Casino Enterprise Management

There are many components in the formula for player satisfaction. Manufacturers attempt to create a secret sauce that will result in a perfect mix of casino revenue, player payback, entertainment value and excitement. Operators try to select games that will match their desired hold, create an exciting casino floor to draw new players and retain current patrons, and operate in a reasonably stable environment where the volatility of the machines does not create a negative hold for too long.

Of course, there is no secret formula that applies to slot machines. Games that perform well above projection in one area may be seriously underperforming in another. A popular theme in one casino may not fit well into the atmosphere of another. Your patron mix and demographics are constantly changing like the weather. Should you find a mix that works—and works well—the dynamics of your patrons and the outside world will always cause it to move and change. It can be as simple as the lighting in your casino, burnt out bulbs in your machines, the friendliness of your floor staff or myriad other factors out of your control and unknown to you.

There are, however, many attributes that can help you move closer to this elusive perfect mix, and these can have a tremendous effect on your bottom line, both positively and negatively. Player payout itself does not create satisfaction, and a bank of machines paying a 99 percent return to the player can sit idle while another bank returning only 87 percent can have lines of patrons waiting for an empty seat. Of all the mathematical parameters that you find on a PAR sheet, one of the most important is hit frequency.

Hit Frequency
Hit frequency is relatively easy to calculate and is typically shown on both PAR sheets and marketing brochures. It is the number of winning games (those games that return some payment to the player) divided by the cycle (the total number of possible game outcomes available). The value is expressed as a percentage of winning games compared to all possible game outcomes. A hit frequency of 25 percent, for example, means that the player will win, on average, one out of every four games played.

Hit frequency varies based on the type of game. A multiplier—where every possible payout is available for all wagers—will have a constant hit frequency throughout the entire range of credits played. A three-credit Double Diamond stepper game, for example, will have an identical hit frequency no matter how many credits are wagered. A buy-a-pay game, however, will have varying hit frequencies. This is due to increasing credit wagers purchasing extra winning combinations. Normally, a single credit wager will offer the lowest hit frequency. Additional coins that purchase additional “payouts” will increase the hit frequency. A Blazing 7s game, for example, will have the lowest hit frequency for a single credit wager purchasing Bar symbol pays. The top wager, which purchases “7” symbol pays, will have a higher hit frequency.

Line games are generally stated showing the hit frequency per line wagered. These are typically multiplier games, where additional credits wagered purchase additional line combinations. The PAR sheets will usually report a hit frequency value for a single line and also for all lines played. In most cases, the game hit frequency cannot be determined by multiplying the single-line hit frequency by the number of lines played. As more lines are played, symbol locations overlap, resulting in multiple lines paying at once. In this case, the hit frequency will be somewhat less than the single-line hit frequency multiplied by the maximum lines available. Hit frequency refers to winning games, not the quantity of winning combinations. Figure 1 illustrates this point. This changes the math, making the total hit frequency more complicated to determine. However, the overall game hit frequency will tell you this value.

Suppose we have a 20-line video slot where the player can wager up to 10 credits per line. The PAR sheet shows us that the single-line hit frequency is 5.5 percent. This means that the player, wagering only on line 1 will win 5.5 percent of the time. Of course, this is an average based on the total number of combinations on the machine. The actual win may be more or less, but on average, this is the amount.

If the player bought all 20 lines, a simple multiplication would not calculate the hit frequency: 5.5 percent x 20 lines = 110 percent, and you can’t win more than 100 percent of the time.

As many combinations overlap, many winning combinations are awarded together. This brings the total hit frequency down, but “maintains” the total number of winning possibilities. In our fictitious machine, the overall game hit frequency is 87 percent. This means that the player will win something almost nine times out of 10, assuming he or she always purchases 20 “paylines.” This must be a good thing, since the more the players win, the happier they are.

Or are they?

Conventional Wisdom
Conventional wisdom would dictate two truths:

1. Playing more lines will result in the player winning more frequently—a higher hit frequency; and
2. The higher the hit frequency, the better it is for the players—the players wins more frequently, therefore they must be more satisfied with this game.

The first of these truths generally is, in fact, true. When a player wagers on only nine of the 20 lines, there will be many times when winning combinations appear on the other 11 lines and the player therefore misses out on these awards. When more lines are purchased, more paying combinations are possible.

The second truth, however, is not always true. In fact, player satisfaction can significantly decrease when hit frequency sharply increases. By trying to give your players more, you may be driving them out the door.

Our Old Friend Volatility
Many video slot games feature high volatility. These games have been on your casino floor for years, and players like the ability to win large amounts of money. High volatility means that the payouts will vary considerably, from no payouts or little payouts to extremely large payouts, perhaps in the millions of dollars. Generally speaking, the player may win lots or win nothing. There are a number of possibilities between these extremes, but players can expect to have the game play differently every time they sit down. Low volatility games, on the other hand, see a narrow range of paying combinations. The top jackpot isn’t going to pay millions, but players are less likely to sit for a long time and win nothing. Bonus rounds may not pay up to 250,000 credits, but the narrower range of 100 to 1,000 credit awards may appeal more to some players.

This is a general rule of thumb for volatility. There are many other factors involved, but in order to keep our analysis simple, we’ll keep this general rule in mind.

