FredP, Claiming that James Hall is eagleeye2 Proves that you are: 1) As Blind as a BAT! 2) As Dumb as a ROCK! eagleeye2

Harley: I f you read on further you would have seen I retracted my statement. How's your bias dice crusade going?

Fred, Careful what you say. You see I can tell you biased dice do exist. For the past year or more, I've been tracking sticks of dice from Kansas Star casino south of Wichita, Ks, and the dice are horrible. I have tested several sticks for outcome possibilities as well as with calipers. Harley is right. Have also tested dice from the Prairie Band casino owned by the Pottawatomie tribe which are 3 to 4 years old and they too are bad. This joint is north of Topeka, Ks about 20 minutes drive. I've purchased several sticks and mailed them to acquaintances so they could practice with them to see how to shoot bad dice. They're learning and managing their bankroll better as a result. Harley's right again. So you see, just like our issue over permutations, if it walks like a duck, quacks like a duck it is a duck. No titles or math required.

Couldn't accuse old eagleeye of being boring now could we? Why do the tops and bottoms = 7? Dumb as a rock! Blind as a bat! You're an idiot! If you don't play like me or you disagree with me you're an amateur. Keep up the good work Eagleeye never a dull moment with very in depth, interesting, knowledgeable posts about this great game from our resident expert

I do not doubt that dice can be biased for many reasons. And I do not say Harley is wrong. I don't know how you inferred that from my asking how his crusade was going. I disagree that no math is required. What is missing here is the mathematical quantification of the effect of bias on the game. Some biases favor the player, some don't. Without quantifying the effect all we can say is there's a physically measurable bias but how much it changes the probabilities of a dice game is unknown. It can be determined but it will take more than just saying bias is not fair.

And we had no issue over permutations. I simply asked a question about the type you used. You replied "random" after a wikipedia search. Then, you yourself said it was nonsense and I assume it was because it did not apply to your work. I do get confused by your posts.

7uwin, As usual, YOU are the IDIOT! Post one thing incorrect about my Postings, other than the usual you are an IDIOT, which is my Opinion of you!! eagleeye2

FredP, Just as I stated, Blind as a BAT, Dumb as a ROCK! I have posted this several times & It Remains 100% true, ""Quantifying the effects of Dice Unbalance" & per FredP's own request, WOW! Freddie, You are a Mathematical IDIOT! TDVegas, You had better re-study your Mathematics as you fail to comprehend the following! Of Course with the Biased Dice as Freddi indicated, (two three's per 7 throws) the probability distribution of throws is: 1/7 = 1 ~ Vs 1/6 = 1 for the Balanced DIE! Thus the Balanced DIE has an EQUAL chance of landing with each of it's 6 FACES UP, producing #'s 1, 2, 3, 4, 5, & 6! The Biased DIE has the SIX #'s shown above PLUS an EXTRA # 3 SHOWING UP, in the 7 throws, that it takes to complete the sequence you set up. Now Freddie, there are TWO DIE used in CRAPS & that EXTRA 3, can only Match with the EQUAL Probabilities of #'s 1, 2, 3, 4, 5, & 6 from DIE # 2 in your example. Using Mathematics, you can NULL OUT the 36 Combinations, consisting of DIE # 2, when combined with the #'s 1, 2, 3, 4, 5, & 6, of DIE #1. What you have left is THAT EXTRA PESKY #3, (from DIE # 1) which of Necessity can only Combine with #'s 1, 2, 3, 4, 5, & 6 from DIE # 2; resulting in #'s 4, 5, 6, 7, 8 & 9, when combining the TWO DIE used in CRAPS. Doing the Simplified Math, we have 6 / 36 or 1 in six or 0.166666666666667 % SEVENS with FULLY Balanced Dice. With the Biased Dice (AS SPECIFIED IN YOUR EXAMPLE) we have 6 / 36 + (1/7 * 1/6); or our BASE of 0.16667 Plus 1/42 or 0.02381 (For a CASINO TAKE INCREASE of 2.3581%) or a 7 hit rate of 0.19048 in your specified example. And eagleeye2's Generalized Proof that any unbalance in CASINO DICE Produces an increase in 7's over that of FULLY BALANCED DICE, has been proven valid! Sorry, TDVegas, but that is MATHEMATICS that cannot be DENIED, by you or FredP! eagleeye2

Thanks man! A visit to this board without an insult to my intelligence by you is like a day without sunshine.