The theoretical odds are built into the design and program of the machine, and it is possible to calculate the exact payout percentage for any machine over the long-term. Except for the video slots, slot machines have wheels called reels with symbols printed on each wheel.

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.

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:

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 Odds Of Winning

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.

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%.

Many people will be visiting a casino this summer, whether on a trip to Vegas, on a cruise ship, or just at a local casino during a 'staycation.'

But before you go, you may want to know which games give you the best chance of winning.

So we went behind the scene at two casinos, and spoke with the game managers, to find out which games give you an edge.

Table Games Your Best Bet

Jay Bean, a Caesar's floor manager, agreed to sit down with us and talk about the games with the best odds.

He said many people don't realize that table games have much better odds than slots. They are intimidated by thoughts of card sharks taking their money, with images of an intense Texas Hold 'Em tournament in their minds, and so they stick with the safe games: the slots.

But they are doing themselves a disservice, he said.

Bean's advice? After you've spent some time on the slot machines, move on to the Blackjack table, and start by just observing.

1. Blackjack

Blackjack has the best odds of winning, with a house edge of just 1 percent in most casinos, Bean said.

Plus, you are playing against only the dealer, not hooded poker champions.

'Blackjack is one of our easiest games to play,' Bean said. 'You're just looking for a number that beats the dealer's number without going over 21.'

If you're a novice, Bean said to sit down during a less busy time, such as the afternoon, and the dealer will walk you through the game.

But the same is not true with poker: You should practice the game with your friends first, at home, Bean said, until you are comfortable with it. Bean said novices are best off passing on the poker tables, where yes, the competition can be tough.

You can find out more information about the game of blackjack at the following link:
http://wizardofodds.com/games/blackjack/

2. Craps

So from the Blackjack table, he suggests moving on to the dice game Craps, the game with the second best odds, also nearly 50-50.

The Craps table can be a bit intimidating for the beginner with all the boxes on the table, Bean admitted. But it's really not tough, and it has one of your best chances of winning. In the end, all you are really doing is betting on a dice roll.

For more information on craps, visit:
http://wizardofodds.com/games/craps/

3. Roulette

On A Certain Slot Machine The Probability Of Winning

Bean said your next stop should be the Roulette wheel. It's simple, and pays fairly well.

Slot Machine Probability Of Winning California Lottery

'So you bet on your favorite numbers,' Bean said. 'The dealer spins, and if your number comes in you win.'

If you stick to betting on just Reds or Blacks, you have nearly a 50-50 chance of walking away a winner. If it lands on red when you choose red, you will double your bet, Bean explained.

While it may seem you have an even chance of winning by simply choosing a color, there is one catch that gives the house its edge: the extra green 0 and 00 position on the wheel. It's on all American roulette wheels.

Or, if you feel lucky, play just one number. It's hard to win, but if you do it pays out 36 to 1.

For more information on roulette, visit:
http://wizardofodds.com/games/roulette/

Worst Odds

Your worst odds? The casinos, understandably, did not want to talk about games with poor odds.

So we turned to Forbes Magazine, which in a report about Best Bets at the Casino, said two popular games -- the Wheel of Fortune and the ever-popular slot machines -- have the lowest odds of winning, with a house edge of 10 percent or more.

The Experts Agree

Professor of Analytics Michael Magazine has crunched the numbers, and agreed that blackjack is the best way to go home with money in your pockets. He said if you take a little time to learn the game, you have the best odds of winning.

'You are somewhere between 44 percent to 48 percent in every single hand of winning,' he said, noting that no other casino game gives you odds that good.

But Magazine cautioned that he's not promoting gambling, because he said even games with the best odds still favor the house.

'Play it long enough and you will lose. In the long term the house doesn't lose,' Magazine said.

If You Love The Slots....

Finally, if you really enjoy playing the slots, here is some good information to know, from state casino reports we examined.

With slots, the more money you put in per bet, the higher your chance of winning. If you put the max in a penny machine, which is usually around 50 cents, you have much better odds than if you put in 2 cents.

In addition, penny slots have the lowest odds, with $1 and $5 slots paying much better.

Always gamble responsibly, and don't waste your money.
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Probability Of Winning Slot Machine Jackpot

You can learn more about specific odds of slots machines in each state that has casino gambling by visiting the American Casino Guide.

Probability Of A Winning Slot Machine

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Slot Machine Probability Of Winning Prizes

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