Slots machines, as games of chance (rather than skill), are generally more about having fun than they are about making money.
However, there are things you can do to maximize your wins and minimize your losses. For example, by calculating a slot machine's payout percentage, you can obtain a larger picture idea of how much money you stand to win back. Other tactics include using effective bankroll management techniques, joining a slots club to benefit from its rewards programs, and more.
These games include roulette, craps, baccarat, keno, the big-six wheel of fortune, and slot machines. Of these, baccarat and craps offer the best odds, with house advantages of 1.2% and less than 1% (assuming only pass/come with full odds), respectively.
What Are the Odds of Winning on a Slot Machine?
Slot machine odds used to be easy to calculate. When you're dealing with three reels, ten symbols on each reel, and a limited pay table, then it's just a simple math problem. But the rise of electromechanical slot machines and (later) video slots added some complexity to the situation.
How Probability Works
Probability has two meanings. One is the likelihood of whether or not something will happen. The other is the branch of mathematics that calculates that likelihood. To understand the odds as they relate to slot machines (or any other gambling game), you have to understand the basic math behind probability.
- In roulette the odds on a single number bet are 35 to 1, but the probability of winning a single number bet is 1 divided by the number of slots on the wheel (36 to 38). Hence the odds are never the inverse of the probabilities. This way the casino maintains a 'house edge' that ensures the casino retains some percentage of player wagers.
- Aspire Global International LTD (or 'The Company') is a company Slot Machine Probability Calculator registered in Malta for the purposes of operating online games and mobile application games with registration number C42296 and registered office at Slot Machine Probability Calculator 135 High Street Sliema Malta.
Don't worry though. The math isn't hard. Probability involves addition, subtraction, multiplication, and division, all of which you learned in middle school.
Calculate Probability Of Slot Machines
The first principle of probability is that every event has a probability of between 0 and 1. If something has no chance of ever happening, then its probability is 0. If something will always happen, no matter what, then its probability is 1.
Calculate Probability Of Slot Machines
Probability is, therefore, always a fraction. It can be expressed in multiple ways, as a decimal, as a fraction, as a percentage, and as odds.
A simple example is a coin flip. The probability of getting heads when you flip a coin is 50%. That's common sense, but how is it determined mathematically?
You simply take the total number of possible outcomes, and divide the outcome you're trying to determine the probability of it by that number. There are two possibilities when flipping a coin, heads or tails, but only one of them is heads. That's 1 divided by 2, which can be expressed as ½, 50%, 0.5, or 1 to 1 odds.
Odds are expressed as the number of ways something won't happen versus the number of ways that something will happen. For example, if you're rolling a single six-sided die, and you want to know the odds of rolling a six, you're looking at 5 to 1 odds. There are five ways to roll something other than a six, and only one way of rolling a six.
When you want to determine the probability of multiple things happening, you use addition or multiplication, depending on whether you want to determine whether one OR the other event will occur, or whether you want to determine whether one event AND the other event will occur.
If you're looking at an 'OR' question, you add the probabilities together. If you're looking at an 'AND' question, you multiply the probabilities by each other.
So if you want to know what the probability of rolling two dice and having one or the other come up with a six, you add the probabilities together. 1/6 + 1/6 = 2/6, which is rounded down to 1/3.
If you want to know the probability of rolling two dice and having BOTH of them come up six, you multiply the probabilities. 1/6 X 1/6 = 1/36.
How Slot Machine Odds USED to Work
Early slot machines were mechanical devices. They had three metal reels that had ten possible stops each.
To calculate the odds of a single symbol appearing on a reel, you just divide the one symbol by the total number of potential outcomes. So if you had one cherry on a reel, your odds of hitting that cherry were 1/10, or 10%.
To calculate the odds of getting three cherries, you multiple 1/10 X 1/10 X 1/10 and get 1/1000, or 0.1%.
If the odds of hitting that symbol are the same as all the others, then you have 10 possible jackpots you can win, which means that your chances of winning SOMETHING are 10/1000, which is 1%.
