What surreal numbers are representable by Red-Blue Hackenbush games?

All surreal numbers are representable by a Red–Blue Hackenbush game. This is discussed in On Numbers and Games, although it is left to the reader to fill in the details of the proof for the transfinite case. In Chapter 3 it is explained that every (surreal) number has a sign expansion. Then in Chapter 8 it is explained that the value of a Red–Blue Hackenbush chain is the number whose sign expansion is given by reading off the colors of the edges of the chain from the ground up, interpreting black edges as + and white edges as –. Of course one has to allow chains (or "beanstalks") whose edges are arranged in accordance with the structure of an arbitrary ordinal.