Which Slot’s Symbols Affect the Win the Most?

Historically, slot machines have been one of the worst gambling games to analyze. All other casino games are quite transparent and thus easily quantifiable. Their odds are easy to calculate. However, you can’t see inside a video slots machine, so you stake your fate on reels built by someone else. To be more precise, you are facing an unknown random number generator programmed by someone else.

How the Symbols Are Dealt on Reels

The casino, of course, won’t tell you the distribution of individual symbols on the cylinder and how they are “balanced”. Nevertheless, it seems that most players do not worry about that (mostly they do not even have the slightest idea).

To keep it short and avoid an unnecessarily long article: The following numbers and their conclusions are based only on the first video which contains a total of 212 spins. The basic finding was that the individual reels do not have the same number of symbols and they appear in different sequences. This, of course, has a major impact on the resulting number of combinations. You can see the following number of symbols on the five reels.

The second reel introduces a bit of confusion, because one sequence of symbols appears twice. The individual reels therefore look as follows:

As you surely know, slot machines are based on the following scheme: they pick a random number for each reel and the reel stops on that number. The rolling effect is only for player’s entertainment. According to the height of the image, the machine should select between 1-26 for reels 1, 3 and 5 and between 1-29 for reels 2 and 4.

The following table shows what kind of symbols each reel contains:

We still need to capture what the payout table looks like – the video shows it right at the beginning.

Count along with Me

Let’s do it! We’ll count.  The following table shows the number of total winning combinations on individual reels. If you happen to attempt to produce your own table based on the video, it may turn out slightly different since, in some cases, there are several ways you can achieve the win. However, their total number will not be affected in any way. The total number of winning combinations is 1,516,294.

The total number of combinations is a simple calculation of 26×29×26×29×26 = 14,781,416. If we would like to count the so-called hit frequency, i.e. how often a “winning” combination happens on the slot machine, we can do so as follows: 1,516,294 / 14,781,416 = 10.258%. That means you win in 10.3% of all cases when you press the button.

Payout for Individual Symbols

The following table shows the probability of winning for each symbol.

The following table shows how the individual symbols contribute to the overall payout ratio of the slot machine. The player can thus see that classic winning combinations account for almost 60% of the total payout.

So where does the rest of the payout come from? It’s in bonus payments! With our slot machine, the bonus is won with the help of “party” symbols. There’s a total of three such symbols on the reels. It’s enough to get them to appear on a single screen, you do not have to get three in a row. You can also encounter the term “scatter” symbol. There is usually a bonus round. In our case, it contains a total of 30 bonus symbols or gifts. The player collects individual gifts until he selects the “Party Pooper” option. There are six of them in total. The following table shows how individual prizes are distributed among the Party Pooper symbols.

The following table shows the likelihood that you will hit the winning symbols. The right column contains the expected hit ratio of the individual symbols in the bonus round. Overall, you can expect a total of 4.43% bonus hits in the bonus round. You can get this number with a relatively simple mathematical calculation: (n+1)/(p+1). In our case that is (30+1)/(6+1) = 4.428571.

The total achievable winnings on bonuses are $150 on our slot machine. A total of 6 out of 150 is associated with the Party Pooper, the remaining 144 of them are relatively certain.

There is a total of 30-6 = 24 secure symbols. On average, you hit the winning symbols in 144/24 = 6 cases. As shown in the previous table, there is a total of 4.428571 winning hits on average. One of them, however, is the Party Pooper symbol, so 3.42 true winning symbols remain on average. The average win before showing the Party Pooper symbol will be 3.42 x 6 (average win plus the number of reliable symbols) which results in 20.571429. By adding the Party Pooper, we get the average win of 21.57 in the bonus round.

You get the bonus by hitting the party symbol on either of reels 1, 3 or 5. There are 26 or more symbols on each reel. There are two Party symbols on each of them. The chance for them to appear on at least one reel is 2 × 3/26 = 23.08%. The chance for them to appear on all three at a time is then (6/26) 3 = 0.0122895, so about one percent.

The returns from bonuses can, therefore, be calculated as follows: 0.0122895 × 21.571429 = 0.265102. All in all, we can expect our slot machine to afford us a total of 26.5% of bonus wins + 59.6% returns from normal play. So that’s a total of 86.1%, not really a dizzying percentage. The house edge, in this case, is 13.8%.

That’s our proof.