Most people wouldn't play a slot machine that lost 99 times out of 100, though, so slot machine designers added additional, smaller prizes for getting two symbols out of three for certain symbols. And as long as they paid out less in prizes than the odds of hitting those jackpots, then those slots are guaranteed to make a profit in the long run.
For example, if a prize for hitting three cherries was $1000, you'd be playing a break-even game, but if the prize were $750, it's easy to see how the casino would be guaranteed a profit. The difference between the odds of winning and the payout odds is where the casino makes its money.
How Slot Machines Work Now
Modern slot machines use a computer program called a random number generator to determine the outcomes of the various spins of the reels. This creates an imaginary reel with a number of symbols limited only by the program in question.
A mechanical slot machine with 256 symbols per reel would be huge, too large to play, much less to build. But a computer can create an imaginary reel with 256 symbols per reel and take up no more space than an iPod Shuffle.
To make things even more interesting and entertaining, slot machine designers can program different probabilities for each symbol to come up. Most symbols might come up once every 256 spins, but others might come up twice as often, while still others might only come up half as often.
This enables slot machine designers and casinos to offer slot machine games with far larger jackpots than they were able to when they were limited by mechanical reels. And they're able to offer these large jackpots and still generate a healthy profit.
How Does This Relate to Payback Percentages?
The payback percentage is the amount of money that the slot machine is designed to pay out over an enormous number of spins. This number is almost always less than 100%. The difference between 100% and the payback percentage is the house edge, and that's where the casino makes its profits.
A simple example can help illustrate how this works. Suppose you have a slot machine with three reels with ten symbols on each, and it only pays out when three cherries hit. The odds of winning that jackpot, as we determined earlier, is 1/1000.
If we set the jackpot as $900, and charge $1 per bet, the payout percentage for that game will be 90%, or $900/$1000. Of course, no one would play a slots game which only paid out once in every 1000 spins, which is why there are various smaller payouts programmed in.
There's no way to tell what the payback percentage on a particular game is unless you have access to the par sheet for that machine. Casino management has that information, but players never have access to that info.
The best slot machine odds are almost always found in real casinos. If you see slot machines in an airport or a bar, be aware that the payback percentages on those games is much lower than you'll see in a real casino.
How to Win at Slot Machines
Everyone would like to know how to win at slots, but the truth is that winning at slot machines isn't any harder than losing at slot machines. You put your money in the machine, spin the reels, and hope for the best. Slot machines are meant to be fun; they're not intended to provide the player with an income.
In fact, the reality is just the opposite. Slots are there to provide the casino owners with an income. How that works is one of the subjects of this page.
On the other hand, you can minimize your losses and increase your enjoyment of slots games by understanding how they work. You can also learn which slots pay back the most money. In the long run, the house will still have an edge over you, but understanding how much you can expect to lose in a given venue can help you make better bankroll management decisions.
In fact, it might be a good idea to modify you definition of 'winning at slots'. Instead of considering yourself a winner if you bring home a big profit, consider yourself a winner any time you played and had a lot of fun.
How Slots Work
All slot machines in modern casinos use a random number generator (an 'RNG) to determine the results of each spin. An RNG is a tiny computer that does nothing but constantly generate numbers. When you push the spin button, that microcomputer selects a number which determines the outcome. In fact, this happens before the reels have even stopped spinning.
On modern slot machines, the reels are just there for show. From a practical standpoint, you could put a quarter in a machine, push a button, and have the screen flash: 'You lose!' or 'You win $10'. The mechanism that determined the outcome would be the same, but who would want to play a game like that, especially if you know that the house has a mathematical edge over the player.
The spinning reels, the sound effects, and the bonus games are all there to make the game more interesting to play. If you don't like the artwork, the music, or any other aspect of a slots game, don't bother playing it, because those are the real rewards of playing. The chance of getting lucky and winning a jackpot is a real reward, too, but don't ignore the other aspects of the game.
