Casino Enterprise Management

Paul Simon may have come up with 50 ways to leave your lover, but Konami Gaming has a much better spin on numbers. They may only have 27 ways, but each one is a winner! “27 Ways” refers to a new way to win on Konami’s three-reel mechanical stepper Advantage Series platform. What might initially seem like an interesting or unusual spin on a slot game is based upon a solid mathematical foundation. Let’s take a moment to see just how this came about.

Once Upon a Time...
The first slot machine, Charles Fey’s Liberty Bell, was a three-reel mechanical slot. It had a small cycle and a low top-award. As machines progressed and technology evolved, new innovations allowed both larger and more frequent awards. One of these innovations involved the addition of more paylines. The first slot machine, and many that followed, had a single payline. Symbols had to appear centered vertically along this horizontal payline.

Today’s steppers, including the standard three-reel stepper, follow the same basic principle. If a symbol appears centered on the first payline, then there will be a blank symbol immediately above and below it. If a blank appears centered on the first payline, then a symbol will appear both above and below it. Expanding from the single payline, two additional paylines were added. Payline 2 is above the center payline, with the third payline immediately below the center payline.

By adding paylines, the player was given more opportunities, or more ways to win. They could win on one, two or three paylines at the same time, increasing their awards. They could also be charged for each payline, increasing the coin-in amount. This could end up in a wash—you collect more coin-in but pay more coin-out. However, the amount of coin-in per game increased, therefore the hold increased, even though the hold percentage may have remained constant.

In order to provide more paylines, and even more ways to win, two additional paylines were added. These were diagonal, with Payline 4 starting in the upper left-hand corner of the reels and ending in the lower right-hand corner. Essentially, Payline 4 consists of three symbols—Payline 2 on the leftmost reel, Payline 1 on the center reel, and Payline 3 on the third reel. The fifth payline went in the opposite direction. (See Figure 1.)

Four additional paylines were easily added, and equally as easily recognizable by players. Even today the nine-line, three-reel stepper games are seeing an increase in popularity. These additional lines are in a V or inverted V shape, both above and below the center payline. (See Figure 2 at right.)

From here things get a little funky. The paylines aren’t necessarily symmetrical and the players may not easily recognize them. However, there are a lot more paylines to add. How many you ask? Let’s see if you can guess . . .

There is a limit to the number of paylines available, based upon how many different combinations of symbols we can arrange together. On the standard mechanical stepper there are three possible symbol stops visible for each reel. If we consider only the first two reels, we come up with nine combinations of symbols. For each of the stops on the first reel, there are three stops on the second. We multiply these values together to get the possible outcomes. Adding a third reel, we expand our options geometrically. For every one of the nine possible combinations available for the first two reels, there are three combinations available for the third. We multiply this as well, getting the maximum number of combinations on a three-reel game: 3 x 3 x 3 = 27. And that, my friends, is where the 27 Ways to Win originates. (See Figure 3 above.)

27 Ways
Konami has designed a series of games that sets up paylines based upon every possible combination available in the reel windows at any time. It has also made the reel window larger, allowing for three symbols to be visible at any one time. By making the machine cover every combination, it has essentially become a scatter-pay machine. If a symbol is visible anywhere, it falls on some payline. If three symbols appear on Reels 1, 2 and 3, then they land on one of the 27 possible paylines. Although the end result is the same, there is a subtle difference in how this works.

Consider the game’s minimum wager of 25 credits. Looking at this as a 27-line game, then the minimum wager is 25 credits for 27 lines, or 25/27 = 0.926 credits per payline. If the player wins 100 credits on a particular combination, then they have won 100 / 0.926 = 108 times the line wager. The remaining 26 lines would have won nothing in this example.

If we consider the game as a scatter pay, then the same 100 credit win would be 4X the overall game bet. The math works out the same in the end, it just allows you to think about the game in whatever mode makes it easier for you to understand.

This concept has been used in the video platform by different manufacturers. In these games, whether it’s a 243-ways to win or Reel Power, the premise is the same. If you see the symbols, then they fall on a payline. It doesn’t matter on which payline they appear, they match some mathematical payline. It’s a scatter pay.

One Step Further
Konami wasn’t satisfied in leaving the game design there. Although it’s good, there was a further step that could be taken to enhance the players’ “entertainment value.”

Let’s consider the hit frequency for this game. Suppose we take a look at the reel strips for the game and determine every possible outcome. We learn that the hit frequency, for the sake of an argument, may be 20 percent. This means that 20 percent of all game outcomes are winners, and that the player will win something, on average, on 20 percent of their wagers. Assuming this, the player will win on a single payline each time, but never more than once. If the player gets three Red 7s on Payline 18, there won’t be a combination of three Bars on Payline 9, for example.

This sees the player winning frequently (one out of every five games, on average), but the amounts may not be stellar. They may infrequently win a few thousand credits, quite frequently a few hundred, and very frequently about the amount of the wager.
What would happen if we grouped several of these winning combinations together? Let’s make the game so that sometimes the players will win three Red 7s on two paylines and win three Bars on a different payline. (See Figure 4 at right.)

In this case we have grouped three payouts together, increasing the overall winning amount for this game. But we have also removed two separate winning combinations. Our hit frequency, per game, will now be less than 20 percent. While the players will win the same amount overall, because of the triple win, they will win slightly less frequently.

