  The MACHO project is a search for dark matter in the form of massive compact
halo objects (MACHOs). The project has photometrically monitored tens of
millions of stars in the Large Magellanic Cloud (LMC), Small Magellanic Cloud
(SMC), and Galactic bulge in search of rare gravitational microlensing events
caused by these otherwise invisible objects. In 5.7 years of observations
toward the LMC some 13-17 microlensing events have been observed by the MACHO
survey, allowing powerful statements to be made about the nature of the dark
population in the halo of our Galaxy. A critical component of these statements
is an accurate determination of the survey's detection efficiency. The
detection efficiency is a complicated function of temporal sampling, stellar
crowding (the luminosity function), image quality, photometry, time-series
analysis, and criteria used to select the microlensing candidates. Such a
complex interdependence is most naturally solved using a Monte Carlo approach.
Here we describe the details of the Monte Carlo used to calculate the
efficiency presented in the MACHO 5.7-year LMC results. Here we correct several
shortcomings of past determinations, including (1) adding fainter source stars
(2.5 magnitudes below our faintest detected "stars"), (2) an up-to-date
luminosity function for the LMC, (3) better sampling of real images in both
stellar density and observing conditions, (4) an improved scheme for adding
artificial microlensing onto a random sample of real lightcurves, and many
other improvements. [Abridged]