Best Casinos in Riverside County, CA - Fantasy Springs Resort Casino (498 reviews), Agua Caliente Resort Casino Spa Rancho Mirage (901 reviews), Tortoise Rock Casino (50 reviews), Augustine Casino (138 reviews), Spotlight 29 Casino (145 reviews), Morongo Casino, Resort & Spa (1289 reviews), Red Earth Casino (64 reviews), Agua Caliente Casino - Cathedral City (7 reviews), Indio Bingo Palace. Oct 10, 2019 he new Cahuilla Casino Hotel is under construction in Anza, Riverside County, and slated for a Spring 2020 opening. It will replace its next door neighbor, the original Cahuilla Casino, which has operated out of a tent-like structure for 23 years. New casino in riverside county.
The random number generator is programmed to pay back a certain percentage of the money paid into it over a period of time. This period of time is known in gambling math as 'the long run', and it's a lot longer than most people think. We're talking about tens of thousands of spins, not dozens or hundreds.
This percentage that's programmed into these machines is always less than 100%. If a slots game were programmed to pay back more than 100% of the money put into it, it would lose money for the casino.
Casinos aren't in business to lose money.
The trick is to find slot machines that have the highest payout percentages.
Which Slots Pay Back the Most Money
If every slot machine game in the world had a payback percentage posted on the machine somewhere, it would be easy to determine which slots pay back the most money. You could limit your play to machines with a payback percentage of over 95% for example.
It's too bad casinos don't provide that information on specific games, though.
You can find information about specific locations and their payback percentages, though. Some gambling guides and magazines publish this information. For example, The American Casino Guide provides certified information about the payout percentages in various states. Not all states reveal this information, but it's not a huge leap of logic to expect better payback percentages in states that do reveal this information.
For example, the overall payback percentage for slots in Black Hawk, Colorado is 92.8%. In Central City, Colorado, it's 92.93%, and in Cripple Creek, it's 93.66%. Alabama doesn't release the numbers on their payback percentages.
Which casinos do you think offer the better game?
A couple of guidelines hold true no matter where you play, though. One of those is that payouts are better in large cities with lots of gambling. For example, the payouts in Vegas are higher overall than the payouts in Colorado. And the payouts improve when you play for higher stakes. For example, penny slots in Vegas average around 88% to 91%, but dollars slots average between 93% and 96%. Finally, slot machines at airports usually offer the lowest payouts.
What does that mean for the player? It means that over the long run, if you wager $x on a particular game, you'll win back $x times the payback percentage for that machine. If you're playing a dollar slot machine on the Strip in Las Vegas, for example, and the payout percentage is around 93%, then if you place $10,000 in wagers, you'll win back $9300. You lost $700.
That's only a long term mathematical expectation, though. In the short run, anything can happen, and that's what keeps people playing.
How to Maximize Your Winnings and Minimize Your Losses
There are three ways to maximize your winnings and minimize your losses. The first is to always join the slots club, and always use your member card while you play. Slots club members get a percentage of their play returned to them in the form of casino rewards and cash back. This is normally a tiny percentage (think 0.1% or 0.2%), but it adds up, especially if you play a lot.
Don't buy into the myth that playing with your slots club card lowers your expected return on the game, either. That's not true. The random number generator in these games has no way of knowing whether or not you're using your slots club card or not.
The second way to increase your winnings and minimize your losses is to use effective bankroll management techniques. This means limiting the amount of time that you play, limiting the amount of money that you're willing to lose in any session and in any given gambling trip, and finding other fun things to do with your time besides just playing the slots.
Finally, try to play the machines with the highest payout percentage. Over the long run, if you keep playing, you'll probably eventually wind up a loser at the slots (unless you hit a huge progressive jackpot), but you'll lose your money more slowly and get more entertainment value for the money you gambled.
You want to know how to calculate probability in gambling?
The first step is understanding what the word means.
The word probability has 2 meanings:
- The likelihood that something will or won't happen.
- The branch of mathematics that measures that likelihood.
If you're a casual gambler, you might have a vague idea that the probability of a win can be measured.
But until you understand the specifics of how to calculate probability, you can't be considered a sophisticated gambler.
This post explains how to calculate probability in gambling and why it matters to gamblers.
How to Calculate Probability as a Fraction
Whether something will happen can be measured on a scale from 0 to 1. If something can never happen, its probability is 0.
