No real choice at all - the only options being to either accept or refuse the offer that is given to you.
Two options: take it or leave it; that's 'Hobson's choice'. The expression is best known in the UK, but became used worldwide following the successful eponymous 1954 film starring Charles Laughton.
There is a story that this expression comes from a Mr. Hobson who hired out horses and gave his customers no choice as to which horse they could take. This has all the credentials of a 'folk etymology' myth but, in this case, the derivation is correct.
A search of Google returns several thousand hits for 'Hobbesian choice'. The mistaken uses of that phrase, in place of the correct 'Hobson's choice', originate from a confusion between the celebrated philosopher Thomas Hobbes (who, incidentally, was the originator of another commonplace phrase - 'nasty, brutish and short') and the less well-known carrier Thomas Hobson, to whom the phrase refers.
Thomas Hobson (1545–1631) ran a thriving carrier and horse rental business in Cambridge, England, around the turn of the 17th century. Hobson rented out horses, mainly to Cambridge University students, but refused to hire them out other than in the order he chose. The choice his customers were given was 'this or none'; quite literally, not their choice but Hobson's choice.
The phrase was already being described as proverbial less than thirty years after Hobson's death. The Quaker scholar Samuel Fisher referred to the phrase in his religious text, The Rustick's Alarm to the Rabbies, 1660:
"If in this Case there be no other (as the Proverb is) then Hobson's choice ... which is, chuse whether you will have this or none."
The Spectator, No. 509, 1712, explained how Hobson did business, which shows clearly how the phrase came into being:
"He lived in Cambridge, and observing that the Scholars rid hard, his manner was to keep a large Stable of Horses, ... when a Man came for a Horse, he was led into the Stable, where there was great Choice, but he obliged him to take the Horse which stood next to the Stable-Door; so that every Customer was alike well served according."
After his death in 1631, Hobson was remembered in verse by no less a figure than John Milton, saying "He had bin an immortall Carrier". That seems rather a strange thing to say just after he had died. Eighty-six was a very good innings in the 17th century, but hardly immortality.
The phrase was still well enough known in the 20th century for 'hobsons' to be adopted then as Cockney rhyming slang for 'voice'. It has no connection with the similar sounding 'Hobson-Jobson', which derived as a corruption by British soldiers in India of the Arabic street cry 'Yā Ḥasan! Yā Ḥusayn!' = 'O Hasan! O Husain!'' (Hasan and Husain were grandsons of Muhammad).
The most celebrated application of Hobson's choice in the 20th century was Henry Ford's offer of the Model-T Ford in 'any colour you like, so long as it's black'.
See also: Buggins' turn.