Slot Machine Payback Percentages: The Devil is in the Moment

The average payback percentage from slot machines is important to gamblers, casinos and governments. While apparently simple to define several complications can exist, among them which measure to average and potentially misleading formulas to calculate the average. Daily slot machine data from the state of Maryland for 19 months are analyzed for the expected value of the average payback ratio per machine and per dollar gambled. On a per dollar gambled basis, the payback percentage meets legislative requirements that the gaming floor payback be at least 90 percent. On a per machine basis, that requirement is not met which can imply a significant shift of money from gamblers to casino operators and the state. Other payback measures are hypothesized to also be less than the per-dollar gambled measure but data are lacking.

The maximum rewards at the minimum price: Reinforcement rates and payback percentages in multi-line slot machines

Past research has shown that gamblers frequently use the mini-max strategy in multi-line slot machines, whereby the player places the minimum bet on the maximum number of lines. Through a detailed analysis and explanation of the design of multi-line slot machine games, we show that when using the mini-max strategy, the payback percentage remains unchanged, yet the reinforcement rate is significantly increased. This increase in reinforcement rate is mainly due to spins in which the amount won is less than the amount wagered, which we call losses disguised as wins. We have verified these conclusions by playing an actual slot machine game for 10,000 spins and recording the results. We believe that the high reinforcement rate that results from playing multiple lines on games of this type contributes to their potential addictiveness. We provide three theories for why players use the mini-max strategy and suggest further areas of research.

Slot machine structural characteristics: Distorted player views of payback percentages

This paper presents a sample three-reel three-coin slot machine game with a bonus for three coins, and a true payback percentage of 85.6% when one or two coins are wagered and 92.5% when three coins are wagered. The player sees the winning or losing combination of three symbols on the payline as well as (a) the physical reels as they scroll by and (b) what is just above and just below the payline at the end of play. An analysis of this game shows that observing the physical reels and what is just above and just below the payline indicates that the slot machine would lose money, and thus the player would make money, as the game would have a payback percentage in the range of 192%-486% if this reflected reality. The paper concludes by discussing the results of the analysis in terms of gaming regulations and problem gambling.