Here's an example of something with a 0 probability:
You have a standard 6-sided die. It's numbered from 1 to 6. The probability of rolling a 7 is 0. It's not possible.
Here's an example of something with a probability of 1:
You have a trick coin with 2 heads. When you flip the coin, the probability of it landing on heads is 1. (And the probability of it landing on tails is 0.)
Most events have a degree of uncertainty to them, though. You can measure how often you expect those events to happen as a fraction.
Here's an example:
You flip a normal coin with a heads side and a tails side. The probability of getting heads is 1/2.
The Magic Formula for Calculating a Probability
The formula for calculating that probability is simplicity itself:
You divide the number of ways you can achieve the desired event by the total number of possible events.
In the case of a coin toss, there's only one way to get heads. But there are 2 possible results.
1 divided by 2 is 1/2.
This probability can be expressed in any of the following ways:
- As a fraction.
- As a decimal.
- As a percentage.
- As odds.
Some of these are more useful than others in certain situations. I'll get into that a little more later in this post.
But for now, let's convert that 1/2 probability of getting heads into each of those 4 ways:
- As a fraction, the probability is represented as 1/2.
- As a decimal, the probability is represented as 0.5.
- As a percentage, the probability is represented as 50%.
- As odds, the probability is represented as 1 to 1.
Most of us are familiar with probability represented as a percentage. After all, most people watch the nightly news or at least look at the Internet for the weather report.
And they always express the probability of rain with a percentage.
If there's a 20% chance of thunderstorms, we know that there's a roughly 1 in 5 chance of rain, thunder, and lightning.
Bigger Probability Problems
Probability gets more interesting as you start calculating probabilities for multiple events.
Let's say you want to know the probability of getting heads twice in a row.
This is an example of an 'and' probability. You need to get heads on the first throw AND on the second throw to win this bet.
When calculating a probability for multiple events that use the word 'and', you multiply the probability of event 1 by the probability of event 2.
In this case, that can be represented as 1/2 X 1/2 = 1/4.
The probability of getting heads twice in a row is, therefore, 1/4, which can also be expressed as 25%.
Notice that the probability is lower. That's what happens when you multiply fractions.
Let's say you want to calculate an 'OR' probability instead. This time, let's use a 6-sided die as an example.
You want to know the probability of rolling a 6 on at least one of 2 rolls.
That's an example of an 'or' probability. You want to know how likely it is that you'll roll a 6 on the first roll OR on the second roll.
You have 6 possible results, but only 1 of them is the 6. So your probability of rolling a 6 on either roll is 1/6.
In an 'or' probability, you add the probabilities together. In this case, that would be represented as 1/6 + 1/6 = 2/6. Of course, most people would reduce 2/6 to 1/3, which is also often expressed as a percentage, 33.33%.
Expressing Probabilities as Odds
The tricky expression of this isn't as a fraction, a decimal, or a percentage. Most of us are familiar with these expressions. That's basic math.
But most of us don't have backgrounds in statistics, so we're not used to expressing probabilities in odds format.
Here's how to calculate probability in odds format.
When expressing a probability as odds, you just compare the number of ways something can't happen with the number of ways it can happen.
If you want to look at the odds of rolling a 6 on a single 6-sided die, you'd look at the number of ways you could possibly roll anything else versus the number of ways you can roll the 6.
In this case, you're looking at 5 to 1. You have 5 ways to roll anything but a 6, and only one way to roll a 6.
This becomes useful when you start looking at the expected profit or loss on a bet.
Bets always pay off at certain odds–how much you win versus how much you risk.
Many bets pay off at 1 to 1, or even odds. This is especially true of bets you make in a casual situation.
Here's an example:
You're shooting pool at your local bar, and you bet your buddy $20 on the next game. If you win, he gives you $20. If he wins, you give him $20.
But let's suppose that your levels of skill are different.
Let's suppose that he's better than you, and he stands to win 2 out of 3 times.
The odds of him winning are 2 to 1.
If the bet pays off at even odds, in the long run, he'll profit from playing pool against you under those terms.
