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Maths Genius?

Discussion in 'Online Casinos' started by Tropicana50, Jan 10, 2015.

    Jan 10, 2015
  1. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    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: You must register/login in order to see the link.

    - T
     
    1 person likes this.
  2. Jan 10, 2015
  3. KasinoKing

    KasinoKing WebMeister & Slotaholic.. CAG MM PABnonaccred webmeister

    Occupation:
    House-Husband and Casino Advisor
    Location:
    Bexhill on sea, England
    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
     
  4. Jan 10, 2015
  5. dunover

    dunover Unofficial T&C's Editor Staff Member CAG PABnononaccred PABnonaccred PABinit mm3 webmeister

    Occupation:
    International Money Launderer
    Location:
    the bus shelter, opposite GCHQ Benhall
    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?
     
    Last edited: Jan 10, 2015
  6. Jan 10, 2015
  7. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    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
     
    1 person likes this.
  8. Jan 10, 2015
  9. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    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
     
  10. Jan 10, 2015
  11. KasinoKing

    KasinoKing WebMeister & Slotaholic.. CAG MM PABnonaccred webmeister

    Occupation:
    House-Husband and Casino Advisor
    Location:
    Bexhill on sea, England
    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
     
  12. Jan 10, 2015
  13. dunover

    dunover Unofficial T&C's Editor Staff Member CAG PABnononaccred PABnonaccred PABinit mm3 webmeister

    Occupation:
    International Money Launderer
    Location:
    the bus shelter, opposite GCHQ Benhall
    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!
     
  14. Jan 10, 2015
  15. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    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
     
  16. Jan 10, 2015
  17. KasinoKing

    KasinoKing WebMeister & Slotaholic.. CAG MM PABnonaccred webmeister

    Occupation:
    House-Husband and Casino Advisor
    Location:
    Bexhill on sea, England
    I haven't the faintest idea where he got that figure from... or what the "20 spins" means... :confused:

    KK
     
  18. Jan 10, 2015
  19. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    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
     
  20. Jan 10, 2015
  21. dunover

    dunover Unofficial T&C's Editor Staff Member CAG PABnononaccred PABnonaccred PABinit mm3 webmeister

    Occupation:
    International Money Launderer
    Location:
    the bus shelter, opposite GCHQ Benhall
    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.
     
  22. Jan 10, 2015
  23. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    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
     
  24. Jan 10, 2015
  25. dunover

    dunover Unofficial T&C's Editor Staff Member CAG PABnononaccred PABnonaccred PABinit mm3 webmeister

    Occupation:
    International Money Launderer
    Location:
    the bus shelter, opposite GCHQ Benhall
    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.....
     
    1 person likes this.
  26. Jan 10, 2015
  27. Chipkin9

    Chipkin9 I'm not a Senior

    Occupation:
    Between Jobs
    Location:
    Tyrone, Ireland
    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.
     
  28. Jan 10, 2015
  29. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    Ok, so, this is what I have so far..

    [​IMG]
    Bonus odds = 1 / 134 (4.25 x 6.083 x 5.2)

    Maths Genius?: k.jpg,Jan 10, 2015
    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)

    Maths Genius?: c.jpg,Jan 10, 2015
    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)

    Maths Genius?: s.jpg,Jan 10, 2015
    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)

    Maths Genius?: n.jpg,Jan 10, 2015
    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)

    [​IMG]
    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)

    [​IMG]
    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)

    [​IMG]
    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)

    [​IMG]
    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)

    [​IMG]
    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)

    [​IMG]
    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)

    [​IMG]
    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)

    [​IMG]
    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
     
    2 people like this.
  30. Jan 10, 2015
  31. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    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
     
    1 person likes this.
  32. Jan 10, 2015
  33. Chipkin9

    Chipkin9 I'm not a Senior

    Occupation:
    Between Jobs
    Location:
    Tyrone, Ireland
    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.
     
  34. Jan 10, 2015
  35. Chipkin9

    Chipkin9 I'm not a Senior

    Occupation:
    Between Jobs
    Location:
    Tyrone, Ireland
    Seems you got it figured then.

    1 / 158,267,224

    You could play a lifetime and never hit that bad boy. ;)
     
  36. Jan 10, 2015
  37. Tropicana50

    Tropicana50 Senior Member

    Occupation:
    Programmer
    Location:
    England
    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 :thumbsup:

    - T
     
  38. Jan 11, 2015
  39. Wild Reels

    Wild Reels Meister Member webmeister

    Occupation:
    IT
    Location:
    United Kingdom
    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.
     

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