  We investigate the Busy Beaver Game introduced by Rado (1962) generalized to
non-binary alphabets. Harland (2016) conjectured that activity (number of
steps) and productivity (number of non-blank symbols) of candidate machines
grow as the alphabet size increases. We prove this conjecture for any alphabet
size under the condition that the number of states is sufficiently large. For
the measure activity we show that increasing the alphabet size from two to
three allows an increase. By a classical construction it is even possible to
obtain a two-state machine increasing activity and productivity of any machine
if we allow an alphabet size depending on the number of states of the original
machine. We also show that an increase of the alphabet by a factor of three
admits an increase of activity.
