[verb (dictionary form)] + まい [v1] 食べる → 食べるまい / 食べまい [する] する → するまい / すまい [来る] 来る → くるまい / こまい
まい is a literary negative with two meanings: "I will not", a firm decision about what you yourself will do, and "probably won't", a guess about someone or something else. It follows the dictionary form of a godan verb; an ichidan verb takes either the dictionary form or the stem.
With the speaker as subject, まい is a resolution. It often comes with にど二度と or もう, or is reported with とおもう思う or ときめる決める.
With anyone or anything else as subject, まい is the speaker's guess, the negative partner of だろう.
まい belongs to writing, speeches and resolutions said to oneself. In conversation, "probably won't" is きごう〜ないだろう and "I won't" is きごう〜ないつもりだ or もうきごう〜ない.
The pairing きごう〜ようがが〜まいが, "whether or not", is a separate point: あめがふろう雨が降ろうがふる降るまいが、しあい試合はおこなわれる行われる。