Editing Warhammer 40,000/9th Edition Tactics (section)

===Dice Roll Math===
*It is almost always better to re-roll dice than to get +1. For instance, re-rollable 4+ has almost a 10% edge over 3+.
**The exception is re-rolling 6s, which is 1/36 worse than 5+.
**Because of how people throw dice, a re-rollable 2+ has a lower chance than math suggests. People tend to use the same rolling motions, which means those dice often end up in the same position ("1" both times). So use a dice tower or roll your dice more thoroughly for a longer period of time in order to increase randomness and adherence to estimates made via mathhammer. (this bullet should be deleted - this is only true in highly refined laboratory experiments as it requires that starting conditions be the same across consecutive dice rolls - initial die facing, height, surface, etc etc)
*The average roll on 1d6 is 3.5, and the average roll on 1d3 is 2.
**The average of XdY is X*1dY, so 2d6 is 7, 3d6 is 10.5, etc. 
*Picking the highest of 2d6 adds about 1 (actually 35/36) to the average roll.
*4+ re-roll 5+ is the same as 3+.
*Re-rolling 1s is always equivalent to multiplying your odds of succeeding by 7/6, which means, additively speaking, it's better the higher your original odds are: you'll get an extra success in every 12 dice for a 4+, 9 dice for a 3+, and slightly more than 7 dice for 2+ (actually 7.2).
**Re-rolling all failures has a larger benefit the lower your original odds; you'll get an extra success every 4 dice for a 4+ base, every 4.5 (i.e. 2 successes every 9) for a 3+, and every 7.2 for a 2+.
*The odds of getting a 9 or more on 2d6 is 10/36, a little less than a third (27.78%). Re-rollable, it's a bit less than half (47.84%)
*And, if you're into it, there's [[MathHammer]].
*GW dice are not mathematically fair! This set of mathematical data presumes you are using perfectly balanced casino dice which are. See following for details. http://www.dakkadakka.com/wiki/en/That%27s_How_I_Roll_-_A_Scientific_Analysis_of_Dice