Learn Polish: Gdzie jest mój kupon? Oby nikt go nie wziął. - Where is my betting slip? Hopefully no one took it.

The particle oby is always followed by the past-tense form (the L-participle) to express a strong wish, hope, or fear. In this sentence, you are hoping that the action of someone taking the ticket did not already happen. Even if you were hoping for a future event, oby would still require this past-tense structure.

Why does wziął take the masculine singular form here?

The negative pronoun nikt (no one) grammatically acts as a third-person singular masculine subject. Whenever nikt is the subject of a past-tense sentence, the verb must take the masculine singular ending -ł, regardless of the actual gender of the unknown person who might have taken it.

Why is the pronoun go placed right in the middle of nikt and nie wziął?

Short-form pronouns like go are unstressed clitics, meaning they sound unnatural at the very beginning or the very end of a clause. Tucking go into the middle of the sentence, right before the negative particle nie, is the most natural and standard position for it in Polish.

Does the double negative of nikt and nie wziął cancel out to make a positive?