What is the root of Tyrion and Cersei's conflict?

Cersei has hated Tyrion since birth — she believed a prophecy that she would be murdered by the valonqar (Valyrian for "little brother") and applied it to Tyrion immediately. She also blamed him for their mother's death. Their conflict is therefore personal, irrational, and nearly impossible to resolve because it was never about anything Tyrion actually did.

How does Cersei outmaneuver Tyrion politically?

Through emotion and ruthlessness. Tyrion thinks in systems; Cersei thinks in people. She understands Tywin's vanity, Joffrey's cruelty, and Jaime's love for her in ways that let her leverage them against Tyrion. Where Tyrion is playing chess, Cersei is flipping the board. He consistently underestimates how far she'll go.

What does Tyrion understand about Cersei that others miss?

That her greatest strength — her love for her children — is also her greatest vulnerability. She will do anything to protect Joffrey, Myrcella, and Tommen. This makes her predictable in ways that pure power calculation doesn't. Tyrion uses this in the Blackwater defenses; he also fails to use it adequately in later seasons.

Are there moments of genuine connection between them?

Brief ones. In season 5, imprisoned separately, they share wine through Jaime and have something close to honest conversation. Both know what the other is. There's a dark mutual respect alongside the hostility — they're the two Lannister children who understand the game most clearly, which makes them natural rivals.

What does their dynamic reveal about Game of Thrones' themes?

That intelligence and ruthlessness are different instruments, and the game rewards ruthlessness more consistently than intelligence. Cersei loses eventually — but she outlasts Tyrion's best efforts for seven seasons.