倒 (actually / on the contrary)

Not what you'd expect

• Your friend expected the small restaurant to be cheap, but it was pricey and the fancy one was cheap.
• 这家zhè jiāsmall小xiǎorestaurant饭馆fàn guǎnactually倒dàostraight挺tǐngexpensive贵guì(modifier / structural particle)的de。 — "This little restaurant is actually quite expensive (surprisingly)."

actually倒dào + predicate = actually, contrary to expectation

• actually倒dào marks a result opposite to what you would expect: "actually, on the contrary".
• It sits after the subject, before the verb or adjective: he他tāactually倒dàonot不bùanxious着急zháo jí.

everyone大家dà jiāall都dōuvery很hěnworried担心dān xīn，he他tāactually倒dàonot不bùanxious着急zháo jí。

Softening or conceding

• the goods东西dōng xiactually倒dàoto be / is是shìfine不错bú cuò，it's just that就是jiù shìtoo太tàiexpensive贵guì(completed / change)了le。 — "The goods are fine, it's just that they're too expensive." (actually倒dàoto be / is是shì concedes a point before a "but")
• you你nǐvariant of 说说shuō(degree marker)得deactually倒dàoeasy容易róng yì！ — "That's easy for you to say!" (ironic)

the goods东西dōng xiadmittedly倒是dào shìfine不错bú cuò，it's just that就是jiù shìtoo太tàiexpensive贵guì了le。

Contrast with an expectation

actually倒dào versus but却què and instead反而fǎn ér

• but却què = "but, yet", a plain contrast: he他tāvery很hěnrope累lèi，but却quèto sleep睡shuìnot不bù(ongoing -ing)着zhe.
• instead反而fǎn ér = "on the contrary, instead", stronger: take吃chī(completed / change)了lemedicine药yào，the illness病bìnginstead反而fǎn éreven more更gèngserious重zhòng(completed / change)了le.

take吃chī了lemedicine药yào，the illness病bìnginstead反而fǎn éreven more更gèngserious重zhòng了le。

Recap

Read the full reference: HSK 4 grammar — "But" statements.