beta=  0.05: F*=+0.5270  closed form=+0.5270  min gap to 5000x3 random pi=0.0015  TV(pi*, p)=0.417  mass on argmax R=0.208
beta=   0.5: F*=+0.3761  closed form=+0.3761  min gap to 5000x3 random pi=0.0140  TV(pi*, p)=0.244  mass on argmax R=0.077
beta=   1.0: F*=+0.3212  closed form=+0.3212  min gap to 5000x3 random pi=0.0494  TV(pi*, p)=0.151  mass on argmax R=0.065
beta=   5.0: F*=+0.2590  closed form=+0.2590  min gap to 5000x3 random pi=0.3858  TV(pi*, p)=0.036  mass on argmax R=0.053
beta=  50.0: F*=+0.2425  closed form=+0.2425  min gap to 5000x3 random pi=2.8790  TV(pi*, p)=0.004  mass on argmax R=0.050
