Calculating odds and probabilities for classic slot machine games with 3 reels with 10 symbols on each reel is simplicity itself. You simply multiply the chances of hitting the correct symbol on each real times the chances of hitting it on the other 2 reels. The formula looks like this in fact:
1/10 X 1/10 X 1/10 = 1/1000
A brief explanation: if there are 10 possible symbols on each reel, then the chances of hitting 1 of those 10 is 1/10. The chances of hitting that same symbol on all 3 reels is the product of the chance of hitting it on each reel.
A casino makes its money by having payouts that aren’t equivalent to the true odds of hitting the jackpot. In a case where you have a 1 in 1000 chance of hitting a jackpot, if you paid out 999 to 1 or 998 to 1, the difference in the payout versus the actual odds would be your resulting profit.
But progressive jackpots are sometimes tremendous. Sometimes you can even find progressive jackpots of $1 million or more. In order to accomplish this, slot machine manufacturers had to become programmers, because realistically, a mechanical slot machine was limited to 3 or 4 reels with 20 or so symbols on each...
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