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1. 8. 2017
Slots

Which Slot’s Symbols Affect the Win the Most?

In the following article, you will find an accurate and simple to understand observation of how the machine works.

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.

Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
26 28+1 (one appears 2x) 26 29 26

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

Jackpot Party Reel Strips
Position Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
1 Cherry Orange Bell Bell Watermelon
2 Wild Fruit Bell Cherry Orange Cherry
3 Green 7 Plum Jackpot 7 Jackpot 7 Orange
4 Plum Green 7 Watermelon Wild Fruit Bell
5 Cherry Watermelon Plum Orange Cherry
6 Blue 7 Orange Cherry Watermelon Plum
7 Plum Blue 7 Green 7 Cherry Blue 7
8 Party Plum Orange Blue 7 Orange
9 Green 7 Orange Bell Orange Bell
10 Orange Watermelon Plum Watermelon Plum
11 Cherry Jackpot 7 Watermelon Plum Party
12 Blue 7 Wild Fruit Bell Green 7 Green 7
13 Bell Plum Orange Cherry Cherry
14 Party Orange Cherry Bell Orange
15 Plum Blue 7 Party Green 7 Blue 7
16 Watermelon Cherry Bell Plum Party
17 Jackpot 7 Orange Blue 7 Bell Watermelon
18 Orange Bell Cherry Orange Cherry
19 Cherry Jackpot 7 Wild Fruit Plum Blue 7
20 Wild Fruit Cherry Orange Blue 7 Watermelon
21 Watermelon Bell Watermelon Cherry Orange
22 Orange Plum Bell Watermelon Bell
23 Plum Cherry Cherry Jackpot 7 Green 7
24 Cherry Green 7 Party Plum Plum
25 Bell Orange Watermelon Watermelon Wild Fruit
26 Green 7 Bell Orange Bell Jackpot 7
27 Watermelon Blue 7
28 Blue 7 Plum
29 Plum Cherry

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:

Jackpot Party – distribution of symbols
Symbol Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Jackpot 7 1 2 1 2 1
Green 7 3 2 1 2 2
Blue 7 2 3 1 3 3
Bell 2 4 5 4 3
Wild Fruit 2 1 1 1 1
Watermelon 2 3 4 4 3
Plum 4 5 2 5 3
Orange 3 6 4 4 4
Cherry 5 3 5 4 4
Party 2 0 2 0 2
Total 26 29 26 29 26

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

Jackpot Party – payout table
Symbol 5 pays 4 pays 3 pays 2 pays 1 pays
Jackpot 7 5000 100 40
Green 7 250 50 25
Blue 7 200 50 20
Mixed 7 100 40 5
Bell 200 50 20
Wild Fruit 2000 50 10 5 2
Watermelon 150 25 10
Plum 150 25 10
Orange 50 10 5
Cherry 50 10 5

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.

Jackpot Party Line Pay Combinations
Symbol 5 4 3 2 1 Total
Jackpot 7 4 80 1,144 1,228
Green 7 24 240 3,432 3,696
Blue 7 54 360 3,432 3,846
Bell 480 3,680 26,000 30,160
Wild Fruit 2 22 572 15,080 980,200 995,876
Watermelon 1,598 8,756 48,672 59,026
Plum 2,590 14,212 63,388 80,190
Orange 4,373 18,333 107,952 130,658
Cherry 4,198 17,598 103,584 125,380
Mixed 7 5,210 16,960 64,064 86,234
Total 18,533 80,241 422,240 15,080 980,200 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.

Jackpot Party Line Pay Probabilities
Symbol 5 4 3 2 1 Total
Jackpot 7 0.00000027 0.00000541 0.00007739 0.00008308
Green 7 0.00000162 0.00001624 0.00023218 0.00025004
Blue 7 0.00000365 0.00002435 0.00023218 0.00026019
Bell 0.00003247 0.00024896 0.00175897 0.00204040
Wild Fruit 0.00000014 0.00000149 0.00003870 0.00102020 0.06631300 0.06737352
Watermelon 0.00010811 0.00059237 0.00329278 0.00399326
Plum 0.00017522 0.00096148 0.00428836 0.00542506
Orange 0.00029584 0.00124027 0.00730322 0.00883934
Cherry 0.00028401 0.00119055 0.00700772 0.00848227
Mixed 7 0.00035247 0.00114739 0.00433409 0.00583395
Total 0.00125380 0.00542851 0.02856560 0.00102020 0.06631300 0.10258111

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.

Jackpot Party Line Pay Returns
Symbol 5 4 3 2 1 Total
Jackpot 7 0.00135305 0.00054122 0.00309578 0.00499005
Green 7 0.00040592 0.00081183 0.00580459 0.00702233
Blue 7 0.00073065 0.00121775 0.00464367 0.00659206
Bell 0.00649464 0.01244806 0.03517931 0.05412201
Wild Fruit 0.00027061 0.00007442 0.00038697 0.00510100 0.13262599 0.13845899
Watermelon 0.01621631 0.01480914 0.03292783 0.06395328
Plum 0.02628300 0.02403694 0.04288358 0.09320352
Orange 0.01479222 0.01240274 0.03651612 0.06371108
Cherry 0.01420026 0.01190549 0.03503859 0.06114435
Mixed 7 0.03524696 0.04589547 0.02167045 0.10281288
Total 0.11599362 0.12414305 0.21814689 0.00510100 0.13262599 0.59601056

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.

Jackpot Party Prizes
Prize Number
1 2
2 5
3 1
4 1
5 9
10 3
15 2
20 1
Party Pooper + 1 6
Total 30

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.

Number Picks in Bonus
Picks Probability Expected
1 0.200000 0.200000
2 0.165517 0.331034
3 0.135961 0.407882
4 0.110783 0.443131
5 0.089478 0.447392
6 0.071583 0.429496
7 0.056670 0.396687
8 0.044350 0.354801
9 0.034271 0.308435
10 0.026111 0.261109
11 0.019583 0.215415
12 0.014430 0.173156
13 0.010421 0.135479
14 0.007356 0.102989
15 0.005057 0.075862
16 0.003372 0.053946
17 0.002167 0.036847
18 0.001334 0.024009
19 0.000778 0.014783
20 0.000424 0.008488
21 0.000212 0.004456
22 0.000094 0.002075
23 0.000035 0.000813
24 0.000010 0.000243
25 0.000002 0.000042
Total 1.000000 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.

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