Don't forget ties require checking and only net hits means a burned SIN. You could check my
Accuracy Tables as well, which note 11.37 for (8,5) and 385.94 for (8,7). So a Rating 4 checker vs a rating 4 fake has ~9% busting chance, and vs a rating 6 fake it's about 0.25%, with 56.08 = <2% chance to get checked
or busted.
As for AnyDice, what you want to do is use d{0,0,1} for normal dice and d{0,0,1,0,0,1,1,1,1} for rerolled dice. Exploding dice are a bit more complicated and require using a rough estimate or 1000 vs 1001, since the highest value is the only one that can explode.
So for example:
output 14d{0,0,1}-13d{0,0,1}
output [highest of 0 and 11-15d{0,0,1,0,0,1,1,1,1}]
output [highest of 0 and [highest of 2 and 12d{0,0,2}]-15d{0,0,1,0,0,1,1,1,1}]
output [highest of 0 and [highest of 2 and 14d{0,0,2,0,0,2,0,0,2,0,0,2,0,0,2,0,0,4}]-15d{0,0,1,0,0,1,1,1,1}]
The first can be used the odds at winning with e.g. 14 vs e.g. 13 dice.
The second would for example be someone Centering against 11 Drain with 15 rerolled dice, where results under 0 are filtered into 0. Useful for all kinds of soak calculations.
The third is resisting the drain of summoning a Force 12 Spirit with the same 15 rerolled dice, illustrating that Oversummoning isn't a real risk if the defender uses Edge, even with 15 drain dice. It applies minimum drain as well.
The fourth is rather complicated. Rather than having exploding dice, an approximation was used where there's 5/18 chance to score 1 hit and 1/18 chance to score 2+ hits, with the 2+ set to 2 instead. So this would be a Force 9 Spirit Pushing The Limit (with 5 Edge) against Oversummoning, making it far more risky than the Force 12 without Oversummoning. The complicated nature is necessary because exploding dice are hard to boss around in AnyDice.*
The rough version, by the way, averages to 0.389 hit per die, instead of the real 0.4.
*: In fact, it feels as if I only get the right result if I remove one zero... Which is rather weird. So basically if I remove one 0, I get the right results. Here, try comparing these:
set "explode depth" to 10
output [highest of 0 and [highest of 2 and 14d{0,0,2000,0,0,2000,0,0,2000,0,0,2000,0,0,2000,0,0,4000}]-15d{0,0,1000,0,0,1000,1000,1000,1000}]
output [highest of 0 and [highest of 2000 and [explode 14d{0,0,0,2000,2001}]]-15d{0,0,1000,0,0,1000,1000,1000,1000}]