Progressive Craps - Six Sixes

Discussion in 'Prop Bets & Side Bets' started by Jacob, Feb 23, 2015.

  1. goatcabin, Feb 24, 2015

    goatcabin

    goatcabin Member

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    ????
    64.8 / 30 = 2.16
    29 / 25 = 1.16

    Do they "pay" in fractions of a dollar? If so,
    30 * 29 / 25 = 34.8.
    Is this just a typo?
     
    #21
  2. Morgue, Feb 24, 2015

    Morgue

    Morgue Member

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    The figure must include the $30 outlay returning
     
    #22
  3. Dogalot, Feb 25, 2015

    Dogalot

    Dogalot Member

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    It did include the orig bet... Didn't see that it returned the bet at first . My bad :oops::eek: (too bad it wasn't programmed a 2.16 payout ;) )
     
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    Last edited: Feb 25, 2015

  4. FredP

    FredP Member

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    The probability of a 6 on 1 die is 1/6. Raise that to the sixth power and divide it into 1 to get 47847. Thats how much the payoff should be to have true odds.

    Fred

    Make that about 46296. The decimals count when you get to higher powers.
     
    #24
    Last edited: Feb 25, 2015
  5. goatcabin, Feb 25, 2015

    goatcabin

    goatcabin Member

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    You are overlooking the other payouts for 4 and 5 sixes. I think Sally's numbers are correct.
     
    #25
  6. The Midnight Skulker, Feb 25, 2015

    The Midnight Skulker

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    As do I. I did some preliminary analysis thinking it would be similar to one I did to update Don Catlin's figures for Powerball in his book on lotteries. Turns out not to be that simple; lottery numbers are drawn without replacement while die rolls are basically numbers drawn with replacement. Sally's numbers looked reasonable and added up to what they should add up to so I opted to leave that wheel unreinvented.
     
    #26
  7. MustangSally, Feb 25, 2015

    MustangSally

    MustangSally Member

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    only looked reasonable

    I did them real fast

    after I listed all 46,656 possible sequences and had Excel count the ways
    maybe there are errors in there?
    How would one really know?

    I mean combinations with dice is simple math, in my opinion
    I showed a few ways of getting the 6s, well for all 6,5 4 and 3 of them

    we can do 0 6s right now too
    5 ways each die could NOT be a 6
    5*5*5*5*5*5
    6 dice
    15,625

    for just 1 6 from 6d6
    1 die has to be a 6 and ther are 6 dice
    1*6
    and 5 dice can be the other 5 numbers and not a 6
    5*5*5*5*5 = 3,125
    1*6*3,125 = 18,750

    I leave you to show the work for 2
    ====================================
    anyways, this still may not be right
    ====================================
    how about a simple example for those that come here later
    2 dice craps (ok)

    my bet I call
    "Super 6" (yes there are other "supers" too

    a one roll bet
    if the next roll shows just one 6 from 2 dice
    you win 2 to 1 on your bet
    with both dice showing 6s (the 12) you win 5 to 1 on your bet
    no 6s, you lost the bet

    this bet is offered between 6am to 7am and 6pm to 7pm at Sally's Casino and Sex Shoppe
    all other hours the double 6s (guys love double Ds, yes)
    pays 4.5 to 1

    (yes I hear on the strip they only pays 4 to 1)

    now, what is the HA on this bet?
    any takers??


    one could easily list all permutations of rolling 2 dice
    OK
    then count the ways
    OK
    then see if the math works too
    OK

    well here they are
    no 6s in light red
    [​IMG]
    only 1 6
    [​IMG]
    both 6s
    we can see just 1

    now the math

    for 0 6s
    5*5
    why?
    because the 1st die has 5 non-6s
    so does the 2nd die
    5*5 = 25
    checks out!

    just 1 6s
    1 die has to be a 6
    the other die has the 5 ways of not being a 6 and the 6 could be one of two dice
    1*5*2 = 10
    another check

    the math is nice
    I now know my results for 6 dice are 100% correct
    time for skittles

    what about the HA on the Super Six Bet?
    let me know
    I be back laters

    Sally
     
    #27
  8. goatcabin, Feb 26, 2015

    goatcabin

    goatcabin Member

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    I have verified columns J, K and L. Column I is really irrelevant, as it uses the specific order of different dice outcomes. The column-J numbers are based on combinations, not permutations. For example, row zero is just .83333^6, row 1 is (.833333^5 X .166667 X 6) not X 18750. etc. etc. The combinations numbers are 1, 6, 15, 20, 15, 6 and 1, as Sally has shown some of.

    Now, if we had six dice of different colors... >:)
     
    #28
  9. The Midnight Skulker, Feb 26, 2015

    The Midnight Skulker

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    I was bored to tears today so I also verified Sally's numbers, though my approach was a little different. Being as we are, in effect, drawing numbers with replacement it does not matter whether we roll six dice all at once or one die six times and record the results.

    In my experience Probability and Statistics textbooks have an affinity for opaque urns containing balls of various colors. Hence I translated the problem into that environment: six urns each containing one black and five white balls.
     
    #29
  10. MustangSally, Feb 26, 2015

    MustangSally

    MustangSally Member

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    nice
    you used the binomial probability distribution (Pascal's triangle) and got the same results as I did while I used a different method
    That is the beauty of math
    not always one way to arrive at the correct answer

    and 18750 (5^5 * 6)
    is the total number of ways out of 6^6 total sequences
    of getting exactly 1 6s using 6d6
    (I did list all of them where {1,2,3,4,5,6} is different from {6,5,4,3,2,1}
    for me order matters, for you it did not (but I already had the list to view)

    ok
    the probability = (18,750 / 46,656) = (.833333^5 X .166667 X 6)
    or
    mine = yours

    so you going to make my "Super Six" bet?
    that has lots of player action

    when one says Super Six fast at a loud craps table,
    like when betting $600 on the Place 6,
    everyone thinks you said
    Super Sex

    sure why not
    Sally
     
    #30
  11. Morgue, Feb 27, 2015

    Morgue

    Morgue Member

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    Especially with a New Zealand accent.
     
    #31