Death Pierce

This item causes projectiles that "overkill" a block (hit a block with less HP than the bullet's damage) to pierce thru the block, carryin some of its remaining damage onward.

Whenever a bullet overkills a block, its damage is first reduced by the block's remaining HP. It's then reduced by a further factor, based on how many **Death Pierce** items are applied to the bullet.

For example, imagine you are using a Death Pierce item, and no skills. In that case, if a 100 damage projectile hits a 10 HP block, the projectile will first be reduced to 90 damage (100 - 10), then will be further cut in half, and will continue on with 45 remaining damage. If it hits another 10 HP block, it will reduce to 35 (45 - 10), then cut in half again to 17.5. It could pierce a third 10 HP block, reducing to 7.5 (17.5 - 10) and then halving to 3.75, whereupon a fourth similar block will finally fully absorb it and take 3.75 damage.

Adding more of the same item will mean more of the remaining damage is kept. See the math notes below for detailed info.

## Skill Upgrades

This item has 2 skills, which don't depend on each other. (You can take either, depending on which direction you approach them from.)

One of them gives a 20% chance to pierce instead. What this means is that when the projectile hits a block, there is a 20% chance that it will continue through without losing any damage at all. (So a 100 damage projectile hitting a 10 HP block would continue on with 100 damage.) So it behaves exactly like Pierce in this case.

The other skill gives a 50% chance not to lose any remaining damage. This means that when the game is working out how much remaining damage to lose (see Math notes below), it will have a 50% chance to not lose any of the remaining damage. If this procs then a 100 damage projectile hitting a 10 HP block would continue on with 90 remaining damage. Note this skill does not prevent the projectile losing the damage it deals to the block. If the projectile pierces, then this skill is not needed.

## Interaction with other items

When using Pierce items as well, the Death Pierce item will be ignored until the Pierce Charges have been used up.

When using bounce Items, the Death Pierce item will be applied before those items. This means bounce items are not worth using with Death Pierce in most cases, since they only work once the projectile has not enough damage left to destroy a block.

**Death Pierce** is only effective with high-damage projectiles, so it combos well with items that significantly increase your per-projectile damage, notably Combine 10 or the Random Split items.

## Usage Notes

This item should only be used when your projectile damage is much higher than the block HP for the level you are playing. That way one projectile can destroy many blocks in a row without losing all its damage. The most common situation where this is useful is in Waves.

## Math notes

The formula for the amount that the remaining damage is reduced by is 1/(n\*(n+1)), where n is the number of Death Pierce items in the path. So for example, with 1 item, the remaining damage is reduced by 1/2 or 50%. With 2 items, it is only reduced by 1/6, and with 3 items it would be 1/12 etc...

So for the initial example (a 100 damage projectile, piercing 10HP blocks), with two **Death Pierces** the first block would reduce the damage to 90, and then remove just a sixth, leaving it with 75 damage (rather than 45). The next would reduce it to 65, then remove a sixth leaving it with 54.2 damage. Etc.

Note, that formula only affects the remaining damage. That means the damage used to destroy the block initially is removed from the projectile before the formula is applied.