Maths Genius?

[Tropicana50]

It has long been hailed as one of the most difficult bonuses to achieve. The Bruce Lee 1 double bonus is something that some of the hardiest of gamblers havn't even achieved. I know from previous forum posts that many users (including myself!) would love to know the mathematical odds of getting such a bonus...

I was wondering if we have anyone who wants to have a shot at working out the odds of getting this feature. (4 held symbols + 3 chests). I have spent the last few hours compiling the reel layout for the game, however the next part requires a little input from someone with more maths knowledge then I.

The reel layout PDF is in the link below. The 4 symbols on the left side all spin individually but the left side and the right side have the same reel layouts.

Reel Layout: Old / Expired Link

- T

 

[KasinoKing]

Do we know for sure that this slot runs by producing a "truly random" reel stop?
Most WMS slots are "gimped" and so I always assumed this one was no different.

If it is truly random, then you're right - you really would need a maths genius!
If it was just triggered by scatter symbols I could work it out - but as the first 4 symbols can be ANY matching ones - it makes it WAY more difficult.
The chests part is easy enough.

KK

 

[dunover]

WMS have 'gimped' reels. Bruce Lee has 'tells' when the bonus drops in with the slow spin, as Chopley used to point out. Same on Rogering Rhino, when you are going to get the 3 or 4 wilds in FS the reels spin oddly and very deliberately pick out the win, as happens in normal play with a big combo. I think as with MG the result is decided by the RNG as soon as you press start, and the graphics then appear very clumsy afterwards.

As KK says the last 3 reels is easier to work out as only 3 chests-outcome is required. The first 4 are the issue.
The calculation starts with 1/1 (any symbol on first reel) x the chances of hitting same/wild on the second and so-on. Unfortunately you will have a separate calculation necessary starting with EVERY different symbol on reel one! What I would do is take the most common low-value symbol on reel 1 along with wilds, and do THAT specific calculation through the slot. Then do the hardest (dream hit-4 wilds only) and repeat. This will give you the 2 extremes. Anything else obviously in the middle.

P.S. Are you sure those reels are correct - if so you can't get more than 2 wilds in first 4 boxes. Or does reel 1 fill both the left 2 boxes, and reel 2 fill both the right 2 boxes of the 4?? I'm pretty sure I've seen 3 wilds in the first 4 boxes, or am I mistaken?

 

[Tropicana50]

WMS have 'gimped' reels. Bruce Lee has 'tells' when the bonus drops in with the slow spin, as Chopley used to point out. Same on Rogering Rhino, when you are going to get the 3 or 4 wilds in FS the reels spin oddly and very deliberately pick out the win, as happens in normal play with a big combo. I think as with MG the result is decided by the RNG as soon as you press start, and the graphics then appear very clumsy afterwards.

As KK says the last 3 reels is easier to work out as only 3 chests-outcome is required. The first 4 are the issue.
The calculation starts with 1/1 (any symbol on first reel) x the chances of hitting same/wild on the second and so-on. Unfortunately you will have a separate calculation necessary starting with EVERY different symbol on reel one! What I would do is take the most common low-value symbol on reel 1 along with wilds, and do THAT specific calculation through the slot. Then do the hardest (dream hit-4 wilds only) and repeat. This will give you the 2 extremes. Anything else obviously in the middle.

P.S. Are you sure those reels are correct - if so you can't get more than 2 wilds in first 4 boxes. Or does reel 1 fill both the left 2 boxes, and reel 2 fill both the right 2 boxes of the 4?? I'm pretty sure I've seen 3 wilds in the first 4 boxes, or am I mistaken?

The reels are correct. I screen recorded the spins and then frame by frame collected the reel data into a spreadsheet and then constructed the graphics.

Based on these reels you can get a wild in all 4 boxes, it is just very rare.

The top left hand side had a 1/35 chance of being a wild.
The bottom left hand side had a 1/35 chance of being a wild.
The top right hand side had a 1/31 chance of being a wild.
The bottom right hand side had a 1/31 chance of being a wild.

You have to remember that the left and right reels actually spin as individual reels, so each corner spins separately, not as one whole reel. Hope this makes sense.

- T

 

[Tropicana50]

For the dream result (4 wilds + bonus) this is what I get, but I am unsure of how to get this into a final percentage/fraction, any ideas? If someone can help with that then I can do the same for all outcomes and then get an average percentage.

