Shall and will
On shall and will:
In formal writing, the future tense requires shall for the first person, will for the second and third. The formula to express the speaker’s belief regarding the future action or state is I shall; I will expresses determination or consent. A swimmer in distress cries, «I shall drown; no one will save me!» A suicide puts it the other way: «I will drown; no one shall save me!» In relaxed speech, however, the words shall and will are seldom used precisely; our ear guides us or fails to guide us, as the case may be, and we are quite likely to drown when we want to survive and survive when we want to drown.
William Strunk jr. and E. B. White. The Elements Of Style.
It’s always appeared to me that shall has a tinge of “should”.
Highly recommended reading.