Jun 05, 2015
This week we are mainly going to discuss slot machines throughout three articles and then have a fourth article highlighting another WoO promotion.
As with anything else involving gambling, slot machines are all about Math, but, they are also about Psychology. One of the most important components of slot machine design is not just making sure the Math yields a House Advantage within a certain range, (that part is easy) but also about making sure that the player is having fun playing the machine while bucking the House Advantage.
In so doing, the slot machine designer must tap into the Psychology of the players, and one of the most important ways to do this is to design a machine with, "Near-Misses," which make it appear as if the player almost hit a jackpot. These near-misses accomplish two things: First of all, they make it appear, Psychologically, as though the player is close to getting a jackpot, secondly, they must happen frequently enough to make hitting the jackpot SEEM much more likely than it actually is.
We're going to throw up a completely fabricated slot machine here called Golden Goose Eggs, and this will be a single line game with thirty reel assignments for each of the three reels. The reel assignments will be as follows:
Golden Goose Egg: 2, 2, 5
Golden Goose: 5, 5, 2
Three Bars: 4, 4, 2
Two Bars: 4, 4, 4
One Bar: 5, 5, 5
Cherry: 10, 10, 12
Not only are the reels assigned this way, but, the Cherries are also going to be designed such that each reel is only going to have two different physical spots representing the Cherry and there shall be a Golden Goose Egg above the Cherries on Reels 1 & 2 with a Golden Goose below as well as Golden Goose Eggs BOTH above and below the Cherries on Reel 3 and also above the One Bar, in one instance, on Reel 3.
The probabilities, pays, and contributions to the return are as follows:
Three Golden Goose Eggs: 0.00074074074 * 200 = .148148148
Three Golden Geese: 0.00185185185 * 100 = .185185185
Three Three Bars: 0.00118518518 * 75 = .088888888
Three Two Bars: 0.00237037037 * 50 = .11851851851
Three One Bars: 0.00462962962 * 25 = .11574074074
Three Cherries: 0.04444444444 * 5 = .222222222222
The overall return on a bet is going to be 0.87870370247, thus the House Edge is about 12.12963%. The House Edge is probably actually a little high for such a simple game, especially given the low hit rate which is just north of 5%, but this works just as an example.
If a player is going to get, "Hooked," to playing this machine, so to speak, it is going to be because of the seemingly frequent appearance of the Three Golden Goose Eggs which would yield a $200 Jackpot per dollar bet. It is important to remember that, every time a player sees Two Golden Goose Eggs on the Payline, there is a reasonably good chance the player will see a Third Goose Egg on one of the other reels either above or below the Payline.
Remember, every time a player hits a Cherry on the Center reel on Reel 3, the player is going to see a Golden Goose Egg both above and below said Cherry. Also, if the Cherry is just above appearing on the screen, then a Golden Goose Egg will appear on the screen in the top spot on the third reel, if the Cherry is just below appearing on the screen, then a Golden Goose Egg will appear on the bottom part of the Third Reel.
Now, what we're going to do is situate the Cherries two reel spots away from the One Bar symbols, when we can. Effectively, this is going to put a Golden Goose Egg between the Cherry and the One Bar symbol, which means, if either of those results hit, there will be at least one Golden Goose Egg appearing on the third reel.
Effectively, this makes the probability of hitting a Golden Goose Egg 5/30 on the third reel, that's unchanged, but the probability of one appearing on the screen without hitting is now 17/30!
If we combine the probability of Golden Goose Eggs landing on Reels 1 & 2 with the probability of Golden Goose Eggs being visible, but not hitting, on Reel 3, the probability of such an occurrence is 0.00251851851 or 1 in 397.06.
For our next trick, we're going to design the First and Second Reels the same way with respect to our two Golden Goose Eggs. We're going to wedge them below two of the One Bar symbols and above two of the Cherry symbols. However, this Reels are going to have a more accurate visual representation.
This means that if a One Bar symbol lands on the payline, there will be a Golden Goose Egg below it and if a Cherry lands on the Payline, there will often be a Golden Goose Egg above it. The result of this is going to be a 2/30 probability of appearance, per reel, without it being on the Payline.
This way, the probability of it appearing on EITHER Reel 1 or 2 as well as one Reel 3 with two of them on the Payline is: 0.00148148148.
The new combined probability of at least Two Golden Goose symbols appearing on the Payline without hitting is: 0.00399999999
That represents Odds of 1 in 250 on a Jackpot with a probability of 1 in 1350.
Okay, now we can throw in the probability of a Golden Goose Egg being visible on either Reel 1 or Reel 2, but not on the payline, while one is on the Payline for either Reel 1 or Reel 2 and one is visible on Reel 3, but not on the Payline. The probability of that result is 0.00503703703 or 1 in 198.53, approximately. There's also a 0.00251851851 or about 1 in 397.06 probability that it will be visible on all Reels, but not hit any of the Paylines.
0.00251851851+0.00503703703+0.00399999999 = 0.01155555553
Thus, there is a total probability of about 1 in 86.5384617298 that Three Golden Goose Eggs will be somehow visible without that 1 in 1350 result hitting, and that's if I didn't miss anything.
The point of this little thought experiment is that we go our entire lives watching objects in motion and our brains are trained, by our surroundings, to believe that the closer an object comes to hitting a desired target, the more likely it is to actually do it.
Imagine learning how to shoot free throws in basketball. For all but the naturally gifted who intuitively project an object in an accurate parabola with the desired amount of force, it is going to be a process. With modicum physical ability, you're going to get closer and closer to accurately making free throws until your percentage is significantly better than it was.
This is how our minds are trained to believe and behave by our surroundings. This is also the reason why some people claim to be able to, "Predict," when Free Games are, "Due," by the behavior of the slot machine. When we see things get closer and closer to happening, or better yet, getting close to happening with great frequency, we tend to believe that it is closer to happening within the next few attempts.
The most important thing for a slot player to understand is that the slot machine is specifically designed to take advantage of the player's Psychology and get into the player's head. It is also important to recognize that slot machines do not do this in spite of being fun, it is the fact that they do this that makes them fun.
Think about it: How many players have you seen leaving a machine saying, "This machine isn't even pretending it's going to hit," or, "This machine doesn't even look like it's going to hit," or some other variation of that complaint?