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Last Updated: August 19, 2016

Deconstructing Jackpot Party

Introduction

Historically, slot machines have been one of the few casino games that were nearly impossible to analyze without inside information about how an individual game was programmed. Every other casino game is open about its rules so the odds are quantifiable. However, with slots, the player is at the mercy of unknown reel strips. The casino doesn't tell the player the distribution of symbols on the strips, nor how they are weighted for single-line slots. While that doesn't seem to bother most players, it bothers me.

In an effort to break this wall of secrecy, I recorded 212 spins of the game Jackpot Party on my cell phone. Then I went home and hand entered every outcome into a spreadsheet. Finally, I did the math to determine what I was up against. This page shows what I found.

Step One - Data Collection

I decided to study the game Jackpot Party because it is a simple design and typical of the way video slot machines work. The game is somewhat outdated as I write this, but I managed to find a "classic" penny version at the Wynn on January 24, 2012. Armed with a cell phone camera, I played as fast as possible for eight minutes. I broke for lunch then returned to record another 10 minutes of play. The videos of my play can be found on YouTube:

Jackpot Party part 1
Jackpot Party part 2

When I returned home, I hired my brother in law to record, by hand, the three visible symbols on each reel for all 212 bets in the first video. It turned out that video was enough, and I didn't need the second one.

Step Two - The Reel Strips

To make a long story short, I found that there were only so many different combinations of three symbols on each reel, just as I suspected. To be specific, from the first video I noticed the following number of patterns for reach reel:

  • Reel 1: 26
  • Reel 2: 28 (one of these patterns occurs twice, so 29 total positions on the reel strip)
  • Reel 3: 26
  • Reel 4: 29
  • Reel 5: 26

The 212 spins in the first video were enough to ensure I saw every combination at least once. If I found there was a missing segment in the reel strips, I still had the second video to fall back on, but I never needed it.

The next step was like a jigsaw puzzle. I had to find how the different sequences of three symbols overlapped to form a complete reel. It took a few hours, but I eventually figured it out. A tricky part was that in reel 2 one sequence (blue 7-plum-orange) appears in two separate places.

The following table shows the result of many hours of labor, the complete reel stripping for Jackpot Party.

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


The way multi-line video slots work is they draw random numbers, one for each reel, to determine where on the reel strips to stop. In this case, the game would choose three random integers from 1 to 26 for reels 1, 3 and 5, and two random integers from 1 to 29 for reels 2 and 4. It would then map these random numbers to a position on on the reels.

For example, if the game chose the numbers 10,7,7,3,21 for reels 1 to 5 respectively, and mapped them to the position on the reels on the top row on the screen, then the screen would look like this:

The next table shows the total number of each symbol on each reel.

Jackpot Party Symbol Distribution

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

Step Three - The Pay Table

The pay table is easily seen from the rule screens. That is why the first video shows me running through it. There are three types of symbols: the 7s, the fruits, and the bonus. Three to five of the the same colored 7 symbol is a win. In addition, three to five mixed 7 symbols is a lesser win. There are also wins for three to five fruits, but no win for mixed fruits. However, there is a "wild fruit" symbol, which can substitute for any fruit. The player is also paid for 1 to 5 wild fruit symbols. All sevens and fruit wins are left aligned, meaning that all wins start with the left-most reel. The player is paid the highest award per line.

Following is the complete pay table.

Jackpot Party Pay 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

Step Four - Line Pay Math

The next table shows the number of combinations for each possible win. If you tried to replicate this table it may not come out the same, because some wins can be scored equally two different ways. For example, wild fruit-wild fruit-cherry-blue 7-watermelon wins 5 for either two wild fruit or three cherries. Cells are left blank if they don't produce a win.

The wild symbol and mixed seven wins make a mathematical analysis of line pay wins tedious, complicated, and error prone. In my strong opinion, the safest and easiest way to analyze the line pay wins is to score every possible outcome with five nested loops.

The lower right cell shows the total winning combinations is 1,516,294. There are 26×29×26×29×26 = 14,781,416 total possible combinations in Jackpot Party. That makes the hit frequency per line 1,516,294/14,781,416 = 10.258%. In other words, the probability the player will win something on any given line is 10.3%.

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 next table shows the probability of each possible win. This is simply the number of combinations in each cell above divided by the total number of combinations of 14,781,416.

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 next table shows the product of each winning probability and what it pays. The lower right cell shows that the player can expect to win 59.60% of his bet per spin from line pays.

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

Step Five - The Bonus

There are two "party" symbols on reels 1, 3, and 5. If the player gets one on all three reels, then he will play the bonus. Note that the party symbols don't need to be on the same line. It is scored as a "scatter" symbol, meaning it can be anywhere to get credit for it.

You can see an example of a bonus round at the 3:20 point in the first video.

In the bonus round there are 30 gifts. The player will keep picking gifts and accumulating the money inside them until he selects a "Party Pooper." There are six Party Poopers. Even the Party Poopers have a minimum win of 1. The following table shows how all the prizes are distributed. All prizes are relative to the total amount bet on the initiating spin.

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 next table shows the probability of 0 to 25 picks in the bonus round, including the bonus ending Party Pooper pick. The probability of exactly n picks is permut(24,n-1)×6/permut(30,n), which is the number of ways to pick n-1 successful picks out of 24, times the 6 ways to pick the Party Pooper, divided by the number of ways to pick n items out of 30.

The right column shows the product of the probability and number of picks. The lower right cell is sum of the expected number of picks, which shows the average number of picks is 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


By the way, a handy formula for the expected number of picks for the general case of n total icons and p Party Poopers is (n+1)/(p+1). In this case it would be (30+1)/(6+1) = 4.428571.

The total prize money in the bonus is 150. Of that 150, 6 is accompanied with Party Poopers, so 144 of it is what I would call safe money. There are 30-6=24 safe picks. So the average safe pick award is 144/24=6.

As shown above, the average number of total picks is 4.428571. However, one of those is the Party Pooper, so there would be 3.428571 safe picks, on average.

So, the average win before the Party Pooper would be (average win)*(number safe picks) = 6 × 3.428571 = 20.571429. Then add 1 for the Party Pooper consolation prize and the average bonus win is 21.571429.

The bonus is triggered if the player gets the Party symbol anywhere on reels 1, 3, and 5. There are 26 symbols on each of those reels. There are two Party symbols on each odd-numbered reel and three positions visible on each reel. So the probability of a Party symbol on any odd-numbered reel is 2×3/26 = 23.08%. The probability of getting the Party symbol on all three reels is (6/26)3 = 0.0122895, or 1 in 81.4.

The bonus return is (bonus probability)×(average bonus win) = 0.0122895 × 21.571429 = 0.265102.

Step Six - Summary

I've shown that the player can expect to win 59.601% of his bet from line pays and 26.510% from the bonus. Taking the sum, the total return for the game is 86.111%. In other words, the house edge is 13.889%.

An 86% return is pretty low for a slot machine. However, it doesn't come as a surprise to me. This is a penny game in a luxury casino, which both work against a high return. This does not mean that Jackpot Party is always set to 86%. The slot maker, WMS, would have other versions available, letting the slot director choose which program chip, known as an EPROM, to put into the machine.

The purpose of this page was not to embarrass anybody but to show an actual example of how a slot machine works.


Written by: Michael Shackleford

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