Originally posted by TheNiceOne
Well, taking the average number from four rolls is about as horribly bad as the first misinterpretion of the change. For those of you who fall asleep when reading the more mathematical posts, here is a simple example:
Assume you play a board game where you need to roll six on a normal six-sided dice. Everyone knows that your chance is 1/6 = 16.67%. Now assume that this board game is changed so that your average of four rolls have to be six. That means that you need to roll 6 all four times to get an average of six!
Changing this board game from rolling once to rolling four times, decreases your probability from 16.7% to 1/6^4 = 0.077%!
Now, this is an extreme example. But as others have shown, this suggested change makes horses close to unusable against anything stronger than a warrior, and UUs like the Greece hoplite and the Persian immortal becomes god-like.
I will again propose the sensible solution I made on page one that Warpstorm also has voiced:
Add a setting, which is the number of rolls to take the average from. The default should be 1, since that's how CIV3 has been all the time, but anyone who wishes may increase this to 2, 3, 4 or even higher.