Face it man, your a moron. The don't side would get killed by these dice. You can easily simulate this bias, with a normal set of dice. Do an experiment. Set one die on 3 and leave it there. Roll the other die, and make all the don't bets you want to, and see how fast you get your ass kicked. You would lose your ass, playing the don't, with this bias.

I was going under the assumption that no longer being able to roll a 2,3,10,11 or12 would alter the probability curve. Not going to take the time to figure it out since as you noted, one biased die doesn't change the probability of a seven.

Assuming you can identify said bias, a bias die is the perfect set up for a DI. If you know one die is going to roll more of a certain result you only have to attempt to control one die. That is much easier than trying to control two dice.

Actually EE2, it's not really an oversimplification, the problem is really this simple. Though it is unlikely a die would ever be 100% biased, the times that the bias DID show up, would give the same results as our 100% biased die. In real life, the whole thing would likely be diluted, to a substantial degree. Over the years, I have contemplated the biased dice thing, more than most people. It took years, before I came up with what I would consider, the ideal bias for a casino to employ, if they were going to do so. Though I know the best bias, I do NOT know, what mechanism could be used, to actually make the dice show this bias. It would seem to be a very difficult problem, though I don't know everything that might be possible, with modern technology. Now bubble dice, are another thing entirely. Due to their large size, opaque faces, and the fact that you will never get your hands on one, anything might be possible. Not to mention those rounded corners.

von duck, Casino's know which DICE give them the greatest Return over time, & use them to their advantage. Try playing CRAPS during the week on a Cruise Ship Vs the Fisrt & Last day on that same Cruise Ship! Some Land based Casino's also use Biased Dice, to their advantage & as they see fit. Bottom line, learn how to detect Biased Dice in Play, assuming you value your $$$, that is. eagleeye2

For some reason I missed this addition when you alluded to it a few days ago. You're welcome of course, and I mean that sincerely. Apparently I have somehow acquired a reputation here for being a numbers guy; maybe it's because I can count to 7 without using all of my fingers. Regardless, it is never without some trepidation that I post said numbers lest my credibility be adversely affected if I really should have used all my fingers, toes, and the like appendages of some friends. That trepidation peaked when I submitted via e-mail my solution to a problem posed here to the late Don Catlin, the numbers guy for Casino City Times, which he then posted to that blog. I was a math major my first two years at college and one of my instructors spent three days going through a proof of a theorem only to hit a stone wall. He asked if anyone had any ideas as to how to proceed, and after a minute or two of crickets he proceeded to whip out a proof in a couple minutes using a different approach. This taught me that mathematicians can be more concerned with arriving at an answer by some original and elegant means than with how accurate the answer is. To my relief, Dr. Catlin posted another solution to the same problem he had received from a colleague two months later confirming my/our answer.