Do you want a real answer to this or just my best gut feeling?
A real answer would be to look at how many dice rolls occur in an average game and then look at the probability of that many dice rolls falling outside the “perfect” average.Â
Essentially this is a standard deviation calculation where given x number of samples, you need to figure out if the average value of the samples is representative of the average value of the sum total of items being sampled. The measure of how well your sample represents your target group is determined by the shape of the curve of the target group and the number of samples you take. This measure typically uses units of standard deviation.
The real question becomes given the number of die rolls in a game, what are the odds that the average of those die rolls fall outside a standard deviation.
BTW, most decent universities and many good community colleges can get you deeply immersed in the math behind statistics if you are really interested. I do my best to forget all this stuff everytime I am done with it but keep the books on the bookshelf so I can learn it again the next time I need it.
Also, my gut says that all other things being equal, the dice determine the game <10% of the time. There are enough rolls, enough opportunities to change tactics and strategies in face of bad rolls and enough deterministic behaviour in the game that dice are not the significant reason for wins or loses.Â
Of course, I prefer to let my opponents believe that dice will cost them the game and I have mind control over the dice.
:evil: