Abarim Publications' online Biblical Greek Dictionary
The curious verb τυγχανω (tugchano) basically describes a motion that comes to a sudden halt, either in a selected target or in an accidental one. It may mean to gain, attain or obtain (Luke 20:35, Acts 24:2, 26:22, 27:3 and 2 Timothy 2:10), or it may mean to happen or to chance.
In this second sense, it's used in combination with the particle ει (ei), meaning if, and thus acquires the meaning of "if it so happens" or "perhaps" or "for example" (1 Corinthians 14:10 and 15:37). In Luke 10:30 our verb appears to express the unintended condition of the victim of the Good Samaritan story, who "happened to be" half-dead when the robbers left him (it stands to reason that the robbers had wanted to kill the man).
The participles τυχων and τυχον (tuchon) express chance but likely chance: "perhaps" in the sense of "probably" (1 Corinthians 16:6). Combined with the particle of negation ου (ou) it expresses "not probable" or "uncommon" (Acts 19:11, 28:2).
The derived noun τυχη (tuche) doesn't occur in the Bible apart from in the names listed below. According to Liddell and Scott (An Intermediate Greek-English Lexicon) it denotes "the good which man obtains (τυγχανει) by the favor of the gods, good fortune, luck, success."
Secondarily, this word means general fortune or chance whether good or bad, and thirdly it may describe mere chance, happenstance or accident.
A common compound constructed from this word and the prefix ευ (eu), meaning good is the verb ευτυχεω (eutucheo), meaning to be lucky or fortunate. The word τυχικος (tuchikos) means fortuitous or casual. The term τυχικος περιπτωσις, literally the "lucky stumbling-upon ones", applied to empiric physicians.
In the Greek world our word τυχη (tuche) became personified by the goddess Tyche, the equivalent of the Roman deity Fortuna, and our modern derivative Lady Luck.
Also note that these words appear to be somewhat related to the verb τευχω (teucho), meaning to make or make ready, or at least that of certain conjugations it's not clear whether they stem from τευχω or τυγχανω.