2.9% chance of wild landing in top left (1/35)
2.9% chance of wild landing in bottom left (1/35)
3.2% chance of wild landing in top right (1/31)
3.2% chance of wild landing in bottom right (1/31)

23.5% chance of bonus landing in reel 1 (4/17)
16.4% chance of bonus landing in reel 2 (12/73)
18.8% chance of bonus landing in reel 3 (3/16)

- T

 

[KasinoKing]

The top left hand side had a 1/35 chance of being a wild.
The bottom left hand side had a 1/35 chance of being a wild.
The top right hand side had a 1/31 chance of being a wild.
The bottom right hand side had a 1/31 chance of being a wild.

Yeah, that bit is quite easy: the chances of getting 4 wilds is 35x35x31x31 = once in 1,177,225 spins.
That is also therefore the number of possible combinations of the first 4 positions (as there is only 1 wild per reel).

Now you have your first answer: number of 4 wild combinations is 1x1x1x1 = 1
So all you have to do, is the same sum for all the different symbols on the first two reel-strips (remembering to count repeated symbols and a wild in each combination), add them all together and divide into 1,177,225. That gives you the chances of 4 the same in the first 4 spots.

Use the same maths to work out the chances of getting 3 chests (remembering that each chest can land in 4 positions).
Multiply them together, and you have the odds of getting the "dream" trigger.

This all assumes the slot is "truly random" without gimped reels. I suppose it is possible that some WMS slots are constructed different to others - just the same as with MG.

KK

 

[dunover]

Right, your 'perfect' trigger 4 wilds and 20 spins is 160,002,535-1 I.E. you should achieve it 6 times in every 1 BILLION games!

 

[Tropicana50]

Yeah, that bit is quite easy: the chances of getting 4 wilds is 35x35x31x31 = once in 1,177,225 spins.
That is also therefore the number of possible combinations of the first 4 positions (as there is only 1 wild per reel).

Now you have your first answer: number of 4 wild combinations is 1x1x1x1 = 1
So all you have to do, is the same sum for all the different symbols on the first two reel-strips (remembering to count repeated symbols and a wild in each combination), add them all together and divide into 1,177,225. That gives you the chances of 4 the same in the first 4 spots.

Use the same maths to work out the chances of getting 3 chests (remembering that each chest can land in 4 positions).
Multiply them together, and you have the odds of getting the "dream" trigger.

This all assumes the slot is "truly random" without gimped reels. I suppose it is possible that some WMS slots are constructed different to others - just the same as with MG.

KK

There shouldn't be a need to gimp the reels unless something strange is going on. You should be able to build the maths directly into the reel strips. I assume slow downs and wacky things happen when events are about to occur are due to the flash client reacting to what is about to happen rather than it changing the reel strip event.

Any ideas on that above post?

- T

 

[KasinoKing]

Any ideas on that above post?

I haven't the faintest idea where he got that figure from... or what the "20 spins" means...

KK

 

[Tropicana50]

Right, your 'perfect' trigger 4 wilds and 20 spins is 160,002,535-1 I.E. you should achieve it 6 times in every 1 BILLION games!

So in theory the dream hit is 1 / 166,666,666?

These are the odds for the knife symbol (lowest paying symbol, including wild):

14.3% chance of knife/wild landing in top left (5/35)
14.3% chance of knife/wild landing in bottom left (5/35)
9.7% chance of knife/wild landing in top right (3/31)
9.7% chance of knife/wild landing in bottom right (3/31)

23.5% chance of bonus landing in reel 1 (4/17)
16.4% chance of bonus landing in reel 2 (12/73)
18.8% chance of bonus landing in reel 3 (3/16)

- T

 

[dunover]

I haven't the faintest idea where he got that figure from... or what the "20 spins" means...

KK

Your maths boys! I'm referring to the 20 spins trigger, getting 4 wilds in the 2x2 plus 3 treasure chests. Simply use your odds of 1,177,225 (correct) and work out the odds of 3 treasure chests into proper whole numbers (the first for example is 4.25x=4/17) and there you go! Simples.

 

[Tropicana50]

Your maths boys! I'm referring to the 20 spins trigger, getting 4 wilds in the 2x2 plus 3 treasure chests. Simply use your odds of 1,177,225 (correct) and work out the odds of 3 treasure chests into proper whole numbers (the first for example is 4.25x=4/17) and there you go! Simples.

So if I am doing this correctly, even the knife hit odds (+ bonus) are approximately 1/588,000?

(That's 7x7x10x10 = 4900 for the knives/wilds and then the 4.25x6x5 for the bonus)

-T

 

[dunover]

Your bonus (3 x chests calculation) is always the same obviously - in proper numbers it is:

4.25 x 6.0833 x 5.2 = 134.44093.

