Why Is the 33.3% Threshold Significant in the Context of Chain Competition?

The 33.3% (one-third) threshold is significant because if a malicious miner controls this much hashrate, they can, in theory, guarantee that their secret chain will eventually win against the honest chain, even if the honest chain has a head start. This is due to the probability distribution of block discovery; at 33.3%, the selfish miner has enough power to consistently overcome the honest network's lead in the long run.