Minecraft wiki entry for Spider, associated text: 0–2 String. The maximum is increased by 1 per level of Looting, for 0-5 string with Looting III.
5 when killed by a player or tamed wolf.
A 1⁄3 chance of dropping a Spider Eye when killed by a player or tamed wolf. The maximum amount of spider eyes is increased by 1 per level of Looting. The chance of a spider not dropping any spider eyes can be found using the formula 2 / (Looting Level + 3). For example, Looting III gives a 1⁄3 chance of not dropping any spider eyes. All other amounts have an equal chance of occurring.