Lightning Link / Dragon Link type bonus game math

I’m curious how to figure out the math behind the Lightning Link type game bonus rounds. I thought I’d post some links to people who have hit the Grand, because I think it shows how these bonus games work, and then create a hypothetical situation and I’m hoping someone can figure this math out for me. (I’m more interested in the “how” of getting there).

https://www.youtube.com/watch?v=Iv_lBeQpbLg
The “grand” win starts at 8:30 in this video.

Here’s how I think these games work:

Assuming that it takes a spin with 6 pay symbols to trigger the bonus, there are 9 reels left with varying degrees of hit probability. It appears some could be as easy as 1 in 3, but there is always one cell where symbols rarely show up.. it might be 1 in 10000 or something like that. You can see that hard to hit reel in the above video:

Notice the following cell for each spin (numbering at 1 in the upper left and going across the rows):
Spin 1: Cell 1
Spin 2: Cell 6
Spin 3: Cell 1
Spin 4: Cell 1
Spin 5: Cell 13 (and it hit!)
Spin 6 and on: Notice that the symbols pass by frequently

Here’s another one
https://www.youtube.com/watch?v=BUl_i_tRZxA
The video where they hit the grand starts at 11:00

To see the "hard to get" reel, watch the following cells:
Spin 1: Cell 4
Spin 2: Cell 11
Spin 3: Cell 9
Spin 4: Cell 15
Spin 5: Cell 9 (although you can see a chip go by right after the button push)
Spin 6: Cell 9
Spin 7: Cell 5
Spin 8: Cell 9
Spin 9: Cell 4 (and the tough one hit!)
Spins 10+: Notice chips frequently passing by as the reels spin.

So there are 9 reels set up with varying probability and you can see from the videos that the reels get moved around during the bonus game.. so the “tough” reel is not always in the same spot. The tricky part of the math, I think, is the fact that if you hit a pay symbol, your spins counter goes back to 3.
So, for a theoretical game starting with 6 pay symbols each of unit 1, let’s say you have the following probabilities of hitting the unhit pay symbols, and to keep things easy, let’s say the value of each hit is “1” unit:
Reel 1: 1 in 3
Reel 2: 1 in 3
Reel 3: 1 in 3
Reel 4: 1 in 5
Reel 6: 1 in 5
Reel 7: 1 in 10
Reel 8: 1 in 30
Reel 9: 1 in 10000

So: my question to the mathies out there…. 1) What is the probability of hitting the grand in my theoretical game? 2) what is the expected win of a bonus game, assuming that if you win the grand, you win 10,000 units. Remember that after hitting one of the pay symbols, your remaining spins returns to 3. Please show your work, I’m more interested in that than the actual answer.

Sorry for the late arrival. I know almost nothing about this game, but am hearing more and more chatter about it. If anyone could dumb this down a bit, I'd appreciate it.

So, with that first video, it looked kind of like the Miss Kitty bonus, but with sticky flat prizes. Plus, sometimes it would add 3 to the extra spins remaining. If you covered the whole screen you got the Grand bonus. I guess my questions are:

1. How do you trigger the bonus?
2. What are the basic rules of this bonus?
3. What is the question being asked about it?

I've messed with the fire links a little when the mini is inflated. All the lightning links near me have fixed mini and minors. I can't imagine how long a grand cycle would be.

Quote: Wizard

1. How do you trigger the bonus?
2. What are the basic rules of this bonus?
3. What is the question being asked about it?

1. All these lock it games are different, but for the most part you get the feature by getting 6 lock symbols... That's how the game works that the OP described.

2. Those lock symbols stay and the reels turn into more reels for each position. You get 3 spins where you attempt to catch another lock symbol. Should you catch one, you get three more spins. When you spin 3 times and add 0 additional lock symbols, the bonus is over. At the end of the bonus, the machine adds up the totals on the lock symbols and that's what you win. On the off chance that you fill up all the spots with a lock symbol, you win the top jackpot.

Quote: Wizard

Sorry for the late arrival. I know almost nothing about this game, but am hearing more and more chatter about it. If anyone could dumb this down a bit, I'd appreciate it.

So, with that first video, it looked kind of like the Miss Kitty bonus, but with sticky flat prizes. Plus, sometimes it would add 3 to the extra spins remaining. If you covered the whole screen you got the Grand bonus. I guess my questions are:

1. How do you trigger the bonus?
2. What are the basic rules of this bonus?
3. What is the question being asked about it?

