  We study here a variant of the Abelian Sandpile Model, where the playground
is a cylinder of width $w$ and of circumference c. When c << w, we describe a
phenomenon which has not been observed in other geometries: the probability
distribution of avalanche sizes has a ladder structure, with the first step
consisting of avalanches of size up to w c/2 that are essentially equiprobable,
except for a small exponential tail of order about 10c. We explain this
phenomenon and describe subsequent steps.
