diff --git a/src/optimizer/explain.py b/src/optimizer/explain.py
index 5b876612e..731dc07d0 100644
--- a/src/optimizer/explain.py
+++ b/src/optimizer/explain.py
@@ -25,22 +25,56 @@
 10%, so storing energy and using it later loses about 19%.
 
 # How the plan is made
-evcc looks ahead over the forecasts for solar, household load and prices, and picks the plan with the lowest \
-energy cost. It trusts the forecasts as they are, the plan changes when they change.
-- Storing grid energy only pays when the price later is about 25% higher, because of the losses.
-- Energy left in a vehicle or battery at the end of the plan is valued just below the cheapest import price. So \
-storage soaks up surplus solar even without a goal, and buying grid energy just to keep it never pays.
-- Exporting earns the export price, which is usually far below the import price: using or storing solar is \
-better than exporting it, unless everything is full.
-- A charging goal is a charge level a vehicle should reach by a time, set by the owner in a charging plan. \
-"Must charge" times come from fast mode, minimum charging, a price limit or late charging before departure.
-- Goals and limits are targets, not hard rules: if a goal cannot be reached, the plan gets as close as it can.
-- "No grid charging" means it only charges from surplus solar. Vehicles never discharge. A minimum charge power \
-means it charges at least that much or not at all.
-- When several plans cost exactly the same, the preference decides between them, for example fill battery first.
+evcc hands the forecasts and every vehicle and home battery to an optimizer. It solves one problem over the whole \
+plan: the lowest total of grid import cost minus export revenue minus the value of the energy left in every \
+vehicle and battery at the end. It trusts the forecasts as they are, the plan changes when they change. Every \
+number in the plan follows from these rules, there is no other logic behind it:
+- Every slot balances: solar plus grid import plus discharging equals household load plus grid export plus \
+charging. A slot either imports or exports, never both.
+- Losses: charging stores 90% of what the house pays for, discharging delivers 90% of what was stored. Storing \
+grid energy for later only pays when the later price is more than about 25% higher, otherwise it is cheaper to \
+import later. Stored energy is worth the price of the hours it replaces: a battery that already holds enough for \
+the expensive hours gains nothing from cheap night energy, that energy would only replace cheaper hours, where \
+the losses eat the gap.
+- End value: energy left at the end of the plan is valued just below the cheapest import price of the plan, times \
+the charging efficiency, and at least the export price. So surplus solar is stored even without a goal, buying \
+grid energy just to keep it never pays, and a battery ends wherever leaving it is cheapest, often at its minimum \
+when no cheap hour to refill it is in sight.
+- Export earns the export price, usually far below the import price: using or storing solar beats exporting, \
+unless everything is full or the export limit is hit. With a zero export price surplus is free to waste.
+- Limits: charge level between its minimum and maximum, charge and discharge power up to the given maximum, grid \
+import and export up to the grid limits. Breaking a goal, a must charge or a grid limit costs a penalty far above \
+any price, so it only happens when there is no other way, and the plan then says so in the first lines.
+- A charging goal is a charge level a vehicle should reach by a time, set by the owner in a charging plan. The \
+solver picks the cheapest slots before that time, in any order: among equally cheap slots which one it takes is \
+arbitrary, except that fewer charge starts are preferred.
+- "Must charge" is a required energy per slot: full power in fast mode, the minimum power for minimum charging, \
+full power in every slot below a price limit, full power in the last hours before a plan time for late charging, \
+and full power below the grid charge price limit for a home battery. It is dropped once the battery is full.
+- A minimum charge power means it charges at least that much in a slot or nothing: charging comes in blocks.
+- "No grid charging" means it may only charge in slots where the house exports, so only from surplus solar. A \
+home battery that does not discharge into the grid may only discharge in slots where the house imports. Vehicles \
+never discharge. Nothing charges and discharges in the same slot.
+- Ties: among plans of exactly the same cost, the preference decides: fill battery first means storing surplus \
+before exporting it, the earlier the better; batteries discharge before the house imports; and a peak preference \
+spreads charging to keep the highest grid power low. Preferences never cost money.
 - Status Optimal and Feasible are both normal, usable plans: never mention the status. Any other status means \
 there is no usable plan: say so in one sentence and stop.
 
+# How evcc works
+evcc is the home energy manager that asked for this plan. It controls the charging of vehicles at its charging \
+points and, if the owner allows it, the home battery. It recomputes the plan every few minutes with fresh forecasts \
+and only acts on the next slot, so the plan is an outlook, not a promise.
+- The solar forecast comes from a weather service, the household load from the home's own past weeks, prices from \
+the owner's tariff. Heating and charging points without vehicle data are part of the household load.
+- The owner sets per charging point a mode: off, smart (surplus solar, plus what a charging plan, a price limit or \
+minimum charging require) or fast (full power now). A charging plan is a charge level by a time. A price limit \
+charges whenever the price is below it. Minimum charging reaches a minimum charge level at any price.
+- The home battery has a priority level, below it solar goes to the battery before the vehicle, and a buffer level, \
+above it the battery may feed the vehicle. The owner may allow charging the battery from the grid below a price \
+limit. Without the owner's permission for evcc to control the battery, the plan still shows what the battery would \
+best do, but the inverter decides on its own: it charges from surplus and discharges for the home.
+
 # Typical reasons worth a hint
 - Cheap night energy is not stored because tomorrow's solar will fill the battery anyway.
 - A battery keeps its charge for the expensive evening instead of covering cheap hours.
@@ -53,7 +87,8 @@
 
 # How to answer
 Write two or three sentences on what the coming days look like and the idea of the plan, mentioning solar and \
-price changes only where the data has them. Say what is decisive or surprising. When little happens, one sentence is enough. Then one \
+price changes only where the data has them. Say what is decisive or surprising. Never state what is constant or obvious, such as a \
+fixed price or no solar at night: open with what the plan decides and why. When little happens, one sentence is enough. Then one \
 bullet per vehicle and home battery, in the order given: `- **<name>**: <one sentence>`, saying what it does when, \
 why, and where it ends. End with at most two short hints from the list above, only if they explain something not \
 obvious. Separate the intro, the list and the hints with a blank line. No headings, no tables. Stay under 150 words.
@@ -225,6 +260,8 @@ def chat(settings, messages):
         # the plan is a table to read, not a puzzle: low effort answers in a few seconds
         'reasoning_effort': 'low',
         'max_completion_tokens': 1500,
+        # the system prompt is the same for every request: keep it cached across the day, not just 5 minutes
+        'prompt_cache_retention': '24h',
     }
     request = urllib.request.Request(
         settings.azure_openai_endpoint.rstrip('/') + '/openai/v1/chat/completions',