Home Meaningful Hit Frequency, Part II: Significant and Insignificant Wins

Meaningful Hit Frequency, Part II: Significant and Insignificant Wins

After a detailed look at hit frequency and video slot games last month, we come to the heart of our discussion on meaningful hit frequency as we study the two game configurations mentioned last month and look at some PAR sheet snippets.

As I mentioned last month, conventional wisdom tells us that playing more lines will result in the player winning more frequently—a higher hit frequency; the higher the hit frequency, the better it is for the players. However, winning more frequently does not necessarily mean better play and winning more. In fact, winning too frequently can make many of the winning amounts so small that they become relatively insignificant.

Games on the floor have three phases of game payout. The first cycle covers every possible game outcome and belongs to the casino for the particular box. This is the long-haul play and is where the actual play statistics will near the theoretical values. The second is the player’s cycle, which relates to a specific player’s results over his or her play history for a particular game. The third phase is the immediate player experience relating to a game but in the very short term. Here the player relies more on “luck” than anything else.

A Little Homework
Let’s start this month’s article off with a little homework assignment. I’d like you to go out and watch players on your floor. Specifically look for people playing multi-line video slots. Study how they play. Do they cover all lines? Do they wager more than 1 credit per line? Do you see some who will bet fewer than the maximum number of lines but play ­­multiple credits for the lines they do play?

For a 20-line game, players will frequently play all lines. On a lower denomination game, where the financial impact is less, many players will cover all lines. Why wager only 9 cents when you are giving up the potential of winning on an additional 11 lines on a 20-line penny game? The players may have unconsciously stumbled on a problem.

Some games have fixed-line wagering. Players can select the wager but only as a component of credits wagered per line. The pushbuttons read “Bet 25″, “Bet 50″, “Bet 75″, etc. This ensures that all lines are always covered. And in a high-volatility game this can reduce accounting issues. By ensuring that maximum lines are always purchased, it prevents the situation where a large win can occur during the rare time when a player does play maximum lines. In this case the play does not conform to the average play pattern, and it can make the payout appear to be artificially large.

Some Number Crunching
Let’s look at our fictitious games once more and in further detail. A common payout on all video slots is 5 credits for three matching symbols. For a single line wager—1 credit—players win 5 credits, or 5X their wager. If they win this on one payline when playing 9 lines, the win is 5 credits out of 9 or 5/9 (0.55X their wager). Had they played 20 lines, and assuming that only 1 line pays, then they get 5/20 or 0.25X of their wager. Even if 2 lines paid the award it would be (2×5)/20 or .5X of their wager.

The more lines the player selects, the higher the hit frequency they will receive because they have an increased chance of winning due to more lines purchased. However, it costs more to do this and decreases their overall return. The tradeoff is paying more for a better chance to win but winning less as a percent of the wager. One innovation frequently seen on Aristocrat games is to offer multiple lines for the same wager. For a 100-line game, the wager is only 50 credits. This allows the player to cover more lines while decreasing the required investment. Technically it is just a 1/2-credit wager per line, but the game does have some control over the number of lines you can select. As an example, a 5-credit win on 100-lines is 5/100 or a 0.05X return (or see Figure 1 below). By reducing the investment required, the 5-credit win offers a 5/50 or a 0.1X return. This essentially reduces the investment by one-half but also doubles the return rate. It does make the player awards more meaningful and mitigates the situation where the return is highly insignificant. It is a smart implementation.

Played 9 lines, 2 credits per line, win 10 credits
10 / (9 * 2) = 10/18 = 0.56 X wager

For small wins, this is significant for the player. This is especially true when the win is less than the wager for any particular game played. Essentially, if the win is less than the number of lines purchased multiplied by the credits per line, the player receives an “insignificant win”. For larger wins, the number of lines played becomes less important for this calculation. A 1,000-credit win for a 9-line play is a 111X return. If the same win occurred from 20-line play, it is a 50X return. The difference between a 50X return and an 111X return does not “seem” much to the player. For large wins, they are more aware of the amount of the win and less aware of the percentage. While this is not mathematical, it is always important to remember that players are generally more emotional in their play.

One amusing thing I often hear is people who bet 15 credits and win 9 saying “I won! I wish I had bet more.” In terms of a return on their wager, they lost. Had they bet more, they simply would have lost more. What have the players identified in this situation? Winning, or receiving credits back after the game. They “won” because they have received some payment. When the hit frequency is too high, then too many of the pays will be less than the wager. They must be in order to make the math work out. Is it better to win nothing or win something? While the players do recoup some of their money, over a period of time the players are still losing. The entertainment factor of a game is important to players and forms part of their overall game satisfaction, so the average play of the game is important to study.

Configuration “A”, to recap from last month, was a 20-line video slot with a 95 percent payout and a 5 percent hold. The single-line hit frequency was 5.5 percent, but the overall game hit frequency with maximum lines played was a whopping 87 percent. It sounded like a sure hit. But how much of the game return is meaningful or consists of significant returns? In order to determine this mathematically, we need to work with a spreadsheet. Figure 2 illustrates a sample spreadsheet that will serve our purpose.

List the key elements of the game in your spreadsheet. At the top you can type in the general game information such as payout, hold, hit frequencies, cycle size and number of hits per cycle. Below that we will create a small table. I have chosen to list the symbols, single-line award and the number of hits per cycle for this award. There are also two columns that we will use to calculate the significance. The first is labeled “Insignificant” and the second “Significant”. Fill in the symbols, hits and win amount for each entry in the PAR sheet.
In order to determine if a win is significant or insignificant, we need to have a target value. This is the number of lines played. We are going to assume that each game has a single credit wager per line, since this is how the PAR sheet shows the wins. If you have a 20-line game, your target is 20. Take a look at each entry in your spreadsheet and look at the winning amount. If it is less than your target, record the number of hits in the “Insignificant” column. If it is equal to, or greater than, the target, record the number of hits in the “Significant” column. The target can be adjusted based on your preference. Perhaps you feel that receiving 80 percent of your wager is significant. In this case, your target is not 20 but is 80 percent of 20, or 16. If the win is less than 16 then enter the hits in the “Insignificant” column. Tip: Use a formula to copy the value. If the cell containing the number of hits is C20, then under the appropriate column type “+C20″.

After you have completed the spreadsheet, create a sum of the Significant and Insignificant columns. These two sums should equal the total number of hits for the game. If they do not, you have an error in your spreadsheet. Go back and check the values.

This simple exercise helps identify the games where players receive at least their wager back, on a single line. For multiple lines where they overlap, this isn’t entirely accurate, but the math is long and complicated, so this gives us a rough idea.

Underneath the sums, create a formula that divides the sum by the total number of wins in the cycle. In Figure 3, the Insignificant Wins formula would be 810,449/922,747. These values will show you the percent of wins that are significant or insignificant.

In this example, 87.83 percent of the games played resulted in players receiving less than what they wagered. In fact, players won at least their wager in only 12 percent of the games played.

As a result, players receive an insignificant payout almost 9 out of 10 times when they win. The rest of the time their credits decrease even if they win. Although the game hit frequency is 87 percent, its meaningful hit frequency is only 12 percent. This is quite significant.

Same Time, Same Channel
With that we’re out of time (and space) for this month’s installment. You should now have a good start and can begin to study some of the games on your floor. Next month we’ll study Configuration “B” and see how it compares. We will also talk about how important this concept is and whether it really makes that much of a difference to the player or the operator. In the meantime, have fun crunching some numbers, and remember, this exercise was designed to get you thinking about your games in a different way. By playing around with the numbers and trying different values, you begin to form a better appreciation for the games mathematically.

Leave a Comment