CharlesDM's surprise tree here at this link is reproduced in convenient flowchart form below:
I'd appreciate chances to fix, clarify and/or improve, still somewhat a work in progress.
Green is Yes/Success to a question or roll, red is No/Failure.
Note I differ from Charles' presentation in that I assume if you are a thief you would still want to Move Silently against an inattentive target so that you can deny them their Hear Noise - every little bit helps.
The difference in not doing so, perhaps, is movement speed - do you want to take your chance and get up to them right now, or take a slightly different chance and get to them in another round?
Whether or not concealment is available should be irrelevant to an inattentive target - a Judge could allow the thief to be quite nervous about making her throws while knowing that failure doesn't matter.
Operationally, then, what does this tell us?
If no concealment is available, the attentive target gets their regular surprise chance. This is modified by character classes or proficiencies that give a player the ability to impose a penalty on opponent's surprise rolls - barbarians, for example, being Naturally Stealthy.
Note that when we ask if "concealment is available", this is referring to the last critical point in the approach - you may have been hiding behind 300 foot of warehouse wall for the last X number of rounds, but this is at the critical point of coming into contact with your target with intent. (or, alternatively, if an unknown observer is present that could notice the thief)
If concealment is available, for the attentive target, these motions get us to the point where we can attack/interact within one action/round. Again, the naturally stealthy folks get a general bonus, whereas a thief can take the extra options of the two sneaky skills to completely deny the target their surprise rolls.
Any thief should take the opportunity to gain that proficiency if the Judge allows. The math is ever in their favor.
If the target is inattentive, then it's a easier task. The thief may invoke a Move Silently roll to deny the target a hear noise to notice them coming. Everyone else either hopes the Hear Noise fails, or relies on regular surprise.
Interestingly enough, while there's a proficiency/power that allows one to impose a surprise penalty to opponents, there isn't one for Hear Noise - there's no opposing proficiency to Alertness in part or in full. Hear Noise at it's default 18+ is so bad as to not really deserve further penalty.
I've talked about that a bit here in regards to collapsing "sneaking" into a single roll.
Inhibiting Hear Noise is purely the domain of the Move Silently skill, and Hide In Shadows is the only opposing mundane force to an attentive target, if concealment is available.
Also, imposing a -1 surprise penalty is worth more (1 power) than a +1 bonus to one's own roll (usually a secondary benefit to a +1 initiative) (ACKS PC, pg 98). That's the value of surprise, offensively.
A secondary note; Inaudibility (ACKS PC pg 137) can be recast as a very minor (4.41 points, I think) 1st level spell that lasts 1 round/level. If one treats the thief as permanently a 1st level caster, Move Silently is essentially casting that spell with a successful throw.
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