So any odds you conjure for the first 2x2 4-reels always multiply x 134.44093.

I.E. 1,177,225 (4 WILDS) X 134.44093 = 158,267.223/1 (I've done it more accurately this time instead of rounding)

Your most common symbols in the 2x2 reels are crossed-swords/wilds.

Put it this way, playing the slot at 15 spins a minute, you would need to play 24/7 for 1047 days to hit it, or 2.87 years.....

 

[Chipkin9]

The reels are correct. I screen recorded the spins and then frame by frame collected the reel data into a spreadsheet and then constructed the graphics.

Based on these reels you can get a wild in all 4 boxes, it is just very rare.

The top left hand side had a 1/35 chance of being a wild.
The bottom left hand side had a 1/35 chance of being a wild.
The top right hand side had a 1/31 chance of being a wild.
The bottom right hand side had a 1/31 chance of being a wild.

You have to remember that the left and right reels actually spin as individual reels, so each corner spins separately, not as one whole reel. Hope this makes sense.

- T

I don't know where you are getting the 1/35 chance and 1/31 chance of the 4 wilds on the 1st set of reels are but I think they are wrong.

My maths might be wrong but on the first 2 sets of reels there are 4 "symbol spots".

There are 12 possible symbols that can fill these reels (Since the chest is the 13th symbol but isn't included on these 1st 2 reels).

Therefore, your chance of hitting the wild on the 4 reels are as follows.

12 to the power of 4.

Since there is a 1 in 12 chance of it hitting on the top left, 1 in 12 chance of it hitting on the top right, 1 in 12 chance of it hitting on the bottom left and 1 in 12 chance of it hitting on the bottom right.

So that is: 12 x 12 x 12 x 12 = 20736.

So your actual odds of hitting wild on the 1st 4 reels is 1 in every 20736 spins; and it is therefore the same odds for every symbol.

 

[Tropicana50]

Ok, so, this is what I have so far..

Old Attachment (Invalid)
Bonus odds = 1 / 134 (4.25 x 6.083 x 5.2)


Knife odds = 1 / 5,232 (7 x 7 x 10.333 x 10.333)
Knife odds with bonus = 1 / 702,956 (7 x 7 x 10.333 x 10.333 x 134.44093)


Sword odds = 1/ 1,614 (3.888 x 3.888 x 10.333 x 10.333)
Sword odds with bonus = 1/ 216,988 (3.888 x 3.888 x 10.333 x 10.333 x 134.44093)


Star Odds = 1 / 6,005 (17.5 x 17.5 x 4.428 x 4.428)
Star Odds with bonus = 1 / 807,277 (17.5 x 17.5 x 4.428 x 4.428 x 134.44093)


Nun-chucks Odds = 1 / 2,043 (8.75 x 8.75 x 5.166 x 5.166)
Nun-chucks Odds with bonus = 1 / 274,698 (8.75 x 8.75 x 5.166 x 5.166 x 134.44093)

Old Attachment (Invalid)
Vase odds = 1 / 6,006 (5 x 5 15.5 x 15.5)
Vase odds with bonus = 1 / 807,486 (5 x 5 15.5 x 15.5 x 134.44093)

Old Attachment (Invalid)
Scroll odds = 1 / 4,599 (8.75 x 8.75 x 7.75 x 7.75)
Scroll odds with bonus = 1 / 618,231 (8.75 x 8.75 x 7.75 x 7.75 x 134.44093)

Old Attachment (Invalid)
Coins odds = 1 / 8,174 (11.666 x 11.666 x 7.75 x 7.75)
Coins odds with bonus = 1 / 1,098,952 (11.666 x 11.666 x 7.75 x 7.75 x 134.44093)

Old Attachment (Invalid)
Bowl odds = 1 / 18,394 (8.75 x 8.75 x 15.5 x 15.5)
Bowl odds with bonus = 1 / 2,472,925 (8.75 x 8.75 x 15.5 x 15.5 x 134.44093)

Old Attachment (Invalid)
Green dragon odds = 1 / 18,394 (17.5 x 17.5 x 7.75 x 7.75)
Green dragon odds with bonus = 1 / 2,472,925 (17.5 x 17.5 x 7.75 x 7.75 x 134.44093)

Old Attachment (Invalid)
Purple Bruce = 1 / 18,394 (17.5 x 17.5 x 7.75 x 7.75)
Purple Bruce with bonus = 1 / 2,472,925 (17.5 x 17.5 x 7.75 x 7.75 x 134.44093)

Old Attachment (Invalid)
Bruce logo = 1 / 73,577 (17.5 x 17.5 x 15.5 x 15.5)
Bruce logo with bonus = 1 / 9,891,701 (17.5 x 17.5 x 15.5 x 15.5 x 134.44093)

Old Attachment (Invalid)
Wilds = 1 / 1,177,225 (35 x 35 x 31 x 31)
Wilds with bonus = 1 / 158,267,224 (35 x 35 x 31 x 31 x 134.44093)

- T

 

[Tropicana50]

I don't know where you are getting the 1/35 chance and 1/31 chance of the 4 wilds on the 1st set of reels are but I think they are wrong.

