Aug 2, 2017

Probability of Slots and Slot Machine odds Calculator

author Peter S.

In today's little math exercise, we'll show you how to count probability in slot machines. Morever, you can fing here a slot machine calculator. Find out the return and payout with our slots calculator. Enter your bet size, return to player, slot volatility and pace of play into the calculator to get an estimate of how much you could win or lose.

Slot Machine Calculator

Find out the return and payout with our slots calculator. Enter your bet size, return to player, slot volatility and pace of play into the calculator to get an estimate of how much you could win or lose.






What is a Slot Machine Calculator?

The Slot Machine Calculator is a unique web-based application that allows you to calculate your estimated profit or loss on online slots. Our calculator even works by calculating your estimated results for other casino games such as roulette, blackjack or video poker. All you need to know is the so-called return value for the player. 

❓ How to find out the payback for slots

While for games like roulette or blackjack, the RTP is very easy to find out. You simply Google house edge and subtract the house edge from 100. For online slots, the RTP varies for each game. The good news is that for most games this number is very easy to track. Just click directly on the slot information in the game and do a little searching. If you can't find it, you can also try googling RTP under a keyword such as "Starburst RTP"

And what does the calculator tell you? Once you enter all the parameters, the online slot calculator will give you an estimate of your average win or loss and other information. We would like to remind you that since slots are a game of chance and the results are determined by a random number generator, the outcomes of real games and gaming sessions may differ from the calculator's result.

Online Slot Machine Calculator Tutorial

For the slots calculator to interpret the game returns as accurately as possible, you must fill in the appropriate fields. All you have to do is click on the Calculate button.

Slots Calculator input explanation

  • Bet per spin - The total bet per game round. Always enter the resulting bet. For example, if you are playing a slot machine where you bet 3 coins per payline and the machine has 3 pay lines, the Bet per Spin will be 9 coins.
  • Play Pace - Calculate how many game rounds you pay per minute. If you don't know, try the free slots and simply stop the minute.
  • Return to Player - The return to player is given by the manufacturer for each slot machine.
  • Volatility - In other words, the riskiness of playing. It shows us the frequency and size of wins. Generally, the more frequent the wins, the smaller they are. Such slots are more volatile. And vice versa. A good guide is that the more pay lines a slot machine has, the higher its volatility.
  • Bankroll - The total amount of money you have for a given gaming session.

Once you've selected all these parameters, just click the button. We will then show you a table with the following calculations. All the math in the free online slots calculator is based on averages and long periods. 

Explanation of the results table

  • A number of spins - the number of games you play.
  • Play Time - the amount of time you spend on the slot machine.
  • Average win/loss - the average slot return 
  • Terrible visit - This is the worst of the worst options. In this case, you're having a really bad day
  • Half the time - 50% of the time you will end up somewhere in this range.
  • Great visit - What it might look like if you had a really good day and did well.
  • Chance of Being Ahead at all - The chances that your gaming session will be a winning one. If "nil" appears in the table, it means that the chance of a winning session is less than 1 in 1,000,000

You can use the calculator for free and several times in a row. Just re-enter or change the calculator parameters and have it recalculate.

Probability of Slot Machines

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:

  1. Three jokers win 30 coins
  2. Any three fruits win 10 coins
  3. Two jokers win 4 coins
  4. One joker wins 1 coin

The total number of combinations is 216 (6 x 6 x 6).

Total number of winning combinations:

  1. In the first case there is only one winning combination (1 x 1 x 1 = 1)
  2. 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
  3. 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
  4. 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 combination Number of combinations Winning Returns for 1 coin Chance 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:

Symbol Reel 1 Reel 2 Reel 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:

  1. 3x BAR, win 60 coins, number of combinations 1
  2. 3x SEVEN, win 40 coins, number of combinations 3 x 1 x 1 = 3
  3. 3x Cherry, win 20 coins, number of combinations 4 x 3 x 3 = 36
  4. 3x Other fruit, win 10 coins, number of combinations (5 x 6 x 6) x 3 = 540
  5. Cherry on two reels, win 4 coins, number of combinations 651
  6. 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 combination Number of combinations Winning Returns for 1 coin Chance 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%.

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