Appendix A Alternative algorithm to compute the weight

Instead of the method described in section 3.2.2, it is also possible to calculate the probability that a certain path on the tree t is followed explicitly, without having to use terms that represent the probability of generating a set of open/closed directions (Pg (0 tn), Pg (Oq I to,rWo)). This means that Oo and 0 do not appear in the super-detailed balance expression (equations 

6 and 3.8). When the probability to follow a path on the tree is equal to 1, to obey detailed balance and to use equation 3.9 as acceptance/rejection rule we have to redefine the weight W (tv) as 

To obtain the correct expression for W (o), we have to replace n with o  

To calculate , we have to extend all feelers up to the recoil length I and calculate the probabilities that each of these trial segments is open. 

It is instructive to discuss the situation I = 1 and N = 2. This system is schematically drawn in figure 3.2 (left). The probability that the first segment is open is equal to po. For the second 

---