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

===Rerolls===
Much has been said about rerolls. If you go to the separate tactics pages you will bump into the effectiveness of captains reroll auras, and whether they are worth it. First off, we need to have a look at the effect they have, both rerolling 1's, and rerolling all fails:
*6+ is 16.66% chance
*5+ is 33.33% chance
*4+ is 50% chance
*3+ is 66.66% chance
*2+ is 83.33% chance

Reroll 1's:
*6+ is 19.44%, +2.78%
*5+ is 38.88%, +5.55%
*4+ is 58.33%, +8.33%
*3+ is 77.77%, +11.11%
*2+ is 97.22%, +13.89

Reroll fails:
*6+ is 30.55%, +13.89%
*5+ is 55.55%, +22.22%
*4+ is 75%, +25%
*3+ is 88.88%, +22.22%
*2+ is 97.22%, +13.89%

To explain what you are seeing, rerolls are effected by two factors:
*Your roll chance
*And your reroll chance to fail ratio.
The higher these two values are, the better your roll will be. This is why when rerolling 1's, a 2+ roll sees the best increase, as it has the highest initial success chance, but it is also why a 4+ has the best increase when reroll all fails. So like with getting better basic dice rolls, when looking at rerolls you need to consider what that reroll is buying you. Rerolling 1's for orks won't buy you much (although in some builds that increase may be enough for you to have to buy bigger bucket for your dice), but rerolling 1's for custodes for their 2+ to hit sees them only failing their rolls 2.78% of the time.

However, rerolling also buys you something else, and that is avoiding negative effects of dice rolls. The most common effect like this is plasma, which deals mortal wounds or outright kills a model on a roll of 1. Rerolls bypass this by giving you one chance to take that 1, a reroll it. Lets take space marines for example. Plasma in their hands will hit 66.66% of the time, and kill them 16.66% of the time when overcharged. When rerolling (whether 1's or all fails) that 16.66% goes to 2.78%, or a 1 in 36 chance.