Suppose that we were to double up each and every win through a judicious placement of symbols on the reels. While this may not be physically possible, we’ll assume that we were able to manage it. In this case, we’ve reduced the overall game hit frequency to 10 percent. The players will win half of the amount of times that they did previously. However, each time they win, they will win more, as they are matching more than one paying combination. In the end, the game pays out exactly the same, but when players win, they win more.

Win a Little or Win a Lot?
Consider a situation where a player wagers 25 credits for 100 games and wins 20 credits every time. Their payout is 80 percent (20/25), and every game is a winning game, making the hit frequency 100 percent. They never get ahead, however, and are constantly faced with small wins. Some players will feel that they never won anything on this game, although they won on each and every spin of the reels.

In a second situation, the player wagers the same 25 credits per game for 100 games. They win nothing on any game except the last, when they are awarded 2,000 credits. Many players will feel that they won the jackpot on this game, although they are certain to notice a long “dry spell.”

In the end, 2,500 credits were wagered and 2,000 were paid back. Both players received identical overall wins. The only difference was how these wins were distributed—and how the player reacted. After a lengthy walk around the subject, we come back to Konami’s implementation. They have taken the overall wins and grouped many of them together. However, they’ve done this in a way that will appeal tremendously to the player. They have stacked various symbols and wild symbols on top of each other.

On the 27 Ways games, each reel has a symbol that is part of a stack of three vertical symbols. For Cash Reaction, for example, every reel has three stacked Red 7s. This means that on any one reel, the player may have one, two or three symbols landing within view in the window.

As we know about the design of the game, there are 27 ways to win (27 paylines), and there would also be 27 combinations of these stacked symbols. Should each reel show the complete stack of 3 symbols, then the player has won the award 27 times—one for each payline. The base pay for three Red 7s on Cash Reaction (at 25 credit wager) is 300 credits. For 27 paylines matching, the award becomes 300 x 27 = 8,100 credits. Instead of having 27 different paying combinations spread over 27 different games, they’re grouped together into one large payout. It’s a means of increasing the amount won in a single game. In order to do this, however, these payouts must be taken from other games, making the overall hit frequency a bit lower.

Players like this current trend. Not many years ago, players felt that 600 or 900 credits won in a bonus round was a healthy payout. Now they want to see payouts in the thousands or tens of thousands. Certainly an 8,100 credit award for these Red 7s will be exciting. If they had played the maximum wager of 200 credits, their award becomes increased by a factor of eight, since their wager was eight times larger than the 25 base bet. This player receives an award of 300 x 27 x 8 = 64,800 credits. On a penny machine, that’s a $648 award—and certainly an attention grabber.

With the arrangement of the stacked symbols, lesser amounts are also available. For these, multiply the number of symbols landing on each reel together. Two Red 7s on the first reel, one Red 7 on the second reel and three Red 7s on the third reel creates six combinations (2 x 1 x 3), providing a sizeable award of 1,800 credits on the minimum wager.

Stacked symbols appear complicated on first glance, but they are actually quite simple. Just think of the number of matches per reel and the math is easy. In fact, Konami’s math and minimum wager do relate to single payline quarter games, even when compared with multi-payline penny games. Consider the following scenario:

A 1-credit wager on a 25-cent, three-reel mechanical machine awards 80 credits for three Double Bar symbols. That’s a $20 payout for a single credit wager.

If we consider a penny game with a 25-credit minimum wager, the player could win 2,000 credits, which is an exciting amount. That’s a $20 win with an identical wager. The player bet 25 cents in both cases and won $20 in both cases. In this situation, the quarter player winning 80 credits will likely not feel the same level of excitement as the penny player winning 2,000 credits. In the end, it’s exactly the same. It’s all about perception. The penny players feel they are playing a penny game, even though their wager level is the same as it would be on a quarter machine. The amount they won, however, is expressed in cents. The quarter game’s win is expressed in quarters.

If we consider the same example for dollar players, they would have wagered 1 credit and won 80 credits—the same ratio of wager-to-award. This player wagered four times the amount and won four times the amount, too. It seems a little more exciting due to the “real money” value of a one-dollar credit base, but it’s still nothing you will hear your players hollering about.

In reality, it comes down to numbers and the players’ perception of them. If a player wagers 250 credits on a 1/10 cent game and wins 20,000 credits, you’re going to know that it happened.

A Whole Lot of Combinations
For Cash Reaction, one of the 27 Ways games, the three-reel base has a cycle of just over 8.5 million games. With the fourth reel multiplier, the cycle is just over 2.3 billion games. A large cycle is required in order to provide the large payouts and the number of stacked symbols. Without this large cycle, the hit frequency would be extremely low and player satisfaction would diminish.This configuration makes the game highly volatile, a trend which players enjoy.

While 27 Ways sounds like a clever marketing scheme, it’s really based upon a solid mathematical principle. You will notice that the game doesn’t show any paylines running across the glass. Players may not immediately recognize how they won, but they soon learn that the “visible means winning” premise of this game makes it easy to understand. Couple that with stacked symbols and more ways to win, and this game is sure to be a winner with players.

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@icsgaming.com.