For lightning links:

2 ways to trigger the bonus.

A) get at least 6 links (they have dollar amounts or mini/minor/major on them) scattered among the 15 symbols on any spin.

B) during free spins, (3 or more bonus symbols earns 6 spins), reel 1 is 3 symbols, reels 2-3-4 are a giant 3x3 symbol, reel 5 is 3 symbols. Get the giant link symbol (it will have a single dollar value), and the links game will start within that free spin. The giant link counts for 9 link symbols, but that single dollar value towards the bonus total.

............

Whichever type spin activates it, you start with 3 free spins. You're trying to fill the board with 15 symbols. The symbols carry over on each spin.

Each time you get at least 1 more link symbol, the spins reset to 3 more. If you get 3 spins in a row with no additions (which happens virtually every time short of 15), the totals on the symbols get added up to your bonus total, and the bonus is over.

If you get all 15 symbols filled with links, you win the Grand jackpot, usually $10k or more on .01 denom. You do not have to max bet to get the bonus game or the dollar totals on the progressives.

Here's a video that shows how the game plays with a bonus triggered at about 4:10:
https://www.youtube.com/watch?v=ejYYq_Shxa0

As Babs mentioned, there are two types of bonuses: 1) the free spins bonus, where three scattered symbols (flags in the first game of this video) gets you 6 free spins. and 2) the "hold and spin" feature which is really the subject of my question.

As part of the normal game, the "orbs" or fireball symbols with numbers on them are just blockers.. until you get at least 6 of them, at which time it triggers the hold and spin feature and you're going to win the amounts listed on the coins (if betting $$, you win the amounts shown, if betting under dollars, it shows the number of coins you will win).

Babs: Saturday night after leaving the GN, I hit a Grand at the El Cortez for $12,700!

What I'm really looking for is based on the simple game that I proposed, what is the average number of games it would take for the jackpot to hit. I'm trying to put some sort of range around how big the "hard" reel is.

Quote: rsactuary

What I'm really looking for is based on the simple game that I proposed, what is the average number of games it would take for the jackpot to hit. I'm trying to put some sort of range around how big the "hard" reel is.

A sample size to determine that information would be extremely hard to achieve. Just from watching the game in passing a few times (and has been confirmed by others) you often don't even see the symbol by the time you get to the last spot. Furthermore, it's not representative in any way of any card, dice or wheel game, so there is no requirement (even in Nevada) that it has to adhere to any strict probabilities, I wouldn't think.

I believe (but could be wrong) that the whole entire thing might just be a show and the free spins decide how much you are going to win (in total) before the extras even start spinning. Long story short, you'd need a huge sample size consisting of only the extra spins to even hazard a guess.

Finally, it is almost certain that the event is going to be more likely with a Max Bet, that doesn't mean that the sample size must consist of Max Bets necessarily...but it would have to be of a uniform betting amount and likely on the same physical machine due to the possibility of different settings.

Quote: Mission146

so there is no requirement (even in Nevada) that it has to adhere to any strict probabilities, I wouldn't think.

I agree that anything we do would have a high degree of SWAG associated with it. I'm just really curious if it's a reel that's in the neighborhood of 1 in 1000, or 1 in 10000 or 1 in 100000. So very high level.

I think I disagree with your statement above though. Somehow they have to prove out the return of the game for the Nevada gaming board, and it's a class III machine ( in Nevada anyways) and so there has to be some rules with which they can calculate probabilities to prove out the return.

Having said all that, even if we can't get to some high level swag, I'm still curious how you'd even do the math to figure this out.

I'm not saying there aren't probabilities, if you somehow got ahold of a PAR Sheet, I'm sure you would find all the different possible configurations and probabilities associated therewith on there. I'm just saying it would take forever plus three days to do any kind of meaningful Empirical.

ADDED: When I said, "Dice," I mean a visual representation of dice has to adhere to the probabilities of real dice in Nevada. This game is not a visual representation of anything.

If I was going to offer a guess, the probably of filling the screen with lock symbols is so low the payback % of the grand is not meaningful to the total RTP for the game.

I never said I was looking to AP it. Seriously, is anyone else just curious about how the math works behind this??

