A Pom Slice is similar to a Pom of Power, in that it increases the level of one of your boons on acquisition. The primary difference is that it levels up a boon at random, rather than giving up to three choices. Pom Slices can only be purchased from Charon's shop for 50 .
From level 1 to 6, for most boons, strength increases with diminishing intensity, i.e. there is a more significant boost between level 1 to 2 than 2 to 3, etc. With some approximation, the rate between level 1 and 6 can be expressed as divided by 2 every 2 level with a starting value set. For example Poseidon's Special level 2 to 6 is +28%, +20%, +14%, +10%, +7%. Past level 6, for most boons, strength will continue to increase at a small linear value; for example, Aphrodite's Strike level 5 to 6 and upper will always increase by 5% per level. Some exceptions exist, however, such as Ares's Doom-inflicting boons, that will continue to decrease until it will add 1 per level only.
Boons that have low base value (Such as Dionysus's Hangover damage, Artemis's Pressure Points, or Demeter's Glacial Glare) will increase linearly by 1 with each level from the start. A select few, such as Athena's Aid, increases less than 1 per level.
The strength increase from a level is independent of a boon's quality, and the level of a boon is preserved when its quality changes.
Increasing a boon's level also increases its value when being sold at a Pool of Purging.