# Learn How To Calculate Online Slot Machine Probability, Odds And Payouts

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Finding out what is the best type of slots machine to play and how to improve your chances of winning at slots is everyone’s dream in online gambling.

The slots with the best odds are the games with the highest return to player (RTP). Although you can’t be sure you’ll win at these slots every time you play and you can’t tell when these slots are ready to hit, these are the ones that offer the best slot odds.

When you go online to play slots for real money or free, you need to know how to choose good slot games. Many beginners play casino games thinking that all slot machines are similar and that they only differ in graphics, features and bonus rounds. Obviously, this is a mistake.

If you want to know how to get better chances of winning at slots, you need a machine that pays more than the others. And to know which one is a great slot machine, you need to worry about the percentage of return to the player.

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 get a broader idea of how much money you can win back. Other tactics include using effective money management techniques, joining a slot club to take advantage of its rewards programs, etc.

## How Probability Works

Probability has two meanings. One is the probability that something will or will not happen. The other is the branch of mathematics that calculates that probability. To understand slot machine odds (or any other game of chance), you need to understand the basic math behind probability.

Don’t worry though. The math is not difficult. Probability involves addition, subtraction, multiplication and division, all of which you learned in college.

The first principle of probability is that every event has a probability between 0 and 1. If something has no chance of happening, then its probability is 0. If something will always happen, no matter what, then its probability is 1.

So probability is always a fraction. It can be expressed in many ways, as a decimal number, as a fraction, as a percentage, and as odds.

A simple example is a coin toss. The probability of getting heads when you flip a coin is 50%. This is common sense, but how is it determined mathematically?

You simply take the total number of possible outcomes and divide the outcome you are trying to determine the probability by that number. There are two possibilities when you flip a coin, heads or tails, but only one of them is heads. This is 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 will not happen versus the number of ways something will happen. For example, if you roll a single six-sided die and want to know the odds of rolling a six, you have odds of 5 to 1. There are five ways to roll anything other than a six, and only one way to roll a six.

When you want to determine the probability of more than one thing happening, you use addition or multiplication, depending on whether you want to determine whether one OR the other event will happen, or whether you want to determine whether one AND the other event will happen.

If you are looking at an “OR” question, you are adding up the probabilities. If you are looking at an “AND” question, you multiply the probabilities by each other.

So, if you want to know what the probability is of rolling two dice and one or the other rolls a six, you add up the probabilities. 1/6 + 1/6 = 2/6, which is rounded to 1/3.

If you want to know the probability of rolling two dice and BOTH roll a six, you multiply the probabilities. 1/6 X 1/6 = 1/36.

## Calculate Probability And Payouts

First of all, you need to start with the number of possible combinations. In the case of slot machines, this is relatively simple – just multiply the number of symbols on each reel. The oldest slot machines had, for example, 3 reels with ten different symbols on each. The total number of combinations that could appear on the board was 1,000 (10 x 10 x 10).

The number of combinations in today’s slot machines is a bit higher. If we assume five reels with 30 symbols each, we get a total of 243,000,000 combinations.

If you want to calculate your chances of winning on an online slot machine, all you need is this simple equation:

Number of winning combinations / Total number of combinations
To calculate the payout of the slot machine, modify the formula a little:

Σ (winning combination_k * possible payout_k) / (Total number of combinations)
Let’s analyze some basic slot machines. For the purpose of our article and to simplify the calculation, we will assume that the slot machine has only one payline and the bet is one coin per spin.

## Analysis Of The Simplest Slot Machine

Let’s go back in time and assume that the machine has only 3 reels and that there is an apple, orange, lemon, banana, melon and a wild symbol on each. The individual combinations produce these wins:

Three jokers win 30 coins
Three fruits win 10 coins
Two jokers win 4 coins
One joker wins 1 coin
The total number of combinations is 216 (6 x 6 x 6).
Total number of winning combinations:

In the first case there is only one winning combination (1 x 1 x 1 = 1)
In the second case we have 5 winning combinations (3 times apple or 3 times orange or 3 times lemon, …) (1 x 1 x 1) x 5 = 5
The joker can appear on two reels. The calculation is: 1 x 1 x 5 + 1 x 5 x 1 + 5 x 1 x 1 = 15
The joker can appear on any reel. 1 × 5 × 5 + 5 × 1 × 5 + 5 × 5 × 1 = 75
Our simplified model therefore contains 1 + 5 + 15 + 75 = 96 winning combinations. The table below shows the probability of a payout.

Calculation of payments according to the formula

Σ (winning combination_k * possible return_k) / (Total number of combinations)
(1 × 30 + 5 × 50 + 15 × 4 + 75 × 1)/(6 × 6 × 6) = 215/216 ≈ 0,99537
In this case, the slot machine has a 99.53% payout rate, which is very nice, but in a real casino you won’t find the same results. The average slot machine payouts at online casinos will be between 94% and 98%.

The chart also clearly shows how single coin wins affect payouts. If the payout for each combination was equal to one coin, the payout rate would drop to 44.4%. And that’s a very small number.

## Analysis Of A More Complicated Slot

Because the previous example was too far from reality, let’s show another example with higher numbers. For simplicity, let’s assume again that there is only one payline, the slot machine has 3 reels and a total of 6 symbols that can appear on the panel:

The total number of combinations is 23 x 23 x 23 = 12,167.

Winning combinations with single coin returns:

3x BAR, win 60 coins, number of combinations 1
3x SEVEN, win 40 coins, number of combinations 3 x 1 x 1 = 3
3x Cherry, win 20 coins, number of combinations 4 x 3 x 3 = 36
3x Other fruits, win 10 coins, number of combinations (5 x 6 x 6) x 3 = 540
Cherry on two rolls, win 4 coins, number of combinations 651
Cherry on one roll, win 1 coin, number of winning combinations 3880
Calculation for no. 5:

Cherry, Cherry, Other: 4 x 3 x (23 – 3) = 240
Cherry, Other, Cherry: 4 x (23 – 3) x 3 = 240
Other, Cherry, Cherry: (23 – 4) x 3 x 3 = 171
Calculation for no. 6:

First roll: 4 x 20 x 20 = 1,600
Second roll 19 x 3 x 20 = 1,120
Third roll 19 x 20 x 3 = 1,120
The following table shows the payout amount and the odds of winning for the individual combinations.
As you can see, the payout ratio is again very high at 99.721% (12,133 / 12,161). If the slot machine were to pay out a direct payout for each winning combination of 1 coin, the payout ratio would be reduced to 42,007%.

There are three ways to maximize your wins and minimize your losses in Hawkplay. The first is to always join the Slots Club and always use your membership card while playing. Slots Club members receive a percentage of their play that is returned to them in the form of casino rewards and cash back. It’s usually a small percentage (think 0.1% or 0.2%), but it adds up, especially if you play a lot in Hawkplay.

Also, don’t believe the myth that playing with your slot club card reduces your expected return on the game. It doesn’t. The random number generator in these games has no way of knowing whether or not you are using your slot club card.

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 you play, limiting the amount of money you are willing to lose in any given session and in any given game trip, and finding other fun things to do with your time besides just playing slots.

Finally, try to play the machines with the highest payout percentage. In the long run, if you keep playing, you’ll probably end up losing 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 play.

If you want a better chance of winning at slots, you should :

Choose slot machines that offer high payouts
Choose slots with the right level of volatility
Read slot machine reviews on casino sites, forums and Reddit
Play at a licensed online casino site
While this may not be enough for you to beat the slots and pick the winning slot every time you play, it will help you win more often and, more importantly, enjoy the slots much more in Hawkplay !

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