• Slot Machine Probability Of Winning The Lottery
• Slot Machine Probability Of Winning Lottery
• Probability Of Winning Calculator
• Probability Of Winning The Lottery

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.

Basically, when it comes to slot machines, strategy boils down to this: Know the rules, your probability of winning, and the expected payouts; dispel any myths; and quit while you’re ahead. If you win $100, cash out $50 and play with the rest, for example. After you lose a certain amount (determined by you in advance), don’t hesitate to quit. The slot idea started in 1891 when Sittman and Pitt in New York developed a gambling machine which is considered to be the first slot machine. Since 1891, the slots are the most using type of game in the gambling industry. When you know how do online slots work, the main question is ‘’How to calculate the probability of winning an online. Every other slot has a house edge lower than that. Some states allow the casino an edge of up to 25% – a ridiculous number that would make a slot the worst gamble in the casino by far. Slotgamers will be pleased to find out that many video poker machines carry a house edge of 98-99%. Video poker rewards player skill.

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

Slot Machine Probability Of Winning The Lottery

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:

Slot Machine Probability Of Winning Lottery

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

Probability Of Winning Calculator

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%

Probability Of Winning The Lottery

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%.