STREET OUTLAWS Won the Race Fair & Square ~ No FIX! Gas Monkey obviously Spent Much More $$$ & may have had the fastest Car, but their NHRA Driver got Hole Shotted on the First Race & LOST, even though he had a slightly faster time. Gas Monkey set up their Blower a "BIT" for the second, Must Win Run, but Broke the Tires LOOSE & lost by a big margin! Good show though! eagleeye2
No need, there is no increase in the distribution of sevens. You can't have your cake and eat it too.........when you gain an extra seven from an extra 3 rolled on the bias dice, you lose a seven when the opposing side 4 is missing!
The green portion shows one 7 only out of six rolls.....and you could continue to have the bias dice always land on 3, and the expected 7's will be 1-6, always!
I kinda doubt he will waste his time, he has already confirmed that no increase in sevens is expected with one fair dice and one bias dice. Like Duck pointed out........when one continues to argues with an idiot, or troll, what does that make them. Unfortunately, I fit his analogy to a "T" on this one. So when you call me an idiot, I would be hard pressed to argue the point in this case.
There is *NO* increase in the expected percentage of 7s when one (1) fair die is rolled together with one (1) "bias" die. It will remain at 16.67% (1 in 6 ratio). That theoretical figure is a calculated number based (in part) upon well-established probabilities of a fair die over the long term. While the expected total number of 7s will change (e.g., 6 in 36 rolls, 7 in 42 rolls, 8 in 48 rolls, etc.) based upon the total number of rolls, the expected percentage of 7s will be remain unchanged at 16.67%. The reason is even with the bias die, a roll can only result in a 7 if the number on the fair die is the complement to the number on the bias die. So if the bias die is a 3, only a 4 on the fair die will result in a 7. Any of the other 5 numbers on fair die will result in a non-7 number (i.e., 4, 5, 6, 8, 9). Having said that, regardless of the expected percentage of 7s, the actual sequence of rolls on a given craps table can (and often will) deviate for the expected long-term numbers from table-to-table, session-to-session, day-to-day, casino-to-casino. Short-term variance affects all probabilities, sometimes in extreme ways. Perhaps the extremely gifted DI can slightly (and favorably) skew the expected numbers, but that's another issue for different thread. It could be the negative vibes generated by the dumbass late bettor, untimely buy-in, or stick change also affect a roll in ways we cannot currently comprehend. Or something else. Who really knows? Some crazy things happen at the craps table and I understand the desire to come up with an explanation for such occurrences. I've seen 7 consecutive 7s rolled on a come out and another 7 a few rolls later (same shooter). That number of 7s (8) rolled in @10-12 rolls is an extreme outlier from the expected percentage of 7s. But it happens, and sometimes outliers seem to happen a lot during a session. You've probably seen it (or something similar) happen, too. On a few occasions, I've thrown 20+ times with no 7s until the out. Again, outliers resulting from short-term variance (from my perspective). Last week, there were 5 consecutive PSOs at the table I was playing at. That's a relatively high percentage (5 in 10 rolls, 50%) of 7s rolled by multiple players in a small number of total rolls. But even with my observations, I had no idea what was happening at the same time (let alone earlier in the day, during the past week, etc.) on craps tables in Las Vegas, Biloxi, at Grand Victoria (Elgin, IL) 35 miles away, or even on any of the other 4 tables at Rivers Casino. Unfortunately, there is no data gathering methodology that will allow the continuous/accurate/timely collection and analysis of every roll on every craps table in every casino. Even procuring a relevant sample size of rolls under actual casino conditions would be next to impossible. At best, we have a very, very incomplete and insignificant -- statistically irrelevant -- picture of what has happened (or is actually happening) in the world of craps at any given moment, no matter how long we're at the table. In conclusion, I rule out any change in the expected percentage of 7s even where 1 die is fair and 1 bias die are rolled together. It will remain at 16.67%, the same as if 2 fair die were rolled together. However, because of a lack of sufficient information and analysis, IMO nobody can irrefutably prove either everything is as it should be (long-term aggregated rolls are consistent with the expected distribution) or overall the long-term numbers are somehow skewed beyond statistical error. We're all insignificant short-term players (statistically) in the grand scheme of things. Just enjoy the game.
Onautopilot, Reading Comprehension #01 for you! random_roller made NO SUCH confirmation, DUH! random_roller, All here are awaiting your call on Increased (7's), with Biased Dice! eagleeye2
The conclusion is the SUM Table. That limb is pretty strong, there are so many people on it. You, on the other hand, are out on a twig.
Thank you RR for showing the math in a way even a sixth grader like Eagleturd can follow. His sixth grade math requires more than a sixth grade brain to apply it correctly. Wonder what he'll reply.
You don't even read or try to understand posts. You just paste your standard response. Hopeless. So sad. You could have learned something from the forum. "Of all the words of tongue or pen, the saddest are these: It might have been".
He, and many others have debunked your flawed math! Your continued denial of this fact is evidence that you either do not comprehend simple mathematics, or that you are intentionally avoiding the obvious. Either way, it does not put your so called desire to help the less knowledgeable craps players in a very good position. A person that truly wants to help others, readily admits their mistakes and makes a concerted effort to correct them! Your continued denial, and unwillingness to concede that you could possibly be in error on this, speaks volumes about your intentions and agenda here on the forum!
That's how it was fixed. It was supposed to be fixed, but then at the last minute, they got religion, what is this world coming to? Can't even count on "an old fashioned fix" any more. Lost my ass.
Let's say the biased die, as if there was some other kind, instead of landing on 3, was biased in such a way as it would never, land on three. Even if you set it down with the three up, upon release. It would jump to any other face, an equal number of times each. What sort of numbers might we expect, from this RUE-THREE die, and a fair die, if we should be able to find one.
