If you would make a 6 dan problem where you have 2 options, A or B (to be sure about your answer, you have to think it through carefully though), any person has 50% chance of completing the question if they just chance. Thus, the problem would have a difficulty of about 49% (10-8kyu) instead of the 99% (6 dan) which it's real difficulty is. Thus, a lot of 10-8 kyus would have a 50% chance of failing their time trial whenever one of these problems pops up.
I think that the chance of random sucess (the chance you have to solve the problem if you just play randomly) should be removed from the real difficulty.
A 2 choice problem, for example, has a cors (chance of random success, can't think of another word and it's so long to write) of about 50%. About 51% of eveyrone who tries the problem solves it, thus, the real rate of success is about 1%.
In the case with bigger problems, there might be 50 differnt possible moves, but, to solve the problem, you might have to play 2-3 times, each of about 50 possibilities, making the cors about:
1/50*1/50*1/50 = 1/125000
(in this case, it doesn't really matter).
A lot of problems, you have about 5 possible moves, followed by maybe 3, giving a cors of about 1/15 (6.7%). If it's a difficult problem, it's a great difference.
(The cors for multiple solution problems is simple the sum of the cors for each solution).
However, this could make a person able to solve many dan problems, just by guessing (shouldn't be a problem since he'd still have a max chance of 50% and you could see that he has tried the dans many many times.)
{Posted by cen2y}