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Apart from spawning in swamps (added in 1.4), slimes can only spawn in every 10th chunk in average (Slime Chunks). Chunks are 16x16 blocks wide (x and z axis) and 256 blocks high (y axis). Slime Chunks are predetermined by your savegame seed, and are always the same for a specific seed, just like the generated terrain.
Health of a slime is also dependent on its size. When killed, a Big slime splits into about 4 Medium slimes, and each Medium slime splits into 4 small slimes. This allows a player to get 16-48 slimeballs on average for each Big Slime. Slimes will only spawn between bedrock and the 16th layer of the Overworld. There is only a 10% chance of spawning slimes in any game chunk.