He'll win, on average, $40 during 3 games. You'll win $20. His net win is $20.
Average that net win out over the 3 games, and he's winning $6.67 per game on average.
If this were a casino game, you could translate that into a percentage, and you'd have the house edge.
But I'm going to write another post about the house edge, soon. And I don't want to spoil it for you.
Instead, I'm going to leave you with one more example of how odds are used–this time in a game of poker.
In this example, we're going to assume that you have 4 cards to a flush, and you're reasonably sure you'll win the hand if you make the flush. You're playing Texas holdem, and you have 2 cards that are hearts in your hand, and there are 2 hearts on the flop.
You have 2 cards yet to come.
Odds are expressed as the number of ways something won't happen versus the number of ways that something will happen. For example, if you're rolling a single six-sided die, and you want to know the odds of rolling a six, you're looking at 5 to 1 odds. There are five ways to roll something other than a six, and only one way of rolling a six.
When you want to determine the probability of multiple things happening, you use addition or multiplication, depending on whether you want to determine whether one OR the other event will occur, or whether you want to determine whether one event AND the other event will occur.
If you're looking at an 'OR' question, you add the probabilities together. If you're looking at an 'AND' question, you multiply the probabilities by each other.
So if you want to know what the probability of rolling two dice and having one or the other come up with a six, you add the probabilities together. 1/6 + 1/6 = 2/6, which is rounded down to 1/3.
If you want to know the probability of rolling two dice and having BOTH of them come up six, you multiply the probabilities. 1/6 X 1/6 = 1/36.
How Slot Machine Odds USED to Work
Early slot machines were mechanical devices. They had three metal reels that had ten possible stops each.
To calculate the odds of a single symbol appearing on a reel, you just divide the one symbol by the total number of potential outcomes. So if you had one cherry on a reel, your odds of hitting that cherry were 1/10, or 10%.
To calculate the odds of getting three cherries, you multiple 1/10 X 1/10 X 1/10 and get 1/1000, or 0.1%.
If the odds of hitting that symbol are the same as all the others, then you have 10 possible jackpots you can win, which means that your chances of winning SOMETHING are 10/1000, which is 1%.
Most people wouldn't play a slot machine that lost 99 times out of 100, though, so slot machine designers added additional, smaller prizes for getting two symbols out of three for certain symbols. And as long as they paid out less in prizes than the odds of hitting those jackpots, then those slots are guaranteed to make a profit in the long run.
For example, if a prize for hitting three cherries was $1000, you'd be playing a break-even game, but if the prize were $750, it's easy to see how the casino would be guaranteed a profit. The difference between the odds of winning and the payout odds is where the casino makes its money.
How Slot Machines Work Now
Modern slot machines use a computer program called a random number generator to determine the outcomes of the various spins of the reels. This creates an imaginary reel with a number of symbols limited only by the program in question.
A mechanical slot machine with 256 symbols per reel would be huge, too large to play, much less to build. But a computer can create an imaginary reel with 256 symbols per reel and take up no more space than an iPod Shuffle.
To make things even more interesting and entertaining, slot machine designers can program different probabilities for each symbol to come up. Most symbols might come up once every 256 spins, but others might come up twice as often, while still others might only come up half as often.
This enables slot machine designers and casinos to offer slot machine games with far larger jackpots than they were able to when they were limited by mechanical reels. And they're able to offer these large jackpots and still generate a healthy profit.
How Does This Relate to Payback Percentages?
The payback percentage is the amount of money that the slot machine is designed to pay out over an enormous number of spins. This number is almost always less than 100%. The difference between 100% and the payback percentage is the house edge, and that's where the casino makes its profits.
A simple example can help illustrate how this works. Suppose you have a slot machine with three reels with ten symbols on each, and it only pays out when three cherries hit. The odds of winning that jackpot, as we determined earlier, is 1/1000.
If we set the jackpot as $900, and charge $1 per bet, the payout percentage for that game will be 90%, or $900/$1000. Of course, no one would play a slots game which only paid out once in every 1000 spins, which is why there are various smaller payouts programmed in.
