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How to Use Probability to Win at Slots

After a casino hired him to cut their slots' payout (and cheat on their players), Russia's Alex realized he could make a ton more by working solo. But now, after he hacked slot machines from all the top casinos in the world, he wants back.

Think of slots like flipping a coin. If a coin is flipped 10 times, and for the first nine times you get heads, what will be the tenth flip?


Slot machines are casino games with no real winning strategy...

Or so they say:
Unlike other gambling games such as blackjack or even video poker, in which proper application of skills can increase the chances of winning, slot machines are a negative equity game or –EV game.

That means the probability to win at slots in the long term is not great, but that does not eliminate the possibility of earning big in the short term thanks to something known as a Random Number Generator.

Slot Machines and Random Number Generators(RNGs)

Each time the lever is pulled, a button is pushed, and the reels are set in motion, a random combination of symbols is selected by the game. The random selection feature ensures that every spin is independent, thus the results of the previous spins do not affect the next ones in any way.

How to Win at Slots. Or, The Probability of Winning on a Slot Machine

The probability of winning a payoff on any slot machine is determined by thenumber of reels and the number of symbols on each reel and whether the randomly generated pattern will get you a winning combination of symbols.

While it may seem like an impossible task, there are tricks to making your spins work in your favor. Below you will find the ultimate guide on how to use probability to win at slots.

How to Win at Slots. Or, The Probability of Winning on a Slot Machine

The number of possible combinations on any slot machine is easy to calculate. You need to multiply the total number of symbols (stops) each slot (reel) has.

For example, in a three-reel machine with six symbols a piece, the total number of possible combinations is 6 x 6 x 6 = 216 combinations. Similarly, in a three-reel machine with 20 symbols each slot, the total number of combinations would be 20 x 20 x 20 = 8,000.

Calculating the odds of winning on a slot machine is simple: you need to divide the number of winning combinations by the number of possible combinations. That is:

SLOT FORMULA: Number of winning combinations / Number of possible combinations

Different winning combinations have different playoffs. The harder the combinations, the higher the reward.

Analyzing a Pair of Slot Machines to Understand How to Win at Slots

(For the purpose of this guide, we will assume that every slot machine has a single line and only accepts one coin per roll.)

The first machine has three reels. On each reel, there is a banana, a lemon, an orange, an apple, a melon and a joker. The payouts are as follows:

  • OPTION 1: Three jokers - 30 Coins
  • OPTION 2: Any 2 of a Kind Fruit - 10 Coins
  • OPTION 3: Any Pair of Jokers - 4 Coins
  • OPTION 4: Any Single Joker - 1 Coin

The number of possible combinations is: 6 × 6 × 6 = 216

So, How Easy is it to Win at Slots in Each Case?

Depending of which of the previously mentioned four outcomes you're aiming for, there are different probabilities to collecting some cash, which we will explain below.

Option 1: 30 Coins aka. The Big Win

You have only one chance to bring home the machine’s biggest win. It’s hard but don't forget that - at least if you know how to pick a winning slot machine - a 'big win' can be worth millions.

Analyzing a Pair of Slot Machines to Understand How to Win at Slots

Option 2: 10 Coins

Three-of-a-kind that doesn't include a joker. On one of the first reel, you can get any the five fruits (banana, lemon, orange, apple, melon). Once a fruit is chosen, this has to appear also on the paylines in the next two reels. If you do the math, you can see that there can only be 5 of such combinations: three bananas, three lemons, three oranges, three apples and three lemons.

Analyzing a Pair of Slot Machines to Understand How to Win at Slots

Option 3: 4 Coins

The jokers can appear on any two reels: Reels 1 and 2, Reels 1 and 3, and reel 2 and 3. To get this winning combination, the reel that doesn't feature a joker symbol must contain a fruit. Hence, the total winning combinations possible is 1 × 1 × 5 + 1 × 5 × 1 + 5 × 1 × 1 = 15.

Analyzing a Pair of Slot Machines to Understand How to Win at Slots

Option 4: 1 Coin

The jokers can appear on any of the reels of the slot machine. What is important, however, is that the other two reels have a fruit on them. This winning combination is more common as the right calculations suggest there are 75 different scenarios that can lead to it (1 × 5 × 5 + 5 × 1 × 5 + 5 × 5 × 1 = 75).

