Bad statistics make a weak argument, the Illusion issue in SR4A Options

[pbangarth]

In several threads, people are arguing that the OR changes in SR4A make Illusion spells that affect objects unusable. Examples given to support this argument often use a dicepool of 14, saying this dicepool has a roughly 50% chance to affect OR 4, and is out to lunch for OR 6.

This would appear to be based on the idea that 14 dice X the 1/3 chance for each die comes up with 4 and a bit. I think this is seen as being halfway, as people say "on average, 4 hits". I thought about this a bit and figured people are not taking into account all the possible outcomes better than 4 hits. I wasn't sure of the math, so I asked a mathematician on Allexperts.com for a formula for "n dice needing at least h hits". He came back with three methods for calculating the answer. I am still communicating with him, as the first and third methods given currently (as of this posting) use 1/6 rather than 1/3, but I used the second method (long and tedious!) to come up with the following:

Dice pool of 14:

4 hits or better: 73.88 %

6 hits or better: 31.02 %

My conclusion from this? Illusion spells are NOT being nerfed/jerked around/made useless by the SR4A OR changes. They HAVE gone from near infallibility to being effective against even THE WORST STUFF almost one third of the time.

PS. I am extrapolating that the dice pool 18+ characters will still be in the 75% range for OR 6.

EDIT: This arithmetic applies to all spells' dice pools by the way.