Paybacks changing based on coins played on a slot machine

In a recent response to a reader you wrote, "Let's say you're going to play 100 spins and the one-coin payback is 92% and the two-coin payback is 95%." I was unaware that a single machine would have different payback tables merely based on the number of coins inserted. Is this true for a 'straight-multiplier' machine, or are you only commenting on machines that have extra bonus payouts added when you play extra coins?

In the same vein, what about multi-denomination machines? For example, you can change the machine to use 5-cent, 10-cent, 25-cent or 50-cent units. Is a new payback table loaded each time for each different denomination?

Gregg

Dear Gregg,

A straight multiplier machine has the same long-term payback no matter how many coins are played. Remember that we calculate long-term payback by taking the number of ways to make each winning combination, multiplying those numbers by how much each winning combination pays, and then dividing that product by the total number of (virtual) reel combinations and the number of coins played. On a straight multiplier, each winning combination pays exactly twice as much when you play two coins as when you play one coin. The product in the numerator of our long-term payback calculation when playing two coins is exactly twice that when playing one coin. The two (for the number of coins played) in the denominator cancels out the doubling in the numerator and we have the exact same long-term payback on Straight Multipliers no matter how many coins we play.

On a bonus multiplier, the bonus paid over and above the straight multiple on some winning combinations make the numerator in our long-term payback calculation for playing two coins more than twice that for playing one coin. The number of coins played component in the denominator is still only 2, so the long-term payback is greater when playing two coins than when playing one coin.

The situation I described, the long-term payback changing based on number of coins played, occurs on Bonus multipliers, but not on straight multipliers.

On multi-denom machines, it's certainly possible that higher denominations have higher long-term paybacks. We see that with video poker games on multi-denom machines.

Finally, I want to correct your terminology. Slots have virtual reel layouts (which tell how many times each symbol appears on each virtual reel) and paytables (which tell how much each winning combination pays based on the number of coins played). There's really nothing called a "payback table."

Best of luck in and out of the casinos,
John

Send your slot and video poker questions to John Robison, Slot Expert, at slotexpert@comcast.net. Because of the volume of mail I receive, I regret that I can't reply to every question.