor.
This sounds like a good thing, but there are two problems with it. The first problem is that it’s hard to find the base house edge or return to player percentage for these slot machines. You need this information to determine how large the jackpot needs to be to flip the odds.
The second issue is that just because the odds are in your favor it doesn’t mean that you’re going to win. In fact, unless you get lucky and hit the jackpot, you’re still going to lose money.
I’m all for taking a long shot at a big slots jackpot from time to time, but don’t waste too much money chasing a big pay day. The odds are against you every time.
5 – Total Bet Amount per Spin
Almost every slots player has taken a seat at a penny slot machine hoping to play for a penny or a few cents per spin and found that they had to risk $1 or more on each spin.
It’s important to bet enough to unlock all of the pay lines and any jackpots, but you need to concentrate on the total wager amount on any slot machine you play. Ignore terms like penny slots and nickel slots, because these are just marketing words and don’t have anything to do with how much it costs to play every spin.
Mathematics Of Slot Machines Machine
The reason why total wager amount per spin is important is because it’ a big part of how much you bet overall. If you’re wagering $2 per spin and take 500 spins in an hour, you’re risking $1,000 every hour.
If you can determine the return to player percentage or house edge percentage for the slot machine you’re playing, you can quickly figure out how much you can expect to lose playing.
Here are 2 examples.
If the slot machine you’re playing has a return to player percentage of 96% and you’re wagering $1,000 an hour, you can expect to lose $40 every hour you play on average. The way to quickly determine this is to subtract the return to player percentage from 100%. This gives you the house edge. Multiply the house edge of 4% times $1,000 and you get your expected loss of $40.
Sometimes you can find the house edge for a slot machine. When you have the house edge you simply multiply it times the amount wagered. If house edge is 5%, you multiply it times the $1,000 you’re risking. This is an expected loss of $50 every hour.
Conclusion
The slot machines in the casino are a danger to your bankroll. These machines crank out a consistent profit for the casinos, which means that they consistently take money from players.
This doesn’t mean that you should never play slot machines, but you need to be careful about how often you play them and how much you lose when you play.
The 5 mathematical facts about slot machines that you just learned can show you how often you should play and how much you should risk when you do play.
Please enable JavaScript to view the comments powered by Disqus.Today, the mathematics of slot machines. The University of Houston mathematics department presents this program about the machines that make our civilization run, and the people whose ingenuity created them.
Mathematicians first got interested in randomness by studying games of chance. Ever since, the histories of mathematics and gambling have been intertwined. Clever gamblers use mathematics to look for the smallest advantages, and casinos use sophisticated mathematical tools to devise new ways of drawing in players.
Indeed, a patent granted to the Norwegian mathematician Inge Telnaes in 1984 transformed the gambling industry. Prior to Telnaes’ invention, slot machines were essentially mechanical devices. Besides being difficult to tune and maintain, mechanical slot machines suffered from an essential problem: Let’s look at a machine with three reels, each with 12 symbols, with one of those 12 symbols a cherry. The likelihood of getting three cherries, and winning the jackpot, is 1 in 1,728. If the casino wants to make money, the jackpot payout should be, say $1,700 on a $1 bet. That does not seem attractive by today’s standards. However, the only way to increase the payout is to decrease the chances of hitting a jackpot.
Adding another reel is a possibility. For instance adding a fourth reel in the previous example would get us to a jackpot of about $20,000. But people do not like machines with more reels — they intuitively, and rightfully, feel that extra reels diminish their chance of winning. Another possibility is to put more symbols on each reel. But the astronomical jackpots you see in casinos today would then require truly enormous machines.
Inge Telnaes proposed a simple solution: Let a random number generator — a computer chip — determine the combination of symbols that appear when the reels stop. In other words, use a chip to control where the reels stop on a spin, but create the illusion that the wheels stopped on their own. The number of possible outcomes on the slot machine does not change. However, by reprogramming the chip, the operator has full control over the likelihood of each of the different outcomes. For instance, the operator could make the three cherries appear only once in a million spins.
This was a brilliant insight: Suppose I pick a number between one and a million. Would you be willing to bet that you can guess that number? The answer is probably not. But let a computer chip pick such a number, put the chip in a machine with blinking lights and spinning reels, and many people will be more than willing to make the bet. It is simply because what people assume is happening in a slot machine is very different from what is actually happening.
The Magician oil painting by Hieronymus Boschfrom between 1475 and 1480
The history of gambling is also intertwined with that of a less reputable group — tricksters and swindlers. In the long run, the only sure way to make money by gambling is to create the illusion that your opponent can win, while keeping the odds firmly on your side. And that gives those who know math a very solid advantage.
I'm Krešimir Josić, at the University of Houston, where we're interested in the way inventive minds work.
NOTE: In the example with three cherries, I assumed that one only wins in the case the spin results in three cherries, and there is no other winning combination. In actuality, there are typically many winning combination, and as a result, the jackpot would have to be even smaller.
The following story in Wired Magazine shows the drawbacks of the new generation of slot machines — they are easier to hack and to counterfit than their mechanical counterpart http://www.wired.com/magazine/2011/07/ff_scammingslots/.
Here is a more exhaustive discussion of the history of slot machines, and the random number generators within them http://catlin.casinocitytimes.com/article/non-random-randomness-part-1-1243. You may want to scroll towards the end of the article to read about how flaws in the design of gambling machine resulted in somebody picking 19 out of 20 winning numbers in a game of KENO — and doing so 3 times in a row. That person walked away with $620,000, but only after some controversy.
Both images are from Wikipedia. The slot machine image was taken by Jeff Kubina.
For more mathematics in everyday life, visitkjosic.wordpress.com.
This episode was first aired on September 7th, 2011