My maths might be wrong but on the first 2 sets of reels there are 4 "symbol spots".

There are 12 possible symbols that can fill these reels (Since the chest is the 13th symbol but isn't included on these 1st 2 reels).

Therefore, your chance of hitting the wild on the 4 reels are as follows.

12 to the power of 4.

Since there is a 1 in 12 chance of it hitting on the top left, 1 in 12 chance of it hitting on the top right, 1 in 12 chance of it hitting on the bottom left and 1 in 12 chance of it hitting on the bottom right.

So that is: 12 x 12 x 12 x 12 = 20736.

So your actual odds of hitting wild on the 1st 4 reels is 1 in every 20736 spins; and it is therefore the same odds for every symbol.

You need to look at the reel sheets I posted on the first page. Each reel does not have an equal number of each symbol on them.

- T

 

[Chipkin9]

You need to look at the reel sheets I posted on the first page. Each reel does not have an equal number of each symbol on them.

- T

Ah, ok.

I was going on the assumption that the reels had an equal number of each symbol.

I don't play WMS, I just played on demo to try and help out

EDIT: The odds must be really incredible then if not.

 

[Chipkin9]

Ok, so, this is what I have so far..

Old Attachment (Invalid)
Bonus odds = 1 / 134 (4.25 x 6.083 x 5.2)

View attachment 51945
Knife odds = 1 / 5,232 (7 x 7 x 10.333 x 10.333)
Knife odds with bonus = 1 / 702,956 (7 x 7 x 10.333 x 10.333 x 134.44093)

View attachment 51946
Sword odds = 1/ 1,614 (3.888 x 3.888 x 10.333 x 10.333)
Sword odds with bonus = 1/ 216,988 (3.888 x 3.888 x 10.333 x 10.333 x 134.44093)

View attachment 51947
Star Odds = 1 / 6,005 (17.5 x 17.5 x 4.428 x 4.428)
Star Odds with bonus = 1 / 807,277 (17.5 x 17.5 x 4.428 x 4.428 x 134.44093)

View attachment 51948
Nun-chucks Odds = 1 / 2,043 (8.75 x 8.75 x 5.166 x 5.166)
Nun-chucks Odds with bonus = 1 / 274,698 (8.75 x 8.75 x 5.166 x 5.166 x 134.44093)

Old Attachment (Invalid)
Vase odds = 1 / 6,006 (5 x 5 15.5 x 15.5)
Vase odds with bonus = 1 / 807,486 (5 x 5 15.5 x 15.5 x 134.44093)

Old Attachment (Invalid)
Scroll odds = 1 / 4,599 (8.75 x 8.75 x 7.75 x 7.75)
Scroll odds with bonus = 1 / 618,231 (8.75 x 8.75 x 7.75 x 7.75 x 134.44093)

Old Attachment (Invalid)
Coins odds = 1 / 8,174 (11.666 x 11.666 x 7.75 x 7.75)
Coins odds with bonus = 1 / 1,098,952 (11.666 x 11.666 x 7.75 x 7.75 x 134.44093)

Old Attachment (Invalid)
Bowl odds = 1 / 18,394 (8.75 x 8.75 x 15.5 x 15.5)
Bowl odds with bonus = 1 / 2,472,925 (8.75 x 8.75 x 15.5 x 15.5 x 134.44093)

Old Attachment (Invalid)
Green dragon odds = 1 / 18,394 (17.5 x 17.5 x 7.75 x 7.75)
Green dragon odds with bonus = 1 / 2,472,925 (17.5 x 17.5 x 7.75 x 7.75 x 134.44093)

Old Attachment (Invalid)
Purple Bruce = 1 / 18,394 (17.5 x 17.5 x 7.75 x 7.75)
Purple Bruce with bonus = 1 / 2,472,925 (17.5 x 17.5 x 7.75 x 7.75 x 134.44093)

Old Attachment (Invalid)
Bruce logo = 1 / 73,577 (17.5 x 17.5 x 15.5 x 15.5)
Bruce logo with bonus = 1 / 9,891,701 (17.5 x 17.5 x 15.5 x 15.5 x 134.44093)

Old Attachment (Invalid)
Wilds = 1 / 1,177,225 (35 x 35 x 31 x 31)
Wilds with bonus = 1 / 158,267,224 (35 x 35 x 31 x 31 x 134.44093)

- T

Seems you got it figured then.

