I brute forced the encounter counter behavior. It's essentially exactly what I had speculated in the past, but I had not verified it previously.
I think whether or not you get into the battle has to do with an internal formula checking if the game can lay down the battle grid or not. I've never understood exactly how this works, but it's well-known that sometimes you won't get into an encounter up against certain walls.
50 step units is about 0.83 seconds or about 5 Brian steps. Brian's speed is 2 step units per 1/30th of a second (one frame).
Exactly every 50 step units it rolls for EncounterChance = (Step Units / 2000)
50 step units = 0.025 = 2.5% 100 step units = 0.05 150 step units = 0.075 200 step units = 0.1 250 step units = 0.125 300 step units = 0.15 350 step units = 0.175 400 step units = 0.2 450 step units = 0.225 500 step units = 0.25 550 step units = 0.275 600 step units = 0.3 650 step units = 0.325 700 step units = 0.35 750 step units = 0.375 800 step units = 0.4 850 step units = 0.425 900 step units = 0.45 950 step units = 0.475 1000 step units = 0.5 1050 step units = 0.525 1100 step units = 0.55 1150 step units = 0.575 1200 step units = 0.6 1250 step units = 0.625 1300 step units = 0.65 1350 step units = 0.675 1400 step units = 0.7 1450 step units = 0.725 1500 step units = 0.75 1550 step units = 0.775 1600 step units = 0.8 1650 step units = 0.825 1700 step units = 0.85 1750 step units = 0.875 1800 step units = 0.9 1850 step units = 0.925 1900 step units = 0.95 1950 step units = 0.975 2000 step units = 1.0
Cumulative math: P(A or B ) = P(A) + P(B ) – P(A)P(B )
0.025 + 0.05 - 0.025 x 0.05 = 0.07375 0.07375 + 0.075 - 0.07375 x 0.075 = 0.1432
Since the counter resets, it's harder to exactly calculate the chance of two encounters over a set distance. The following covers chance of at least 1 encounter.
Cumulative: 50 step units = 0.025 100 step units = 0.07375 150 step units = 0.1432 200 step units = 0.2289 250 step units = 0.3253 300 step units = 0.4265 350 step units = 0.5269 ~50% 400 step units = 0.6215 450 step units = 0.7067 500 step units = 0.7800 550 step units = 0.8405 600 step units = 0.8883 650 step units = 0.9246 700 step units = 0.9510 ~95% 750 step units = 0.9694 800 step units = 0.9816 850 step units = 0.9894 900 step units = 0.9941 950 step units = 0.9969 1000 step units = 0.9985
