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p13man
p13man
Joined: Jul 14, 2019
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November 22nd, 2019 at 5:44:03 PM permalink
Hold & Spin features are a key part of the game play of all recent Aristocrat games (Dragon, Lightning cash etc) and have been copied by other manufacturers. They're everywhere. I’m curious to know if it is possible to calculate the odds of triggering a Hold & Spin feature…

Hold & Spin features are triggered when 6 or more Hold & Spin symbols appear in the Pay Window. The Pay Window has 5 vertical reels and 3 rows (15 symbol placements in total).

Each of the 5 reels has a one instance of 2 Hold & Spin symbols positioned consecutively (a cluster of 2) and one instance of 3 Hold & Spin symbols positioned consecutively (a cluster of 3), for a total of 5 Hold & Spin symbols per reel. The clusters are at least 5 symbols apart on all reels – so only one cluster (or part thereof) can appear in the window for any single reel.

Reels 1-4 inclusive have 64 symbols in total and Reel 5 has 85 symbols in total.

What are the odds of getting a Hold & Spin feature?

For an example of a H&S feature, put this into google …

lL9Tdns1XbA

… click on the youtube video and then fast forward the video to 2 mins 30 secs (the commentary is worth a listen!)

Thanks in advance
rdw4potus
rdw4potus
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November 22nd, 2019 at 8:12:42 PM permalink
Do you only care about 6 symbol triggers on lightning/dragon link? Or do you also have interest in lock it link (3 symbols) , fire link (4 symbols) , and mighty cash (5 symbols @ high denom)?
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
rsactuary
rsactuary
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November 22nd, 2019 at 8:39:49 PM permalink
Yes, I've done a lot of work on this related to Lightning Link and Dragon Link games. I've focused on Sahara Gold, so my calculations are related to that, based on a machine at Winstar in Oklahoma.

To estimate the odds of getting the hold and spin feature, you can tape your play and record the number of times that you get 0, 1, 2 or 3 orbs on each reel and then using all of the various combinations of ways to hit 6 or more orbs, calculate the probabilities. Note it is not necessary to know the distribution of the amounts on the orbs, just the number of orbs.

For the machine that I've been playing (10 cent denomination, $5 spins) I calculated the following based on 1,300 spins so far:

6 0.0048899388490
7 0.0017111980199
8 0.0005277596371
9 0.0001335915236
10 0.0000327884548
11 0.0000067826221
12 0.0000011150961
13 0.0000001701810
14 0.0000000191783
15 0.0000000009395 <--- awards Grand immediately.. No H&S feature
0.00730336450141 Hold and Spin feature approximately once every 136.92 paid spins
Last edited by: rsactuary on Nov 22, 2019
rsactuary
rsactuary
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November 22nd, 2019 at 8:40:56 PM permalink
The bottom line is the sum of the 6 orbs to 14 orbs probabilities. If you get 15 orbs, you wouldn't get the Hold and Spin feature, you'd be awarded the grand immediately.

My method does not need the entire number of symbols on each reel but my answer is subject to variance as it is based on observed spins. I’m curious how you know the reel mappings.

I will work through the math based on your assertions over the weekend.
Last edited by: rsactuary on Nov 23, 2019
tringlomane
tringlomane
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November 23rd, 2019 at 2:18:42 AM permalink
Quote: rsactuary

Yes, I've done a lot of work on this related to Lightning Link and Dragon Link games. I've focused on Sahara Gold, so my calculations are related to that, based on a machine at Winstar in Oklahoma.

To estimate the odds of getting the hold and spin feature, you can tape your play and record the number of times that you get 0, 1, 2 or 3 orbs on each reel and then using all of the various combinations of ways to hit 6 or more orbs, calculate the probabilities. Note it is not necessary to know the distribution of the amounts on the orbs, just the number of orbs.

For the machine that I've been playing (10 cent denomination, $5 spins) I calculated the following based on 1,300 spins so far:

6 0.0048899388490
7 0.0017111980199
8 0.0005277596371
9 0.0001335915236
10 0.0000327884548
11 0.0000067826221
12 0.0000011150961
13 0.0000001701810
14 0.0000000191783
15 0.0000000009395 <--- awards Grand immediately.. No H&S feature
0.00730336450141 Hold and Spin feature approximately once every 136.92 paid spins



So let me get this straight. You think the probability of getting the grand without going through the hold and spin feature is about 1 in 1.1 billion? Yeah, I could believe that.

How confident are you in the overall probability of the grand if you've calculated it yet? Or not enough Bonus rounds yet?
rsactuary
rsactuary
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November 23rd, 2019 at 9:08:10 AM permalink
Quote: tringlomane

So let me get this straight. You think the probability of getting the grand without going through the hold and spin feature is about 1 in 1.1 billion? Yeah, I could believe that.

How confident are you in the overall probability of the grand if you've calculated it yet? Or not enough Bonus rounds yet?