What to Buy, What to Buy?
Suppose we are looking at a game for your floor. We want to install a bank of super deluxe 20-line video slots with the latest graphics, sound and bonus rounds. The manufacturer has two configurations available in our selection. Both pay 95 percent and hold 5 percent. Both have a maximum wager of 10 credits per line and have the same range of pays. Both have identical bonus rounds. Configuration A has a single-line hit frequency of 5.5 percent and an overall game hit frequency of 87 percent. Configuration B has a single-line hit frequency of 1.7 percent and an overall game hit frequency of 35 percent.

Configuration A will see a player winning almost nine times out of 10. Configuration B will see them lose more than six times out of 10, winning not quite four times. Which configuration is better? Surely Configuration A, with its frequent pay, right? You will win more than twice as frequently. Two players, one at Configuration A and one at Configuration B, may notice that the machines are not paying the same. The player on A is winning less than half the time while her neighbor on B is cashing in almost every single game. How long until Player A gives Player B a cutting look, then moves elsewhere? Or will Player B leave his machine first?
Before we answer these questions, let’s take a brief side-trip through your casino floor.

When you pay attention to your patrons, what are you likely to hear? They sure have tightened these machines. They’re not paying as much. The machines are all turned off. They won’t let me win anything tonight. I wish I could win enough to play for a while. I just lost $20 and won nothing. It’s not fun when you can’t win anything. I just can’t do anything right today. I’m going down fast.

Why do your players feel this way? Apart from a suspicion of conspiracy—the eye-in-the-sky monitoring their winnings and varying the payout and their player’s card being used to control how much they win—there must be some reason that they feel this way. New machines are exciting and every paying combination and bonus round is a new experience with the promise of a big win. Players are less likely to remember how much they won than they are to say, “That new game is a lot of fun. I had a blast!” But as they become more familiar with the game, they pay more attention to pay patterns and frequency. As a result, they feel that the games pay less because they may not be quite as exciting as they were when they were new.
However, this alone does not warrant their dissatisfaction. Part of the problem may be hit frequency. A game that rarely pays is not exciting. How disappointing is it to finally receive the bonus round after hours of waiting (or at least five minutes of play), only to receive five credits?

This relates to the three phases of game payout. The first is the cycle, which belongs to the casino. It is the payout over the long term—the life of the machine. Players will rarely find their play matching the cycle since it is based upon hundreds of thousands of games and more.

The second phase is the players’ cycle—the time that they have put on a machine during their play since it came into your casino. They may have been playing this machine for a year and have a basic understanding of how it has been paying. They remember any hand-pay jackpots and know if they’ve had times when they either just couldn’t win or just couldn’t lose.

The third phase is the immediate player experience, and this relates only to the first few minutes of play. We have all read about people who win a multimillion-dollar jackpot after playing only $200. This is an almost immediate win, where the player’s time on device was low. In this initial time period, the players experience highs and lows and either great excitement or great disappointment. This does not relate well to the game’s hit frequency—the sample population of games is far too low. Their big wins or big losses are just luck, either good or lousy. It is their long-term play of the game that starts to relate to hit frequency.

Surely a player can put $20 into a quarter game and play 27 games without a single win. But it is unlikely that they will play 200 games without a single win. How, then, can a high hit frequency be a bad thing?

Volatility Revisited
I think that high-volatility video slots have run their course. You may not agree, but I believe that players need a break from high volatility and are looking for a return to basics. I’m not suggesting that you tear all high-volatility games out of your casino and replace them with low-volatility games; however, I think we need to temper any large number of high-volatility games with some lower-volatility offerings.

With high volatility, as we learned, comes a wide spread of pay ranges. For every 20,000-credit bonus round comes thousands of games with no payout at all. While the large wins are exciting, the no-pay spins are not. When we consider the second phase of game payout—the players’ long-term association with the game—they will have likely had a few bigger wins, but they have also experienced their share of no-win gaming sessions. This time could be months or years, but over the long term, they’ve ridden the waves up and down. If you reduce the width of pays, then you not only bring the large pays down, but you decrease the non-paying ones as well. Their overall feeling of the game will be one of overall winning, not of hit and miss.

Back to Hit Frequency
Hit frequency plays a vital part in player satisfaction and is partly the result of the volatility of the game. If a game is going to pay something to the player eight out of 10 games, how much can we pay them? And how many more games do we need where, mathematically, we attribute some of the credit-in to the large jackpot amounts? A high-volatility game with high hit frequency is going to see even more games where the player receives nothing—or nothing meaningful.

The mathematics is quite simple. The more that we pay out at any one time, the longer it takes to make up this amount. Yet we still have to allow players to win with enough frequency to keep their interest. By creating wins where players receive less than their wager, we give them a sense of winning but also continue to accrue credits. In the second phase of game play—the players’ long-term association with the machine—players realize that their credits slowly but continually erode. In this case, their wins are not meaningful because the net result is a loss.

Next month we’ll look at some sample PAR sheets and study hit frequencies to determine what a meaningful hit frequency really is and how we can determine it.

John Wilson is the Technology Editor for Casino Enterprise Management and Owner of ICS Gaming, providing slot consulting services and game design. He has designed several slot games in both Class II and Class III markets.  He can be reached at jwilson[at]icsgaming.com.