Because the initial shot only misses on a 1, the simplest way of thinking about it is in terms of how the reroll changes your overall chances of failing. Let’s use the example you cited of the Vindicare. The odds of him missing the first shot is 16.67%, but then he gets the reroll on a 4+ which has a 50% chance of success. To get the overall odds we simply multiply the initial odds of failure by the odds of failing the reroll – so for the Vindicare that’s 16.67% times 50%, gets you 8.33%. **So the Vindicare has over a 91% chance of hitting**.

You can do the same calculation for any of them. So BS 7 gets you a reroll on a 5+, you have a 66.67% chance of failing that reroll; so your overall chance of missing is the 16.67% times 66.67% which gets you 11.11%. Or in other words an 88.89% chance of hitting.

In terms of how this relates to the graph I put up, take a look at the 2+ columns. So a straight 2+ no reroll is circa 83% likely to succeed. A full 2+ rerollable is about 97% likely to succeed. Those rerolls for BS 6 or over are basically taking you in steps from the 83% up to the 97% (i.e. the reroll for BS10 is basically just a straight 2+ reroll).

Hope this answers the question!

]]>Where my analysis falls apart is if you get into rolls that don’t have a strict ‘pass/fail’ such as vehicle damage rolls, or any roll where the reroll could produce a worse result than the initial.

But those situations are unusual enough not to really warrant analysis – well not yet anyway!

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