Posted by Don Schlesinger on June 26, 1997 at 13:21:24: In Reply to: Law of Independent Trials: Is It Flawed? posted by NoMath on June 26, 1997 at 12:44:05:400 is not a very large number, although it is not likely that 400 rolls of fair dice could ever be seven-less (something like 47 chances in one octillion)!
The point is, if this DID happen, not only would the next roll not forecast an increased likelihood of a seven, but I would offer the past results as awfully strong evidence that the dice weren't fair and bet AGAINST a seven! So, if fair, the probability remains 1/6; unfair, the seven may never come up. The last thing I would expect would be for INCREASED chances of seeing the seven.
Translation -- the old saw: The dice have no memory.
By the way, if the casino offers 5 TO 1 on something that happens once out of six times, then you are getting fair odds. Perhaps you meant to say "5 FOR 1."
Don