After 1300 spins, my results are now starting to look a little more normalized. I think I need to get to 2000 to feel better about it, but the 136.92 hasn't moved significantly since about 800 spins. So I think I'm approaching something that has some confidence.

As for the overall probability of the grand, I actually think that is pretty simple to estimate based on some assumptions. For instance, if you're doing a $5 spin and the Grand resets at $10,000 and if 2% of each dollar goes towards the grand (excluding progressive meter rise), then the probability of winning is calculated by solving the following for x:

5 * 0.02 = 10000 * x ====> x = 1/100,000 ( if someone thinks this rather crude formula approach is absolutely wrong, let's discuss please.... I've based a lot of analysis on it)

I've been focused more on how many reel stops are there on the hard to get reel.. the one that spins and rarely shows an orb. I literally calculated a probability for every possible pathway to get to 15 orbs on Sahara Gold to figure this out. A massive amount of work.

I should also point out that if you read the instructions in each of the LL/DL games states that you can win a random Grand (or major) on any spin with 0-5 orbs. Obviously I have no way to know what that probability is, and I've essentially assumed it to be 0 in my calcs since I've not seen a pic or heard anyone on Youtube slots channels getting it.
rsactuary
rsactuary
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November 23rd, 2019 at 9:16:23 AM permalink
Based on initial posters assertion that there are 64 reels stops on the first four reels and 85 reel stops on the fifth reel, I get the following probabilities:

6 0.0057218018700
7 0.0018471493441
8 0.0005366661969
9 0.0001268653309
10 0.0000289019416
11 0.0000056771671
12 0.0000008807463
13 0.0000001262216
14 0.0000000140246
15 0.0000000007012 <--- awards Grand immediately.. No H&S feature
0.00826808354434 Hold and Spin feature approximately once every 120.95 paid spins

Or the instant grand about once every 1.426 billion spins. The poster doesn't say anything about RTP of the machine and it absolutely could vary from the machine I play.

Edited to fix a mistake. My observed spins do not follow the pattern as suggested by the OP, so I have some doubt about his assumptions about frequency of orbs.
Last edited by: rsactuary on Nov 23, 2019
rsactuary
rsactuary
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November 23rd, 2019 at 9:20:14 AM permalink
My observations suggest that the reel mappings for my machine are different than what the original poster suggests.... see below.

Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Orbs
0 998 992 989 1034 1035
1 67 81 81 65 58
2 80 91 91 72 63
3 25 18 19 34 12

BS 130 118 120 95 132 <--- observed bonus symbol occurrences

TS 1300 1300 1300 1300 1300

Percentages

Reel 1 Reel 2 Reel 3 Reel 4 Reel 5
Orbs
0 76.769231% 76.307692% 76.076923% 79.538462% 79.615385%
1 5.153846% 6.230769% 6.230769% 5.000000% 4.461538%
2 6.153846% 7.000000% 7.000000% 5.538462% 4.846154%
3 1.923077% 1.384615% 1.461538% 2.615385% 0.923077%

Bonus Symbol 10.000000% 9.076923% 9.230769% 7.307692% 10.153846%

ETA: sorry this didn't format well.
p13man
p13man
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Thanks for this post from:
beachbumbabs
November 23rd, 2019 at 3:44:24 PM permalink
Quote: rdw4potus

Do you only care about 6 symbol triggers on lightning/dragon link? Or do you also have interest in lock it link (3 symbols) , fire link (4 symbols) , and mighty cash (5 symbols @ high denom)?



Ultimately, yes. But I don't yet have the reels for those other machines. So this exercise is about finding a repeatable formula for calculating the odds of triggering the lightning/dragon games. If anyone has developed that and is able to share, I'd be most gratefull. TIA.
p13man
p13man
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November 23rd, 2019 at 4:05:22 PM permalink
Quote: rsactuary

Based on initial posters assertion that there are 64 reels stops on the first four reels and 85 reel stops on the fifth reel, I get the following probabilities:

6 0.0057218018700
7 0.0018471493441
8 0.0005366661969
9 0.0001268653309
10 0.0000289019416
11 0.0000056771671
12 0.0000008807463
13 0.0000001262216
14 0.0000000140246
15 0.0000000007012 <--- awards Grand immediately.. No H&S feature
0.00826808354434 Hold and Spin feature approximately once every 120.95 paid spins

Or the instant grand about once every 1.426 billion spins. The poster doesn't say anything about RTP of the machine and it absolutely could vary from the machine I play.

Edited to fix a mistake. My observed spins do not follow the pattern as suggested by the OP, so I have some doubt about his assumptions about frequency of orbs.



Genius!

One in 120 feels about right and lines up with experience. Is that a difficult calculation?

I don't know the RTP - there are multiples that the operator can choose from.

The reels mentioned are from Autumn Moon (Aristocrat) but (and I will confirm) I think that the H&S symbol distribution is the same across the current clutch of Lightning/Dragon Cash games.

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