???? 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?

It did include the orig bet... Didn't see that it returned the bet at first . My bad (too bad it wasn't programmed a 2.16 payout )

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.

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.

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 only 1 6 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

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... >

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.

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