von duck, You can't be that DENSE can you??? When any Weight BIAS Occurs in a DIE, ONE # appears more frequently than the other Five, got that, it's gravitational attraction, a basic LAW of Physics!!! In the example I gave, the (6) appeared more than the other 5 #'s, as a result of the Weight Bias within that DIE (With Twice the hypothetical # of (6's) appearing). Now, the Fair Die will yield an even # of hits on each side & will repeat this action forever, by definition. But the Biased Die has an increased frequency of 6's, with the resultant of both dice, being an increased # of 7's with any Weight Biased dice, when thrown with a FAIR DIE, comprehend??? eagleeye2

Oh, oh yeah, I think I comprehend pretty well. YOU, have a "bias" in your brain. Do not be offended, it is NOT your fault. We are dealt the hand we are dealt. Your problem is pathological, so there is no point, in discussing thiis issue any further. One thing though, your belief in more sevens, does give you an option, that would be profitable, if you're right.

von duck, OMG, you are as Dense as I indicated... von duck, You can't be that DENSE can you??? When any Weight BIAS Occurs in a DIE, ONE # appears more frequently than the other Five, got that, it's gravitational attraction, a basic LAW of Physics!!! In the example I gave, the (6) appeared more than the other 5 #'s, as a result of the Weight Bias within that DIE (With Twice the hypothetical # of (6's) appearing). Now, the Fair Die will yield an even # of hits on each side & will repeat this action forever, by definition. But the Biased Die has an increased frequency of 6's, with the resultant of both dice, being an increased # of 7's with any Weight Biased dice, when thrown with a FAIR DIE, comprehend??? eagleeye2

Ok, lets say that the biased die roll 50% more sixes than normal, and all of these extra sixes, are subtracted from the ones that same biased die will roll. Now we have one die that is normal ( fair) and it roll 6 of each number in 36 rolls. We also have a biased die, that rolls 6 twos, 6 threes 6 fours, 6 fives, 3 ones, and 9 sixes, in 36 rolls. List for me the combinations that will be rolled with 72 rolls of these two dice, and then count for me, the resulting sevens. You will see that there will be 12, sevens. The seven, will be the only number, that will NOT be out of the normal proportions. Let's see how bad you can f'k this up.

von duck, Odds on CRAPS are based upon the Combinations of #'s that can be made with a PAIR of Fair Dice! This brings one to the familiar table which follows: ### WTM Where WTM = ways to make the ### as follows: 2,12 1 3,11 2 4,10 3 5, 9 4 6, 8 5 7, - 6

If you find such a table PM me where it is and I'll sell everything I own and can steal to play there...and cut you in for half the profits and you don't have to put up a dime. With that die Pass/Come has a 1.68% player advantage, but I'm buying the 10 with its 9.05% player advantage. Oh, almost forgot: p(7) on that table is 0.16666666...

We all know what a pair of fair dice will produce, but that's not what this discussion was about. We were talking biased dice, remember? Duh! I am sorry to lay waiste to your theory, but we need to get the facts straight, that's all. Ok, so here's what 72 rolls of the dice described in post #45 would produce, to the right is "normal" distribution. 3, 12s. / 2, 12s 5, 11s. / 4, 11s 7, 10s. / 6, 10s 9, 9s / 8, 9s 11, 8s. / 10, 8s 12, 7s. / 12, 7s 9, 6s. / 10, 6s 7, 5s. / 8, 5s 5, 4s. / 6, 4s 3, 3s. / 4, 3s 1, 2 / 2, 2s As you can see, the only number that remained unchanged, was (7). In the word of Kepler, you are left with a "single cart full of dung".

There will be more 6/1 sevens. There will also be fewer 5/2 2/5 4/3 3/4 and 1/6, sevens resulting in the same number of sevens, over a large enough sample size of course. In a small sample like an hour of play, anything can and will happen.

von duck, Total B.S., where do you get 72??? Two Dice, Six Sides per DIE, Six Unique #'s &... 6 Times 6 = 36, at least where I went to school!!! eagleeye2

WRONG!!!! Back to remedial math, for you, give my regards to TD when you get there. Get a calculator, and multiply 36 X 2, see what you get. DUH! GD your dum! I doubled the sample size, to 72 normalized throws, so that we did not have to deal with a bunch of fractions. This does nothing to alter any of the percentages. Two rounds of the dice instead of one. I believe the problem here is becoming VERY obvious. DUH!

No, there is not! OK, lets start with the basics. 2X36 = 72. Are you with me so far, "Poindexter"? Study post # 45 & # 50, real hard. Now, apply for brain transplant, when you find a suitable donor, check with me, before you commit to the surgery, all brains are not created equal, as is evidenced by you.

von duck, There is NO 72, It's 36 Possible Combinations of #'s, on a PAIR of Casino Dice, DUH One DIE Is Fair, i.e. it will statistically repeat #'s 1 to 6 by definition, in 6 throws SIX Of each # 1 to 6! In the example, under review, there are 50% More (6's) than normal; which of necessity will result in MORE SEVEN OUTS, calculated as 8.3% More 7-Outs. eagleeye2

F'k it Man. You're too GD stipid to even be walking around. What you are is pathological, like a few others. There is no point. GD, man!

von duck, You are the IDIOT that is uninformed about Biased Dice. Nope, one cannot educate a ""Know It All""!!! To your own Peril @ CRAPS... eagleeye2

You're one of "them" aren't you. You're a "plant", here to make anybody that mentions biased dice, appear to be an idiot, like yourself. Yeah, that's the only explanation, because nobody could possibly be as stupid as you post, I don't think? Maybe you are that stupid? No, no f'kn way.