The user's request: "when our bot is low OR enemy is low, it is useless to use high
power instead low fast bullets have more chances to finish the enemy. Let's do a
math slope: starting from some health down, the power goes down with it."
1. ENERGY SLOPE (`TR_POWER_ENERGY_*`), replacing the old hard step at 50 energy:
cap = ENERGY_MAX at/above ENERGY_HI, ENERGY_MIN at/below ENERGY_LO, LINEAR in
power between, clamped. Defaults HI=80 LO=20 MIN=0.5 MAX=3.0, so no cap >=80,
0.5 at <=20, and e.g. E=65 -> 2.375, E=50 -> 1.75, E=35 -> 1.125.
Rationale: bullet speed is 20-3p, so lower power = FASTER bullet (less lead
error, higher hit chance), fires more often (10+2p) and drains slower (p/shot).
E[dE] = p(3P-1) => break-even hit probability is 1/3 INDEPENDENT of power, and
our measured rates are 5-27%, far below it.
2. FINISHING CAP (`TR_POWER_FINISH_KILL`, default ON): cap power at the SMALLEST
bullet that still removes the enemy's remaining energy -
`E<=4 -> p=E/4` (min 0.1), `4<E<=16 -> p=(E+2)/6`, `E>16 -> no cap`.
Rationale, and it makes the user's instinct stronger than a heuristic: server
1.3.1 caps the damage SCORE at the energy ACTUALLY REMOVED, so overkill is
WASTED damage AND ~6x the energy for ZERO extra score. Damage is 4p (p<=1) /
6p-2 (p>1).
Both are min-composed with the existing far/below-average caps, may only LOWER
power (exhaustively tested), and are exempt while ramming.
`TR_POWER_POLICY=0` still returns the uncapped control exactly.
MEASURED ENERGY SAVING (offline replay of the DrussGT fixtures, 28,797 ticks):
arm shots energy meanP E/1k ticks vs cliff
control(uncapped) 1913 4646 2.43 161.4 -90.2%
cliff (today) 2363 2443 1.03 84.8 0.0%
slope 2404 2178 0.91 75.6 ** 10.9% LESS **
slope+finish 2404 2167 0.90 75.3 ** 11.3% LESS **
So the slope spends ~11% less energy than the cliff AND fires slightly MORE shots
(2404 vs 2363) - both directions at once.
HONEST NOTE on the finishing rule's reach here: ticks where the enemy is low
(0 < E <= 16) are only 2252/28797 = 7.8% of these fixtures, so finishing adds just
~11 energy of saving against DrussGT. It matters in CLOSER fights, not this one.
Verification: test_power_policy 58 (was 26) in BOTH the default and TR_POWER_POLICY=0
control arms - slope at E=100/80/65/50/35/20/5, powerToKill across E=0.1..100, the
inverse-cover property for E<=16, monotonicity, ram exemption, and an exhaustive
sweep proving power <= preference. Guards: test_gun_harness 39, test_vbullet_metric
11, test_power_selection 3, test_adaptive_radar 41, test_tfil_ring_weights 24,
test_ram_decision 40, test_rack_membership 48, test_selector_tiebreak 19,
test_tm_pattern_registration 20, test_vbullet_admit_gate 12. acceptance
12/12 PASS. ModularBot compiles release.
Adds `common_libs/tests/measure_power_policy.nim` (the energy/histogram tool) and
updates docs/env_reference.md for the new `energySlope|finishKill` log reasons.
NOT MEASURED: the battle/hit-rate effect. The offline figures use the fixture
shooter's energy as a proxy, open-loop; the RELATIVE saving is the meaningful part.
