Tao of D&D’s talks about Hearing Checks.
GURPS B358 has a similar table but only in ranges. Decibel reference would be useful.
Since the Average person should be able to hear this in the distance given, the Basic Task Difficulty Modifier would be +4 (routine or mundane). In D20 this would be a DC5. when circumstances have more Stress and Distractions then you can have TDM +0 or worse and for D20 about DC10 or worse.
False Sensations
Note that in the real world we have false sensations of sounds, especially when we are expecting it. The cool thing about this is that you can make failed rolls, quirks or disads, play in the way of false sensations.
in Fast Twitch Games and in Combat Simulations like Airsoft, we have a Ton of Sensation Noise and False Sensations. When I first began I was struggling to filter these out, and we learned a lot from our Captain and in about 7 years of playing.
There is this thing called Pareidolia and the Cognitive “hacks” our brain has to increase our response time by gaming the statistics its a foe before confirmation results in friendly fire. I’ve had about 4 friendly fire incidents where I accidentally took out an ally in 7 years of airsoft and a innumerable number where I was lucky not to hit them.
Friendly Fire and Decision Making is well discussed in The Art of Critical Decision making by Micheal Roberto in chapter 20 Practical Drift.
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