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What are the Odds of Winning at Slot Machines?

Slot Machine Odds - Slot Machine ProbabilitiesWhen someone talks about odds while gambling, they're talking about one of two things:

  • The odds of winning or losing.
  • The odds that a bet pays out.

The difference between the two is the house or player edge.

An Example

The odds of rolling a particular number on a normal six sided die are 1 in 6, or 5 to 1. Each number has an equal chance of coming up. There are six possible outcomes, but only one of them is the winning outcome. Odds are usually stated in the format of 5 to 1, which means there are 5 ways to lose and 1 way to win, and each of those has an equal chance.

Odds in this situation are just another way of stating a ratio, which can also be converted into a fraction (1/6) or a percentage (16.67%).

If I were a casino and offered a game where you could bet on any number coming up on a roll of a single die, and I paid the bet off at 6 to 1, I'd go out of business very quickly, because over the long term I'd be paying out more money than I'd be bringing in.

Every 6 rolls, assuming someone bet $1 per roll, the player would lose $5 and win $6. So the player would profit $1 on average for every 6 rolls. Over time, long-term. (In the short-term, anything can happen.) And the more rolls that are made, the close the actual results will reflect the statistical expectation.

On the other hand, if I offered this game and paid out 4 to 1 on that bet, I'd be running a profitable enterprise. (Assuming I could find players willing to play this game.) Every 6 rolls I'd see the player lose $5 and win $4, which would result in an average profit of $1 for every 6 die rolls.

Slot Machine Odds and Probability

Slot machine odds used to be determined by a series of mechanical devices. Each reel had a specific number of symbols on it, and the odds of hitting a given symbol would be one divided by the number of symbols. A typical arrangement would be to have 3 reels with 10 symbols on each. The odds of any particular symbol hitting on a single reel would be 9 to 1.

The odds of 2 of the same symbol hitting on a spin would be 1/10 X 1/10, or 1/100, which would be expressed as 99 to 1.

The odds of 3 of the same symbol hitting on a spin would be 1/10 X 1/10 X 1/10 = 1/1000, or 999 to 1.

The payouts on each of the bets are always set below the chances of winning the bet. The payout of each bet multiplied by the probability gives the payback percentage of each bet, and adding them all up results in the payout percentage for the machine. We cover that subject in more detail in our article about slot machine payouts. (See the link in our menu on the left.)

Video Slot Machine Odds

The modern slot machine doesn't work like an old time mechanical slot machine though. Physical, mechanical reels have been replace with video screens, and the mechanical stops which decided where the spinning reel ended up have been replaced with random number generators. This has dramatically chanced how slot machine odds and payouts work.

A physical reel can hold about 20 symbols before becoming too big to be practical in a slot machine. And a physical slot machine can't really accommodate more than 3 reels comfortably.

But a video slot machine has no such limitations. A video slot machine could theoretically have 100 symbols per reel, and a video slot machine could have 5 reels or more.

And to make things even more interesting, the random number generator can and is programmed to give certain symbols a different chance of coming up that is totally unrelated to the number of symbols. The slot machine might have one cherry out of ten symbols, but the RNG might be programmed to only have that cherry land once out of every twenty random spins.

The result is that less likely combinations can be programmed. And the less likely it is to hit those combinations, the more the casino can afford to pay out for them. Progressive jackpots of six and seven figures would have been impossible on any mechanical slot machine, but they're quite easy to program into a video slot machine's random number generator.

And the change in how the winners are determined makes these machines profitable in spite of the new bigger jackpots.

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