There's no way to tell what the payback percentage on a particular game is unless you have access to the par sheet for that machine. Casino management has that information, but players never have access to that info.
The best slot machine odds are almost always found in real casinos. If you see slot machines in an airport or a bar, be aware that the payback percentages on those games is much lower than you'll see in a real casino.
How to Win at Slot Machines
Everyone would like to know how to win at slots, but the truth is that winning at slot machines isn't any harder than losing at slot machines. You put your money in the machine, spin the reels, and hope for the best. Slot machines are meant to be fun; they're not intended to provide the player with an income.
In fact, the reality is just the opposite. Slots are there to provide the casino owners with an income. How that works is one of the subjects of this page.
On the other hand, you can minimize your losses and increase your enjoyment of slots games by understanding how they work. You can also learn which slots pay back the most money. In the long run, the house will still have an edge over you, but understanding how much you can expect to lose in a given venue can help you make better bankroll management decisions.
In fact, it might be a good idea to modify you definition of 'winning at slots'. Instead of considering yourself a winner if you bring home a big profit, consider yourself a winner any time you played and had a lot of fun.
How Slots Work
All slot machines in modern casinos use a random number generator (an 'RNG) to determine the results of each spin. An RNG is a tiny computer that does nothing but constantly generate numbers. When you push the spin button, that microcomputer selects a number which determines the outcome. In fact, this happens before the reels have even stopped spinning.
On modern slot machines, the reels are just there for show. From a practical standpoint, you could put a quarter in a machine, push a button, and have the screen flash: 'You lose!' or 'You win $10'. The mechanism that determined the outcome would be the same, but who would want to play a game like that, especially if you know that the house has a mathematical edge over the player.
The spinning reels, the sound effects, and the bonus games are all there to make the game more interesting to play. If you don't like the artwork, the music, or any other aspect of a slots game, don't bother playing it, because those are the real rewards of playing. The chance of getting lucky and winning a jackpot is a real reward, too, but don't ignore the other aspects of the game.
Best Casinos in Riverside County, CA - Fantasy Springs Resort Casino (498 reviews), Agua Caliente Resort Casino Spa Rancho Mirage (901 reviews), Tortoise Rock Casino (50 reviews), Augustine Casino (138 reviews), Spotlight 29 Casino (145 reviews), Morongo Casino, Resort & Spa (1289 reviews), Red Earth Casino (64 reviews), Agua Caliente Casino - Cathedral City (7 reviews), Indio Bingo Palace. Oct 10, 2019 he new Cahuilla Casino Hotel is under construction in Anza, Riverside County, and slated for a Spring 2020 opening. It will replace its next door neighbor, the original Cahuilla Casino, which has operated out of a tent-like structure for 23 years. New casino in riverside county.
The random number generator is programmed to pay back a certain percentage of the money paid into it over a period of time. This period of time is known in gambling math as 'the long run', and it's a lot longer than most people think. We're talking about tens of thousands of spins, not dozens or hundreds.
This percentage that's programmed into these machines is always less than 100%. If a slots game were programmed to pay back more than 100% of the money put into it, it would lose money for the casino.
Casinos aren't in business to lose money.
The trick is to find slot machines that have the highest payout percentages.
Which Slots Pay Back the Most Money
If every slot machine game in the world had a payback percentage posted on the machine somewhere, it would be easy to determine which slots pay back the most money. You could limit your play to machines with a payback percentage of over 95% for example.
It's too bad casinos don't provide that information on specific games, though.
You can find information about specific locations and their payback percentages, though. Some gambling guides and magazines publish this information. For example, The American Casino Guide provides certified information about the payout percentages in various states. Not all states reveal this information, but it's not a huge leap of logic to expect better payback percentages in states that do reveal this information.
For example, the overall payback percentage for slots in Black Hawk, Colorado is 92.8%. In Central City, Colorado, it's 92.93%, and in Cripple Creek, it's 93.66%. Alabama doesn't release the numbers on their payback percentages.
Which casinos do you think offer the better game?
