It is easy to calculate odds and probabilities in classic slot machines with three reels and 10 symbols per reel. Simply multiply the chance of hitting the correct symbol on each reel by the chance of hitting it on the next 2 reels. This is how the formula works in practice:
1/10 X1/10 X1/10 = 1/10
Let me explain: If there are 10 symbols on each reel, the chance of hitting one of them is 1/10. So you have a chance of hitting the same symbol on all three reels.
Casinos make their money by paying out payouts that aren’t equal to the real odds of hitting the jackpot. For example, if you have a 1:1000 chance of winning a jackpot, your profit would be the difference between the actual odds and the payout.
Progressive jackpots can be huge. You can sometimes find progressive jackpots worth $1 million and more. Because a mechanical slot machine had only three or four reels and 20 symbols per reel, it was impossible to create a program that could do this. The reels of a mechanical slot machine are actually made of metal and have more than 20 symbols per reel. This makes it impossible to operate the machine.
Casinos can create “virtual reels” with unlimited numbers of symbols by using a random number generator program. You can even set up multiple reels. The odds of winning the jackpot decrease, so the payout can be larger.
Here are the odds of hitting the Jackpot on a 3-reel machine with 30 symbols and a 5-reel machine with 30 symbols.
1/30 X 1/30 + 1/30 = 1/27,000
1/30 X 1/30 1/20 1/30 1/30 1/30 1/30 1/30 1/30 1/30 1/30 1/30 1/30 1/30 1/30 1/30 1/30 1/30 = 1/810,000
You could win a jackpot of $500,000, $600,000. And still have a profitable slot game.
If the jackpot is large enough, progressive jackpots will grow continuously until the winner hits it. Therefore, if the jackpot were high enough, you could theoretically place a positive expectation wager on a slot machine game. For example, if the jackpot were $810,001, you would be placing a positive expectation wager.
Problem is the manufacturers of slot machines don’t make it easy. The random number generator software uses algorithms that create a % payout. As a result, a player can’t know the dollar amount of the jackpot to make a positive expectation bet.