Piety Scumming

How to get piety without sacrificing.

Basics

Piety Scumming refers to ways of gaining massive amounts of piety without sacrificing on altars. There are a couple methods for doing this, and both abuse the fact that the more you pray for something, the more piety it costs.

Alignment Switching

Praying reduces your piety with your current god, but increases your piety with the two unaligned gods. If you pray enough to reach summoning wrath, another 200 prayers are sufficient to max out piety with the other gods. At this point you can change your alignment and have enough piety for the rest of the game. The cost of an unheard prayer will be extremely high, so care has to be taken to avoid praying when there is nothing for your new god(s) to grant.

Prayer Cost Overflow

If you make enough unheard prayers, the piety cost will increase so much that it overflows to a large negative value. This takes around 1400 prayers while uncrowned, and 2000 while crowned (the cost of prayers is halved while crowned, so more are required to overflow). Once the cost has overflowed at crowned, it will remain negative for around 100 more prayers, allowing you to reset piety back to the maximum with an unheard prayer.

Surviving Divine Wrath

Precautions need to be taken to avoid getting ruined by divine wrath.

Item Cursing

The first stage of divine wrath curses every single item you are carrying. Unequip and drop everything besides gold (and water, if you want to make unholy water) to avoid this.

Item Destruction and Dooming

The second stage of divine wrath attempts to destroy every item you have equipped. If you don't have any items equipped, it gives you the doomed intrinsic instead. Wield a single gold piece and reequip a new one every time it gets dusted.

Smiting

The third stage of divine wrath deals a large amount of irresistible damage. Have at least 90 HP to survive this. You will get hit by this wrath at most two times. As soon as you've been damaged once, rest up to full and begin preparing for summoning wrath.

Summoning Wrath

The final stage of divine wrath summons several powerful monsters around you: greater daemons for chaotic characters, holy slayers for neutral characters, and solars for lawful characters. Since it takes many prayers at this stage to complete piety scumming, these monsters must be prevented from reaching you.

Ice Queen

Monsters cannot be summoned to snow tiles, so this wrath effect doesn't really do anything in this area. Stick to the right side of the first level to avoid waking the snow golems.

Pros: Simple, safe to do either method of scumming at any alignment.
Cons: Accessing the area requires you to be level 15, and there's a small chance for artifacts to be generated in the treasure rooms, reducing the number of precrowns possible.

High Mountain Village

The down stairs in HMV are easy to isolate from the summons. There are two approaches for this.

Door creation
Create a locked door on the square below the stairs using a wand of door creation.

Pros: Safe to do either method of scumming.
Cons: Requires going through UD and finding a wand of door creation, renders HMV impassible. Can't scum at neutral alignment, because holy slayers can break down doors. If you don't have a key for the door and it ends up being trapped, there's a chance of it being destroyed when a summon attempts to open it.

Companions
Hire two companions from the Borderland Settlement and order them to wait on the two squares below the stairs.

Pros: Works at any alignment.
Cons: Requires going through UD, renders HMV impassible. Risky to do the overflow method of scumming, as there's a small chance for the summons to attack your companions.

Barbarian Glade

There are choke points on either side of the water at the very bottom of the level. Hire a companion from the borderland settlement and order it to wait next to you so that monsters can't reach you.

Pros: Easy to access area.
Cons: Can't scum at chaotic alignment, because greater daemons can hit you with fire breath. Risky to do the overflow method of scumming, as there's a small chance for the summons to attack your companion.

Infinite Dungeon

Divine wrath can only summon monsters within five spaces (horizontally, vertically, or diagonally) of the character. Find a white worm or other non-threatening breeder, take it to a new level with a corner stairs room of sufficient size, close the door, and wait until the room is completely filled with breeders. It's possible to do this in other dungeons as well, but the ID makes it easy to find an ideal room.

Pros: Easy to access area, safe to do either method of scumming at any alignment. Sometimes possible in weekly challenges.
Cons: Need to be tanky enough to survive a long period in melee with three of whatever breeder you use. Have to find an appropriate breeder.

Swamp

It's possible for swamp squares to have areas at the edge that are entirely isolated by water. Leave and reenter a swamp tile until the layout is this favorable.

Pros: Easy to access area, safe to do either method of scumming. Summons can be farmed with missile attacks.
Cons: Can't scum at chaotic alignment, because greater daemons can hit you with fire breath. Can take a lot of real-life time to get the required layout.

Terinyo

There's a one tile island at the center of town. Holy slayers and solars will tend to wander up and to the left, leaving a potential escape route.

Pros: East to access area, safe to do either method of scumming. Summons can be farmed with missile attacks.
Cons: Can't scum at chaotic alignment, because greater daemons can hit you with fire breath. Escape can be tricky without teleportation, especially for a slow character. Makes it difficult to access the NPCs in Terinyo.

[Yulgash]

Good call. One other speedrun strat is the good old Elementalist Frost Bolt -> Frost Bolt -> <- Fire Bolt in whatever lake you like. Not sure where to put it in the guide, but maybe this comment is enough :P

[Batrongordeg]

Time to update the guide with swamp and teryino scumming? Otherwise great guide!