Using a 0th order Markov chain with probabilities of 0.25 for each nucleotide A,C,G,U, 50 random RNA sequences were generated for each length , from 20 to 200 in steps of 20.

For each value of , 1000 structures were sampled, by applying the Ding-Lawrence sampling algorithm [36], as implemented in RNAsubopt with flag -p, and by applying RNAlocopt. For each run, the number of non-redundant samples is computed, yielding the expected number for RNAsubopt and RNAlocopt, where is the error bound (standard deviation , since 50 sequences generated). For each run the percent coverage of the partition function was computed; i.e. the sum of the Boltzmann factors of the non-redundant collection from 1000 samples generated by RNAsubopt [resp. RNAlocopt], divided by the partition function [resp. partition function of locally optimal structures]. Since the number of locally optimal structures is far fewer than that of all structures (see Figure 5), it is not surprising that there is proportionately more redundancy among sampled locally optimal structures than than over all structures. As well, the percentage coverage of the partition function for sampled locally optimal structures is higher than that for the Boltzmann ensemble.