Naturally! It would take a PAR sheet to know exactly or an Empirical to hazard an educated guess...AP or not.

Quote: rsactuary

Here's a video that shows how the game plays with a bonus triggered at about 4:10:
https://www.youtube.com/watch?v=ejYYq_Shxa0

As Babs mentioned, there are two types of bonuses: 1) the free spins bonus, where three scattered symbols (flags in the first game of this video) gets you 6 free spins. and 2) the "hold and spin" feature which is really the subject of my question.

As part of the normal game, the "orbs" or fireball symbols with numbers on them are just blockers.. until you get at least 6 of them, at which time it triggers the hold and spin feature and you're going to win the amounts listed on the coins (if betting $$, you win the amounts shown, if betting under dollars, it shows the number of coins you will win).

Babs: Saturday night after leaving the GN, I hit a Grand at the El Cortez for $12,700!

What I'm really looking for is based on the simple game that I proposed, what is the average number of games it would take for the jackpot to hit. I'm trying to put some sort of range around how big the "hard" reel is.

Wow! Nice hit, rsactuary! You're the first I've heard of to ever fill the screen. I wasn't sure if it was a come-on that never happened.

Quote: Wizard

2. What are the basic rules of this bonus?
3. What is the question being asked about it?

For the purposes of the question, the game rules are thus:

1. Game has 9 positions on a slot machine (or 9 dice, it does not matter; objective is the same)
2. Game is won by achieving a star symbol in each position.
3. Each position has its own probability of awarding star symbol, from 1/3 to 1/10000 (see original post for numbers).
4. Star symbols awarded during game are held during remaining spins.
5. Player gets three initial spins; if one or more winning symbols are awarded on any spin, spins remaining count resets to three.
6. Game ends when player achieves all 9 star symbols or runs out of spins.

Under these rules, what is the probability of winning the game? I guess the other question would be what is the average number of symbols a player would expect to receive during the game.

Quote: itsmejeff

For the purposes of the question, the game rules are thus:

1. Game has 9 positions on a slot machine (or 9 dice, it does not matter; objective is the same)
2. Game is won by achieving a star symbol in each position.
3. Each position has its own probability of awarding star symbol, from 1/3 to 1/10000 (see original post for numbers).
4. Star symbols awarded during game are held during remaining spins.
5. Player gets three initial spins; if one or more winning symbols are awarded on any spin, spins remaining count resets to three.
6. Game ends when player achieves all 9 star symbols or runs out of spins.

Under these rules, what is the probability of winning the game? I guess the other question would be what is the average number of symbols a player would expect to receive during the game.

1. It's 15 spots of which *at least* 6 are filled from the winning spin.. leaving at most 9 open spots.

Please note that my example I listed in the OP is a theoretical one and does not indicate actual probabilities.

Again, just a guess but I suspect the way this feature really works is that the probably of catch a lock symbol gets lower based on the number of locked symbols. E.g. all open spots have the same probably but that changes each time a symbol locks.

Quote: prozema

Again, just a guess but I suspect the way this feature really works is that the probably of catch a lock symbol gets lower based on the number of locked symbols. E.g. all open spots have the same probably but that changes each time a symbol locks.

I don't believe that to be the case. If you watch the videos in my OP, I point out that the difficult to hit reel is always there. I think they move the reels around between spins to give that impression.

Guilty... I didn't watch the video.

Curious if the probability of hitting the grand is somehow effected (or even correlated) by how much you’re betting? Rsactuary, How much were you betting per spin? (If you don’t mind sharing, that is.) I saw these and couldn’t help but ask myself if it’s better to min bet on dimes or max bet on pennies or 2c (or whatever is the equivalent.)

Good question.. I really don't know the answer.. but I have a suspicion.....

I suspect between denomination levels there is some difference; as the higher the denomination, usually the higher the return. Within a denomination, when betting the number of coins, I would guess that the hard reel (and maybe the others as well??) the length would be some how related to amount bet.

So.. and I'm totally making this up... if you're betting $10 on a $1 denom machine, the hard reel is about 1 in 5000 to hit. if you're betting $5 on a $1 denom machine, the hard reel is about 1 in 10000 to hit. That would be the only way you could come close to making sure the RTP is about constant. (of course they could have the EV of the feature be the same, and just make it harder to hit).