A CP run is a fight arranged rather than found: one side puts troops up to be attacked, and the other side collects the Conquest Points for attacking them.
Conquest Points are far harder to come by than Valor Points, and the research that spends them is long. A run is the only way most players get them in quantity.
Two jobs, and they want opposite things. The host hands over as much strength and health as they can stand to lose. The attacker tries to take the points home without paying for them.
It is done two ways, and they are different enough to be worth separating: a whole clan hitting one host from outside the clan, or two players running it between the two of them.
Why Corax
The host puts their highest flying guardsmen in the city, and that means Corax II if they have it. It looks arbitrary and it is not: four things push the same way.
Wu Zetian is worth having at a high level for her own sake — she is the one you take to citadels — so most players have her further along than the legendaries that increase the other troop types. The bonus she puts on Corax ends up being the bigger one, and in a CP city it also means more troops fit.
The Valkyrie Diadem goes the same way: most players have it above the artifacts that do the same job for the other types.
Against Royal Lion the Medallion of Unity settles it. The Lion is a beast and its base bonus can be slightly better, but there is no specialists' answer to a medallion that increases guardsmen's health, and that alone covers the gap almost every time.
And after a run you are left with more Corax than you need, because reviving is cheaper than training and the survivors pile up. A flying unit is the more useful thing to have piled up.
The CP city
A CP city is one city kept for hosting runs, rather than whoever hosts emptying their own.
Your own city does not have to be emptied of everything that is not Corax.
Amanitore's bonus applies, and it is a good one on both strength and health.
The host is a player from another clan, and the clan doing the run hits that one city together — a reinforced attack, one march with the members piling into it, not a queue of separate hits. The sizing is the whole problem: too few troops on the host and the attack takes everything, too many and the clan cannot clear it.
Who takes the hits back
The limits on what each member sends do two jobs: they keep everyone on a similar stack, and they decide who takes the return hits.
The defence hits back, and it hits the fattest attacker. So one player — the shield — sends a little more than everyone else, takes the return, and the rest come away untouched. Everyone else is capped precisely so that they stay under him.
That makes the shield’s losses the only bill of the run, and it is why a clan picks a player who can carry them and rotates the job. It is also why the caps are a list and not a guideline: one member over his number and the return lands on the wrong player.
And more strength does not buy more pointsWhat you take home is set by the defending troops and by your Dustan, not by how hard you hit. Strength is rarely the problem — a clan march beats the host almost every time — and when it does, the battle ends there and a good part of the march never swings. That is fine; it just means the extra power was never what the points were coming from.
Attacking
Dustan, always, in every run.
Amanitore as a second, because a clan run is a group march — a group of players, which is the only case her bonus was ever written for.
Beyond those, the slot is free — and a clan that can already kill the defence can spend it on a captain it wants levelled rather than on more strength. For example, Carter. It stays fair as long as everybody brings the same ones.
Do not hold either of them back for being low level. They earn Experience from the runs themselves, so they climb while you use them.
Beyond those two there is no list. Which captain is worth a slot depends on the levels and stars yours happen to have.
Mercenaries: it depends on the clan, and most advise against them. Not for their strength — with mercenaries in the march it is much harder to keep every member’s stacks in line, and that is what decides who takes the return hits.
Hosting
What you are paid for
The attacker is paid for the strength and the health of what is defending, in equal halves.
Health alone is the common belief and it is wrong. An artifact worth 300 % strength to the defenders hands over more than one worth 200 % health, which is why a defender's kit sometimes has the Fan in it, or Cleopatra among the captains.
How much
One big stack, not a spread. Every health and strength bonus you own for that one type, pointed at it.
Roughly a quarter of what you would field defending your own city through a portal: one player's figures were 160,000 Corax II at home against about 40,000 sent to the run.
What clans do
Captains, best first at the same level and stars: Skadi, Beowulf, Amanitore where her bonus applies, Wu Zetian, and then Aydae or Brunhild.
Equipment: the unique Path of the Skybreaker armour, enchanted and gemmed for flying health, or the Immortal Warrior set, which is generally the better of the two.
Artifacts: the Forest Crown is the best of them for a host, with the Valkyrie Diadem, the Medallion of Unity and the Source Flask behind it.
Sharing it out
A whole clan can run together, but only if the numbers are set so everyone comes away with a similar haul.
What clans do
Fixed squads, the same for everyone: it is what makes the caps enforceable, and what keeps the share even when nobody is counting.
Whoever supplies the troops that get killed rotates from one run to the next, rather than falling on the same player every time.
Run it on a Vault day, so what the shield loses is revived with Silver instead of Gold.
1v1 CP runs
Two players arrange it between them: one defends and the other attacks. There is no ladder to work out and no share to settle, which is most of what makes a clan run complicated.
The attacker pays the host in Silver, at a price the two of them agree. It usually lands between 1M and 2M Silver for every 1B Conquest Points.
Whether the two of you are in the same clan family, which is what moves the price furthest.
The highest tier of flying troops the host can put up.
That is the whole arrangement. A clan run is the complicated one, and it needs the coordination that this does not.
Commonly believed
All that matters in a conquest-point defender is health, since health is what the attacker is paid for.
Strength and health count in equal halves. Given a choice between an artifact worth 300 % strength to the defenders and one worth 200 % health, the strength one hands over more.
Mounted defenders hand the attackers more Conquest Points.
The points follow the strength and health on offer and nothing else — the defenders' own counters do not enter into it. What mounted defenders do is cost the attacker fewer troops, because more of an attacking army counters mounted than anything else, though in a run that is being managed properly the difference does not show. Guard 9 flying Corax are the usual pick over mounted, for reasons that belong elsewhere.