OpenAI holds a 63% implied probability of finishing as the second-largest private company by end of August 2026, with Anthropic at 33%, because Anthropic’s May Series H round valued it at $965 billion post-money—briefly making it the world’s most valuable private AI firm—while OpenAI’s March close at $852 billion keeps it the clear runner-up. These valuations, driven by enormous capital inflows into frontier large language models, have created a durable gap that other contenders such as Databricks, Stripe, or Anduril have not closed in recent months. With no major new funding rounds or IPOs announced for the next few weeks and AI revenue run-rates still accelerating for both leaders, traders see little near-term catalyst that would reorder the top private-company hierarchy before the August resolution.