A couple of guidelines hold true no matter where you play, though. One of those is that payouts are better in large cities with lots of gambling. For example, the payouts in Vegas are higher overall than the payouts in Colorado. And the payouts improve when you play for higher stakes. For example, penny slots in Vegas average around 88% to 91%, but dollars slots average between 93% and 96%. Finally, slot machines at airports usually offer the lowest payouts.
What does that mean for the player? It means that over the long run, if you wager $x on a particular game, you'll win back $x times the payback percentage for that machine. If you're playing a dollar slot machine on the Strip in Las Vegas, for example, and the payout percentage is around 93%, then if you place $10,000 in wagers, you'll win back $9300. You lost $700.
That's only a long term mathematical expectation, though. In the short run, anything can happen, and that's what keeps people playing.
How to Maximize Your Winnings and Minimize Your Losses
There are three ways to maximize your winnings and minimize your losses. The first is to always join the slots club, and always use your member card while you play. Slots club members get a percentage of their play returned to them in the form of casino rewards and cash back. This is normally a tiny percentage (think 0.1% or 0.2%), but it adds up, especially if you play a lot.
Don't buy into the myth that playing with your slots club card lowers your expected return on the game, either. That's not true. The random number generator in these games has no way of knowing whether or not you're using your slots club card or not.
The second way to increase your winnings and minimize your losses is to use effective bankroll management techniques. This means limiting the amount of time that you play, limiting the amount of money that you're willing to lose in any session and in any given gambling trip, and finding other fun things to do with your time besides just playing the slots.
Finally, try to play the machines with the highest payout percentage. Over the long run, if you keep playing, you'll probably eventually wind up a loser at the slots (unless you hit a huge progressive jackpot), but you'll lose your money more slowly and get more entertainment value for the money you gambled.
You want to know how to calculate probability in gambling?
The first step is understanding what the word means.
The word probability has 2 meanings:
- The likelihood that something will or won't happen.
- The branch of mathematics that measures that likelihood.
If you're a casual gambler, you might have a vague idea that the probability of a win can be measured.
But until you understand the specifics of how to calculate probability, you can't be considered a sophisticated gambler.
This post explains how to calculate probability in gambling and why it matters to gamblers.
How to Calculate Probability as a Fraction
Whether something will happen can be measured on a scale from 0 to 1. If something can never happen, its probability is 0.
Here's an example of something with a 0 probability:
You have a standard 6-sided die. It's numbered from 1 to 6. The probability of rolling a 7 is 0. It's not possible.
Here's an example of something with a probability of 1:
You have a trick coin with 2 heads. When you flip the coin, the probability of it landing on heads is 1. (And the probability of it landing on tails is 0.)
Most events have a degree of uncertainty to them, though. You can measure how often you expect those events to happen as a fraction.
Here's an example:
You flip a normal coin with a heads side and a tails side. The probability of getting heads is 1/2.
The Magic Formula for Calculating a Probability
The formula for calculating that probability is simplicity itself:
You divide the number of ways you can achieve the desired event by the total number of possible events.
In the case of a coin toss, there's only one way to get heads. But there are 2 possible results.
1 divided by 2 is 1/2.
This probability can be expressed in any of the following ways:
- As a fraction.
- As a decimal.
- As a percentage.
- As odds.
Some of these are more useful than others in certain situations. I'll get into that a little more later in this post.
But for now, let's convert that 1/2 probability of getting heads into each of those 4 ways:
- As a fraction, the probability is represented as 1/2.
- As a decimal, the probability is represented as 0.5.
- As a percentage, the probability is represented as 50%.
- As odds, the probability is represented as 1 to 1.
Most of us are familiar with probability represented as a percentage. After all, most people watch the nightly news or at least look at the Internet for the weather report.
And they always express the probability of rain with a percentage.
If there's a 20% chance of thunderstorms, we know that there's a roughly 1 in 5 chance of rain, thunder, and lightning.
Bigger Probability Problems
Probability gets more interesting as you start calculating probabilities for multiple events.
Let's say you want to know the probability of getting heads twice in a row.
This is an example of an 'and' probability. You need to get heads on the first throw AND on the second throw to win this bet.
