  We perform an exploratory investigation of how rapidly the physics of SO(2N)
gauge theories approaches its N=oo limit. This question has recently become
topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge
theories, but do not have a finite chemical potential sign problem. We consider
only the pure gauge theory and, because of the inconvenient location of the
lattice strong-to-weak coupling 'bulk' transition in 3+1 dimensions, we largely
confine our numerical calculations to 2+1 dimensions. We discuss analytic
expectations in both D=2+1 and D=3+1, show that the SO(6) and SU(4) spectra do
indeed appear to be the same, and show that a number of mass ratios do indeed
appear to agree in the large-N limit. In particular SO(6) and SU(3) gauge
theories are quite similar except for the values of the string tension and
coupling, both of which differences can be readily understood.