Analyzing a Pair of Slot Machines to Understand How to Win at Slots

All in all, the slot machine we used for this quick example features 96 different winning combinations: (1 + 5 + 15 + 75 = 96).

Let us calculate the total slot’s payout using the table below.

Winning CombinationsNo. of CombWinPayoff for 1CoinPercentage payoff
Three Jokers1303013.96
Any Three Similar Fruits5105023.27
Any Two Jokers1546027.91
Any One Joker7517534.89

Payout percentage = (1 × 30 + 5 × 50 + 15 × 4 + 75 × 1) ÷ 216 —> 215/216 = 0.9954 or 99.54 %

A payoff of 99.54% is quite good for a slot game. However, it can be a little misleading given that harder combinations are given more weight. If everything were paid equally, about 44.44% or 96/216 combinations would win.

Analyzing a Complex Slot Machinemto Figure Out How to Win at Slots

Note: Also in this example, we will use one line, three reels

The distribution of symbols on each reel is as follows:

SymbolsReel 1Reel 2Reel 3
BAR111
SEVEN311
Cherry433
Banana566
Lemon566
Orange566
Totals232323
Each reel has a total of 23 symbols. Hence, the total number of possible combinations is: 23 × 23 × 23 = 12,167.

Note that there is a non-equitable distribution of symbols on each reel. With the lack of Sevens (7s) Cherries and BARs, it is clear that the probability of getting winning combinations involving these three symbols will offer high payoffs.

The payouts and winning combinations are as follows:

  • 3 BARs wins 60 coins. Number of winning combinations: 1
  • 3 Sevens win 40 coins. Number of winning combinations: 3 (3 × 1 × 1 = 3)
  • 3 Cherries win 20 coins: Number of winning combinations: 36 (4 × 3 × 3 = 36)
  • 2 Cherries Wins 4 coins: Can be anywhere on the reels
  • TOTAL for Fruits: 540, For Oranges 5 × 6 × 6 = 180, Bananas 5 × 6 × 6 = 180 and Lemons 5 × 6 × 6 = 180.
Analyzing a Complex Slot Machinemto Figure Out How to Win at Slots

Total number of winning combinations:

  • Cherry, cherry, other: 4 × 3 × (23-3) = 240
  • Other, cherry, cherry: (23-4) × 3 × 3 = 171
  • Cherry, other, cherry: 4 × (23-3) × 3 = 240
  • TOTAL COMBOS: 651

Cherry in any one reel, wins 1 coin. Meaning:

  • First Reel: 4 × 20 × 20 = 1600
  • Second Reel: 19 × 3 × 20 = 1120
  • Third Reel: 19 × 20 × 3 = 1120
  • Total: 3,880 combinations.

The table blow shows how the machine’s payout percentage is calculated:

*Winning CombinationsNo. of CombWinPayout per coinPercent of Payout
Three BARs160600.50%
Three Sevens3401200.10%
Three Cherries36207205.93%
Three of any other symbols540105,40044.51%
Any Two cherries65131,95316.10%
Any One cherry3,88013,88031.96%
TOTAL Payout percentage: 99.77%

The payout percentage for this slot machine is 99.77%. If everything was paid equally at 1 coin, it would go down to just over 42%. For more complex reel machines (more reels and multiple lines), the use of a spreadsheet or a computer program will help in calculating the payoff as the number of calculations will grow with complexity.

Slot Machines Have the Highest House Edge

If you are planning to play on slot machines with the odds of winning set at 95 %, you will be led to thinking that you can win 95 percent of the times you play at the machine.

However, the fact is that 5 percent of every dollar you bet will go to the house of odds. The house edge is higher for slots than any other casino game.

The returns are worked out only after playing on longer period. You may win big in a single betting cycle and also lose big in another. It is all about getting a profitable average.

Determining the House Edge Is Crucial to Know How to Win at Slots

Determining the House Edge Is Crucial to Know How to Win at Slots

It is often impossible to determine the exact house advantage of any given reel machine. Instead, players depend on information provide publicly, such as regulated pay off ranges in most states.

In some states, the Gaming Board states that most slots must have a 73% return to the player. Generally, small slot machines are close to this threshold than larger slot machine. For this reason, it is advisable to skip the skip the penny and nickel slots if your bankrolls allows.

Think of slots like flipping a coin. If a coin is flipped 10 times, and for the first nine times it lands on head, what will be the tenth flip? The chances are still 50/50 regardless of the previous results. Slots are exactly the same in that sense.

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