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Ask the Slot Expert: Computing a slot machine's long-term payback9 October 2013
A slot machine's long-term payback is calculated by taking the value of all the winning combinations and dividing by the total number of combinations possible. To use a very simple example, suppose a 3-reel machine has 10 stops on each reel and each reel has three cherry symbols on it. It costs one credit to play each spin and three cherries pay 30 credits.
There is a total of 1,000 possible outcomes (10x10x10). There are 27 ways to land three cherries on the payline (3x3x3) and three cherries pay 30 credits, so the total value of all the possible outcomes is 810 credits (27x30).
Dividing 810 (the value of our pool of outcomes) by 1,000 (the total number of outcomes in the pool) yields a long-term payback of 0.81, or 81 percent.
Notice that the calculation is based solely on the layout of the reels and the paytable. Time or the amount of money played through the machine do not enter into the calculations.
The long-term payback tells what percentage of the money played on a machine will be returned to its players in the long run. If we look at the performance of our machine when we remove it from the slot floor at the end of its life, it should have paid back an amount very close to 81 percent of the money played on it. Say 1,000,000 credits were played on the machine. The machine should have paid back about 810,000 credits to its players.
A casino can lose money on a slot machine, particularly when it is first put on the slot floor. I've been to a few casino opening nights and I've seen plenty of players hit jackpots in the first few hours the casino has been open. There's no way the machines could have gotten enough play to have won enough money to pay for the jackpots and not show a loss.
As a machine gets more and more play, however, its actual payback gets closer and closer to the its long-term payback. Streaks of good and bad luck that individual players experience are overwhelmed by the sheer volume of total play on the machine, like a few drops of food coloring are lost in the vastness of the ocean.
Given enough play, a machine is practically guaranteed to show a profit for the house, though there is a very (very, very, very,...) small chance that the players have bested the machine.
Jackpots for all,
Thanks for the kind words about my column. Slot machines really are pretty simple devices -- at least as far as computer systems go -- unlike, say, an air conditioner, which runs on magic as far as I'm concerned.
You're absolutely right. You cannot argue with John Grochowski. It's not unusual for a machine's long-term payback to be higher when you play max coins. Consider a Double Diamond machine that pays 800/1600/2500 coins for the jackpot. The jackpot is worth 800 coins for coins 1 and 2 and 900 coins for the third coin, a 100-coin bonus. This type of paytable is called a Bonus Multiplier. Because of the bonus on the third coin, the long-term payback will be slightly higher when you play max coin.
Let's go back to the machine in my prior answer and say three cherries pay 70 credits when you play two credits. We have to redo the calculations for playing two credits per spin.
To find the long-term payback when playing two credits, we once again look at the total amount of money that can be won from the pool of all possible outcomes. There are 27 ways to make three cherries and they now pay 70 credits, so the total value of the pool is now 1890. I have to admit that I fibbed a little in the first example. We don't actually divide by the total number of combinations possible, we divide by that total times the number of credits played (which in the first example was one, so I could get away with ignoring it). We divide 1890 by 2000 (1000x2) to get a long-term payback of 0.945 (94.5 percent) when playing two credits per spin.
We can bet one credit per spin on this machine and enjoy (?) a long-term payback of 81 percent, or bet two credits per spin and get a long-term payback of 94.5 percent.
Jackpots for all,
Send your slot and video poker questions to John Robison, Slot Expert™, at firstname.lastname@example.org. Because of the volume of mail I receive, I regret that I can't reply to every question.
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