A recurring forum topic here at GTO is how our dice roller is broken. The purpose of this post is not to deal with that question. What I am seeking to do is to try and clear up some misconceptions about dice probabilities and how they get applied at GTO and in particular to Axis & Allies. I think part of the problem is that players go in with expectations of results and those expectations are too strong. I am not probability expert and don't expect GTO users to be experts on probability but I would like a to encourage a baseline understanding of what they know and what requires a deeper understanding.
Test question: rolling 3 six-sided dice, what percent of the time will you roll at least one 6? If your answer is 50% you are not alone as you probably used the logic that it is odds of rolling one die and getting 6 multiplied by 3, 1/6+1/6+1/6. The correct answer is actually 42.13% because combinations of multiple 6s should be counted only once for getting a single 6. The 8% seems small but it does mean more often you will not get any 6s throwing 3 dice. http://www.edcollins.com/backgammon/diceprob.htm will back me up on this. The author goes on to note that if you threw 9 dice, 19.38% of the time you will get no 6s on those 9 dice, almost 1 out of 5 times. Please take the time to get the whole picture before you go spouting that you got "diced" or your opponent hacked our server when your 9 infantry got no hits.
