I found a nice pdf by Christopher Thomas that lists common probabilities of dice rolls for Arkham Horror:
http://www.boardgamegeek.com/filepage/30729
This table comes in handy when trying to determine the best of two or more choices (e.g., evade or fight). Granted, consulting the odds before making decisions does take a bit away from the theme -- but in League games, maximizing the chances for success can surely make a difference in the score.
There is a free PC app that can calculate similar odds:
http://www.fnordistan.com/smallroller.html
Ryan Gatti does a nice job explaining the math behind such calculations here (scroll down):
http://www.boardgamegeek.com/thread/255452
Using Ryan's notes I puzzled out how to recreate Christopher's tables in Excel and added additional info for rerolls (e.g., Lucky Cigarette Case) and Grapple. What I need next is to figure out how to add the Shotgun's "6" successes for combat checks. It doesn't seem trivial and I'm not very adept with combinatorics math, so it's going to be slow going for me to work through it on my own.
Has anyone looked into this problem before and come up with a way to calculate the success odds for Shotguns?
Once I complete this, I'll publish the spreadsheet and a pdf for community use and amusement. Thanks.