  We study the behaviour of Yang-Mills and gravity amplitudes under the soft
limit in the four-dimensional ambitwistor string formalism and derive their
soft theorems to arbitrary order. For this purpose, we apply some mathematics.
Methods of combinatorics are used for the expansion of $\delta$ functions, and
knowledge of graph theory is used for the expansion of reduced determinants.
Based on these preliminaries, we expand the formulas of Yang-Mills and gravity
amplitudes about the soft parameter $\epsilon$, and obtain soft theorems to
arbitrary order.
