Casino Roulette Strategies

Slot machines odds of winning

What are the odds of winning on the slot machines?  June 20, 2016 – 11:37 am
Slot machines odds of winning

I took a look at the implementation of the slot machine and calculated some probabilities based off of that. Although some slot machines have different symbols on the reels, they all work the same way, and none of them have better odds than others. I will use the "default" names, which are used as names in the code and for the symbols on the slot machine in Lefty's.

When the slot machine generates a row, it picks 3 random integers between 0 and 12 (inclusive). That means there are 13 different values for each wheel, which is then mapped onto the different symbols to give each symbol a different probability of showing up.

For the first wheel, the probability for each symbol is:

  • 5/13 Cherry
  • 4/13 Bell
  • 3/13 Seven
  • 1/13 Bar

When a Cherry, Bell or Seven shows up, it reduces the probability of that symbol by 1/13 for every subsequent wheel and increases the probability of a Bar symbol by 1/13. In other words, if both the first and the second wheel show cherries, there is a 4/13 probability that the third wheel will be a bell, and a 3/13 probability for each of the other symbols.

With that information, we can enumerate all of the possible outcomes to determine the probabilities of winning. The probability of each payout multiplier is (rounded to 3 decimals):

  • 0: 50.842% (1117 in 2197)
  • 1: 26.627% (585 in 2197)
  • 2: 15.112% (332 in 2197, 200 of which are 2 Cherries)
  • 3: 3.277% (72 in 2197)
  • 4: 3.823% (84 in 2197, 60 of which are 3 Cherries)
  • 5: 0.273% (6 in 2197)
  • 7: 0.046% (1 in 2197)

Over time, you can expect to get 1838 dollars back for every 2197 dollars you spend. This corresponds to a payout percentage of about 83.66%.

In the Steam version, one achievement requires you to hit the jackpot, meaning 3 Bar symbols. As stated previously, the probability for that is 1 in 2197. From this, we get that the probability of winning this achievement within N spins is (1-(2196/2197)^N). We can also determine the expected number of spins for a specific probability P, by solving (2196/2197)^N=(1-P) for N.

The approximate number of spins required for various probabilities of winning this achievement is:

  • 1%: 22
  • 10%: 232
  • 25%: 632
  • 50%: 1523
  • 75%: 3045
  • 90%: 5058
  • 99%: 10115


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What slot machine has best odds of winning ?
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  • avatar What are the odds of winning on a slot machine?
    • It's impossible to tell the odds of winning at a slot machine. It depends on how many winning combos that particular machine has.

  • avatar Which slot machine has the best odds of winning?
    • Research indicates that $5 or higher slot machines have the highest range of percentage payouts. The payouts then decline as the machines become less expensive - from $1 machines followed by 50-cent machines, 25-cent machines, and 5-cent machines.

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