Numerically calculated limiting detection likelihood in stacks of a long and a short observation. For given counts (source plus background) and exposure time ratios, the detection likelihood L_long in the long observation and L_stack in the stack are calculated. The curves show equal likelihoods L_stack = L_long, each for a fixed count number. Counts increase from right to left from 15 to 5000 in 18 steps of 0.14 dex.