Short Summary

Chekhov's Vanka is a short story which ostensibly has a lot of trappings of hope. First, the story takes place on Christmas Eve, a time traditionally associated with redemption (through the birth of Jesus) and the granting of wishes (presents are normally given during the Christmas season and Santa Claus is additionally supposed to deliver presents on Christmas Eve).
Second, the titular Vanka is an orphan apprenticed to an abusive shoemaker, the master dragged me by the hair into the yard and gave me a beating. So fearful is Vanka of his master that he must write his letter in secret, before tracing the shape of the first letter, he looked several times fearfully in the direction of the doors and windows. Usually stories featuring plucky orphans under abusive custodians (like Annie, Oliver Twist or even Cinderella) end up with the orphan escaping their horrid surroundings to a new home of love and sunlight.
Third, there is a hero just waiting in the wings to rescue Vanka. His grandfather, Konstantin Makarich, is a jolly man, his face always crinkling with laughter who Vanka has spent happy times with, They had a wonderful time together. Grandfather chuckled, the frost crackled, and Vanka, not to be outdone, clucked away cheerfully. Based on this descrption, it would be fair for the reader to assume that Konstantin Makarich will come at once to rescue his grandson once he hears of his (Vanka's) plight.
All the elements for a potential happy ending are in place. Vanka ran to the nearest mailbox and thrust his precious letter into the slot. He had learned from clerks how, letters were dropped in boxes and from these boxes they were carried all over the world. However, the clerks did not mention, and Vanka does not realize, that such letters need to have a stamp on them. Vanka clearly only has an envelope without a stamp, Vanka twice folded the sheet of paper and then he put it in an envelope bought the previous day for a kopeck. Without such a stamp, there is no possibility that his letter will reach his grandfather.
The elements of hope which the story lines up so neatly are all for naught for want of a simple but crucial detail. Vanka does not know any better, of course. In fact his knowledge of the postal system is only secondhand, as the clerks did not tell him he needed a stamp, he did not buy a stamp. Thus do the mundane realities of the world oftentimes crush grandiose, perhaps childish, hopes.
Moreover, Vanka's descriptions of Konstantin Makarich call into question as well the character of his grandfather. Certainly Makarich sounds like an amiable chap, but is he really willing to raise his grandchild? There is a subtle hint in the story that it was Makarich that sent Vanka away, when Pelageya died, they relegated the orphan Vanka to the servants' kitchen to be with his Grandfather, and from there he went to Moscow to the shoemaker Alyakhin.... As such, even if the letter somehow reached Makarch, it is most likely that he would not have come and rescued his grandchild.
Sometimes cliches of hope fair little against the cruel realities of the world.

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