What was Gandalf's "Fool's Hope"?

The wheels of the world are being turned by small hands.

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Pippin: 'Tell me, is there any hope? For Frodo, I mean; or at least mostly for Frodo.'

Gandalf put his hand on Pippin's head.

'There never was much hope,' he answered. 'Just a fool's hope, as I have been told. 

Politically speaking, to entrust the One Ring to Frodo was foolishness at its worst. Saruman ridiculed Gandalf for that, adding that…