When calculating a probability for multiple events that use the word 'and', you multiply the probability of event 1 by the probability of event 2.
In this case, that can be represented as 1/2 X 1/2 = 1/4.
The probability of getting heads twice in a row is, therefore, 1/4, which can also be expressed as 25%.
Notice that the probability is lower. That's what happens when you multiply fractions.
Let's say you want to calculate an 'OR' probability instead. This time, let's use a 6-sided die as an example.
You want to know the probability of rolling a 6 on at least one of 2 rolls.
That's an example of an 'or' probability. You want to know how likely it is that you'll roll a 6 on the first roll OR on the second roll.
You have 6 possible results, but only 1 of them is the 6. So your probability of rolling a 6 on either roll is 1/6.
In an 'or' probability, you add the probabilities together. In this case, that would be represented as 1/6 + 1/6 = 2/6. Of course, most people would reduce 2/6 to 1/3, which is also often expressed as a percentage, 33.33%.
Expressing Probabilities as Odds
The tricky expression of this isn't as a fraction, a decimal, or a percentage. Most of us are familiar with these expressions. That's basic math.
But most of us don't have backgrounds in statistics, so we're not used to expressing probabilities in odds format.
Here's how to calculate probability in odds format.
When expressing a probability as odds, you just compare the number of ways something can't happen with the number of ways it can happen.
If you want to look at the odds of rolling a 6 on a single 6-sided die, you'd look at the number of ways you could possibly roll anything else versus the number of ways you can roll the 6.
In this case, you're looking at 5 to 1. You have 5 ways to roll anything but a 6, and only one way to roll a 6.
This becomes useful when you start looking at the expected profit or loss on a bet.
Bets always pay off at certain odds–how much you win versus how much you risk.
Many bets pay off at 1 to 1, or even odds. This is especially true of bets you make in a casual situation.
Here's an example:
You're shooting pool at your local bar, and you bet your buddy $20 on the next game. If you win, he gives you $20. If he wins, you give him $20.
But let's suppose that your levels of skill are different.
Let's suppose that he's better than you, and he stands to win 2 out of 3 times.
The odds of him winning are 2 to 1.
If the bet pays off at even odds, in the long run, he'll profit from playing pool against you under those terms.
He'll win, on average, $40 during 3 games. You'll win $20. His net win is $20.
Average that net win out over the 3 games, and he's winning $6.67 per game on average.
If this were a casino game, you could translate that into a percentage, and you'd have the house edge.
But I'm going to write another post about the house edge, soon. And I don't want to spoil it for you.
Instead, I'm going to leave you with one more example of how odds are used–this time in a game of poker.
In this example, we're going to assume that you have 4 cards to a flush, and you're reasonably sure you'll win the hand if you make the flush. You're playing Texas holdem, and you have 2 cards that are hearts in your hand, and there are 2 hearts on the flop.
You have 2 cards yet to come.
You might think that the probability of getting a heart on the next card is 1/4. After all, there are only 4 possible suits in a deck of cards.
But that doesn't take into account the cards that have already been dealt.
You have 2 cards, and there are 3 cards on the board. So there are only 47 cards left.
The deck has a total of 13 hearts in it, but you know that 4 of them are already gone, leaving 9 hearts.
The probability of being dealt a heart for your next card is 9/47.
If you don't get a card on the next hand, you get another chance, and this time, the probability is 9/46.
The easiest thing to do here is convert those into percentages first.
You have a 19% chance of getting a heart on the turn. You then have another 19% chance, more or less, of getting a heart on the river.
Add those together, and you get 38%. That's close to 38%, or around 3 to 1.
If it costs $100 to get into the pot, you stand to make a profit if the pot has more than $300 in it. If it has less than $300 in it, you stand to lose money over time.
Finally
These are just some rough probability examples. But this is the first step in becoming a savvy gambler–knowing how to calculate probability.
Being able to compare the odds of winning with the odds you're getting paid enables you to decide whether a bet is profitable.
Not long ago, I wrote about the skills you need to master video poker. Learning how to calculate probability in gambling is included as one of those skills.
Tomorrow I'll write more about the house edge in casino games.
