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

Finding what are the best type of slot machines to play and how to improve your chances to win at slots is the dream of everyone into online gambling.

The slots with the best odds are the games with the highest Return to Player (RTP). While you can't be sure to win at these slots every time you play and you can't tell when these slot machines are ready to hit, these are the ones with the best slot machine odds. When you go online to play slots for real money or for free, you need to know how to pick good slot machine games. A lot of beginners play casino games thinking that all slots are similar and they only differ in graphics, features, and bonus rounds. Obviously, that's a mistake.

If you want to know how to get better chances to win at slots, you need a machine that pays out more than the other ones. And to know which one is an excellent slot to play, you need to care about the Return to Player percentage.

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.

## 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.

Don’t worry though. The math isn’t hard. Probability involves addition, subtraction, multiplication, and division, all of which you learned in middle school.

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.

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.

## Calculate Probability And Payouts

First of all, we must start with the number of possible combinations. In the case of slots, it is relatively simple - just multiply the numbers of symbols on each reel. The oldest slots had, for example, 3 reels with ten different symbols on each. The total number of combinations that could appear on the panel was 1,000 (10 x 10 x 10).

The number of combinations in today's slots is somewhat higher. If we assume five reels with 30 symbols on each, we get a total of 243,000,000 combinations.

If you want to calculate your chances to win 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 yield_k) / (Total number of combinations)

Let's analyze a few basic slot machines. For the purposes of our article and in order to simplify the calculation, we will assume that the slot machine has only one payout line and the bet is one coin per round. ### Analysis Of The Simplest Slot Machine

Let's go back to the past and assume that the machine only has 3 reels and there is an apple, an orange, a lemon, a banana, a melon and a joker symbol on each. The individual combinations produce these winnings:

• Three jokers win 30 coins
• Any 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 may appear on any two reels. The calculation is as follows: 1 x 1 x 5 + 1 x 5 x 1 + 5 x 1 x 1 = 15
• The joker may appear on any reel. 1 × 5 × 5 + 5 × 1 × 5 + 5 × 5 × 1 = 75
• Our simplified model thus contains 1 + 5 + 15 + 75 = 96 winning combinations. The table below shows the probability of a payout.
Winning combinationNumber of combinationsWinningReturns for 1 coinChance to win
3 jokers 1 30 30 13.953%
Any fruit 5 10 50 23.256%
2 jokers 15 4 60 27.907%
1 joker 75 1 75 34.884%
Total 96   215
% for the winning combination 44.444% Payouts 99.537%

Calculation of payouts according to the formula

• Σ (winning combination_k * possible yield_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 payout ratio of 99.53%, which is very nice, but in a real casino, you will not find the same results. The average returns of slots online casinos will be between 94% and 98%.

The table also clearly shows how single coin wins affect payouts. If the win of each combination were equal to one coin, the winning ratio would drop to 44.4%. And that's a very small number.

### Analysis Of A More Complicated Slot

Because the previous example was too distant from reality, let's show you another example with higher numbers. To simplify, 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:

SymbolReel 1Reel 2Reel 3
BAR 1 1 1
SEVEN 3 1 1
Cherry 4 3 3
Orange 5 6 6
Banana 5 6 6
Lemon 5 6 6
Total 23 23 23

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 fruit, win 10 coins, number of combinations (5 x 6 x 6) x 3 = 540
• Cherry on two reels, win 4 coins, number of combinations 651
• Cherry on one reel, win 1 coin, number of winning combinations 3,880

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 reel: 4 x 20 x 20 = 1,600
• Second reel 19 x 3 x 20 = 1,120
• Third reel 19 x 20 x 3 = 1,120

The following table shows the amount of payout and the chance of winning for the individual combinations.

Winning combinationNumber of combinationsWinningReturns for 1 coinChance to win
3x BAR 1 60 60 0.495%
3x SEVEN 3 40 120 0.989%
3x Cherry 36 20 720 5.934%
3x Other fruit 540 10 5,400 44.507%
2x Cherry 651 3 1,935 16.097%
1x Cherry 3,880 1 3,880 31.979%
Total 5,111   12,133
% of winning combinations 42.007% Payout 99.721%

As you can see, the payout ratio is very high again at 99.721% (12,133 / 12,161). If the slot were to pay a straight win for each winning combination in the amount of 1 coin, the payout ratio would be down to 42,007%.

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.

If you want better odds to win on slots, you need to:

• Choose the slots that have high payouts
• Choose the slots with the correct volatility level