Who knows, maybe: biết đâu

Biết đâu at the start of a sentence means "who knows, maybe": it raises a possibility nobody can rule out. Biết đâu ảnh lại đồng ý. Who knows, he might say yes (in Hà Nội, anh ấy). Lại before the verb often goes with it, when the outcome would go against what you expect.

Very often it gives a reason to do something: try, ask, or be ready. The suggestion comes first and biết đâu follows: Mua vé số đi, biết đâu trúng. Buy a lottery ticket, you never know, you might win. Mang dù theo đi, biết đâu trời mưa. Take an umbrella, it might rain (in Hà Nội, ô).

As a reply on its own, say Biết đâu được! (in Hà Nội, also Biết đâu đấy!): you never know!

Có lẽ (perhaps) is a guess about what's probably true. Biết đâu keeps a chance open, often a hopeful one. Sợ là expects the outcome you don't want: Em sợ là trời mưa. I'm afraid it'll rain. And liệu simply asks: Liệu trời có mưa không? I wonder if it'll rain.

Watch the place. After a person, biết đâu means the opposite, "how would I know?": Em biết đâu! That's the same push-back as Em đâu có biết!: you're saying you had no idea, not raising a possibility.