The marvelous thing about the game of craps is that you can bet with the house or against the house. You can wager that the players are going to win, or the casino is going to win, and either way, the house enjoys an advantage in the difference between the statistical probability of an outcome and the payout they offer for that outcome. I put myself through college and went on to law school with the income earned as a Nevada croupier, so this question brings me back to a time many long years ago.
You are correct that the statistical odds of a pair of dice rolling 6-1 (or 1-6) are 2/36 or 18 to 1 (that is, out of 36 possible combinations with a fair pair of dice, only 2 positives and 34 negatives). Betting on the combination is not always available on a craps layout (this is called a "hop bet"), but usually pays 14-1 or 15-1. Let's assume you find a table where the hop pays 14-1 and examine the advantage or disadvantage of the bet under the circumstances you present.
Before I delve into it, though, I have to ask, are you such a dedicated Pass/Come Line better that you are statistically disdvantaged by the 6-1, 1-6 combos? Why not capitalize on your knowledge, if you are convinced of its validity, and steadily wager "6-1 on the hop" on any table that is rolling BJ's? If it is true that they are rolling 9.6% or 9.8% of the time, instead of the statistical 5.556%, it sounds to me that you have the best bet in the entire State of Nevada! Player advantage on a combo that wins 9.8% of the time and loses 90.2%, but pays (at most houses) 14-1 is a quick way to get rich, right? Let's see. . . .
The expected return on a bet in craps is calculated by determining the probability of a win, and mulitplying that by the consequence (the payout), then adding the probability of a loss, mulitplied by the consequence (your buck is lost).
The probability of a win from a $1 bet on a 6-1 or 1-6 combo on any given roll (with fair, balanced dice) is 5.556% (2/36) and, thus, the probability of a loss is 94.444% (subtracting the win percentage from 100.000), resulting in a player disadvantage, assuming a payout of 14, of -16.66%. Pretty horrible bet! That is the kind of bet that builds those beautiful hotels and allows us Nevadans to have no income tax.
Change to the probability you have calculated and the formula becomes 0.098 * (14) + 0.902 * (-1) = 47%. WHAT?!? The player has a 47% advantage in the bet? That is completely unheard of in Nevada or anywhere else. Go break the house if they truly are crooked or they use defective dice!
I understand that you are inquiring about a class action suit on behalf of all players at the specific casino or who played with those specific dice. The reality is that you would have an insurmountable task in trying to identify plaintiff claimants, proving the unfairness of the dice (extremely unlikely, I must say, given that one can bet WITH the house, as I mentioned in the intro here), and convincing a court that either the dice manufacturer or the casino knew they were offering a crooked game. It has been a long time since anyone found an unfair or deliberately dishonest game in this State, and there is very good reason for that -- no casino operator will risk losing his livelihood over such an advantage. I respectfully suggest you re-examine your sampling, the mathematics behind your analysis, the validity of your conclusions and the practicality of considering such an action against the enormous behemoth that is the Nevada gaming industry.