1 / 158,267,224

You could play a lifetime and never hit that bad boy.

 

[Tropicana50]

Seems you got it figured then.

1 / 158,267,224

You could play a lifetime and never hit that bad boy.

We have it mostly figured, but we still don't have an overall 1 / X chance of getting a held bonus + chests per spin. We just have the odds for each symbol.

Big thanks to Dunover and Kasinoking btw

- T

 

[Wild Reels]

great work in this thread, i had a look at some of the data, looking at the maths from a different angle,

using the BRUCE LEE symbol there are 15 different combinations including wilds that trigger the first part of the bonus (but not including the 4 wilds trigger).

essentially that's 15/1,177,225 approx 1/78482

slighter higher than your figure for the bruce lee symbols, but from the looks of your calculations its also including the trigger for 4 wilds in each of those, i.e 16/1,177,225

given there is a separate entry trigger for 4 wilds i presume the figures are all out by 1.

the overall chance should be all these figures then averaged out i presume.

my head is already hurting, but great work.

 

[dunover]

We have it mostly figured, but we still don't have an overall 1 / X chance of getting a held bonus + chests per spin. We just have the odds for each symbol.

Big thanks to Dunover and Kasinoking btw

- T

Good summary by the way, all based on the assumption you have double-checked your reel-maps and they are ALL 100% correct!

So we have the odds for all the individual symbol scenarios.

To get the overall odds for ANY 20-spins trigger is easy.

Simply add up all your figures for the first 2x2 reels being the same and divide by the number of different symbols. As you/we've already included wilds in the calculations for each symbol it will come out correct. This will give the average odds for getting it. Obviously this will be higher than the odds for getting the crossed-swords lowest-entry into the 20 spins so is misleading - it cannot be higher!

So you need to take the 1177250 possible permutations of the first 4 reels, and then add up ALL the possible combos of 4 the same from your symbols data. Then 1177250 divided by this total will give you a number to multliply by the 134.

P.S. Now done this! Here is your final odds:

https://www.casinomeister.com/forums/threads/maths-genius.65510/

 

[Tropicana50]

great work in this thread, i had a look at some of the data, looking at the maths from a different angle,

using the BRUCE LEE symbol there are 15 different combinations including wilds that trigger the first part of the bonus (but not including the 4 wilds trigger).

essentially that's 15/1,177,225 approx 1/78482

slighter higher than your figure for the bruce lee symbols, but from the looks of your calculations its also including the trigger for 4 wilds in each of those, i.e 16/1,177,225

given there is a separate entry trigger for 4 wilds i presume the figures are all out by 1.

the overall chance should be all these figures then averaged out i presume.

my head is already hurting, but great work.

Yes, you are correct. There will be a slight offset due to including the 4 wild setup within the results, good spot. However, we are getting slightly closer to getting an overall odds per spin of the double bonus occurring, even if its approximate right now.

- T

 

[dunover]

great work in this thread, i had a look at some of the data, looking at the maths from a different angle,

using the BRUCE LEE symbol there are 15 different combinations including wilds that trigger the first part of the bonus (but not including the 4 wilds trigger).

essentially that's 15/1,177,225 approx 1/78482
slighter higher than your figure for the bruce lee symbols, but from the looks of your calculations its also including the trigger for 4 wilds in each of those, i.e 16/1,177,225

given there is a separate entry trigger for 4 wilds i presume the figures are all out by 1.

the overall chance should be all these figures then averaged out i presume.

my head is already hurting, but great work.

Sorry, you're horrendously out there. There are thousands of combos on the first 4 reels that can trigger the first part of the bonus, not just 15! Put it this way, if there were just 15 you'd likely never see it and yet you know (if you play it) you'll get the first 4 matching two or three times in any session at least.

 

[Wild Reels]

read it again slowly ive checked the maths for 1 trigger type only the bruce lee symbol

 

[dunover]

read it again slowly ive checked the maths for 1 trigger type only the bruce lee symbol

Yes, you did (apologies) and in 2 minutes I will confirm that - just a teaser, there are 2520 possibilities....