he probably has a hard time retaining any staff of servants at all.

"Come," I said, with decision, "we will go back; your health is precious. You are rich, respected, admired, beloved; you are happy, as once I was. You are a man to be missed. For me it is no matter."

When he orders his servants to remain in the palazzo while he is gone overnight, he is not exactly using reverse psychology. Not all servants would behave as Montresor's servants have done. His servants don't respect him because he doesn't pay them enough money. And furthermore, he can't afford to hire the best class of servants. There must be times when he can't pay his staff anything. They stay on because they have a roof over their heads and get something to eat. (They probably also get plenty of wine to drink!) The servants do not "abscond" because Montresor tells them to stay at home; they do so because he tells them he will be gone all night. They don't care if he finds out that they all left to join in the carnival. He can't fire them because he can't get anybody to replace them. And such an enormous old dwelling needs some servants to keep it from ruin. And if he should fire them, they wouldn't have lost anything.

How does Montresor obtain any income at all? Why does he choose to live in an enormous palazzo when he is all alone in the world?

Throughout Poe's classic short story "The Cask of Amontillado," the protagonist and narrator, Montresor, explains how he formulated and executed revenge on his unsuspecting enemy, Fortunato. Montresor cleverly waits to approach Fortunato during the hectic carnival season, where he is certain to discover his enemy intoxicated from hours of partying and drinking. After approaching Fortunato in a friendly manner, Montresor plays on Fortunato's pride and affinity for fine wines by telling him that he has acquired a pipe of Amontillado and was seeking Luchresi's expertise to authenticate the wine. Fortunato falls for Montresor's trap and demands that he taste the Amontillado.

Montresor proceeds to guide Fortunato to his palazzo and the two characters leave the carnival together. Montresor informs the reader that he knew his palazzo would be empty because he purposely told his servants that he would not return until the morning. Montresor understands that his servants will surely leave his home and abandon their duties as soon as he departs. This astute observation reveals that Montresor is an expert on human nature and duplicity. Being of the same mind as his servants, Montresor is aware of their true intentions and anticipates that they will abandon their duties as soon as his back is turned. Montresor's plan works and no one is home when he returns to his palazzo with Fortunato. Therefore, there are no witnesses and Montresor can successfully execute his revenge with impunity.

"The Cask of Amontillado" by Edgar Allan Poe is told from the first person point of view of the villain, Montresor. It appears to be written in the form of a confession, with the "you" being addressed perhaps a priest administering last rites. 

Montresor own the palazzo in question and apparently lives alone there except for his servants. He deliberately chose the night of the Carnival for his plot. He tells his servants that he will be gone all night at the Carnival and orders them to stay in the house and look after it, knowing that the desire of the servants to get out and attend the Carnival will cause them to disobey his orders to remain at the house. This is especially clever, because if the servants are called upon to testify in court, they will lie and say they were at the house in order to avoid getting in trouble with their master

Montresor knew the house would be empty because he told the servants to be home.

Montresor is an expert in reverse psychology.  He knows that if he tells his servants that he will not be home, but orders them to stay there, they will all take off.  Who wants to be home during carnival when the boss is away?

Montresor is trying to give himself an alibi.  He tells her servants that he would not be home until morning to make sure that they all leave his house. 

There were no attendants at home; they had absconded to make merry in honour of the time. I had told them that I should not return until the morning, and had given them explicit orders not to stir from the house. These orders were sufficient, I well knew, to insure their immediate disappearance, one and all, as soon as my back was turned.

If they are questioned, they will tell the police that they were at the house all night for fear of losing their jobs.  Thus Montresor is not there, and the servants are not there, but if anyone would ask they will all say that they were there.  No one will know where he actually was.

If Montresor returns with a trowel and the ingredients to make a brick wall, smelling of nitre from the catacombs, no one will be there to see it.  His servants are all out playing while he kills a man.

Montresor is a very clever man, and he plans the murder out to the most minute of details.  There will be no one to see him out with Fortunato, and even if they did they may not recognize him because of the costume.  Also, many people will be drunk.  There will be no one to vouch for the fact that Montresor was not home or describe the condition he was in when he returned.

Poe uses many things for double purposes. When Montresor tells his servants he will not return until morning and gives them explicit orders not to stir from the house, he knows they will all disappear as soon as his back is turned. This rids the house of servants, so there will be no one to see that he has brought Fortunato home with him. But it also is a sign of Montresor's poverty. He can only afford inferior-quality servants, and he may not be paying them regularly. They do pretty much as they please because they know he can't fire them, and they wouldn't care if he did. With the servants gone, the palazzo is empty. This shows that Montresor is all alone in the world. Poe shows Montresor's knowledge of human nature, his use of reverse psychology, his poverty, his precarious social position, and the absence of loved ones in his life.

Montressor is no fool; he knows human nature and psychology. Because it is Carnival, and everyone wants to participate in the festivities, he shrewdly tells his servants that he will be away from town overnight and orders them not to leave.

Of course, knowing people the way he does, Montressor fully expects his servants to vacate the premisis as soon as he is a safe distance from the house. And he is of course right in this assumption. After all, when the cat's away the mice will play, will they not?

Just like anyone whose parents have set limits, the servants take the first opportunity to get away with breaking their authority's rules. They think they can figuratively get away with murder when the Lord of the house isn't around, but it is Montressor who, in fact, is planning to get away with murder--literally.

The setting of the story is during the carnival season.  The narrator (Montresor) portrays himself as ultra savvy and states:

There were no attendants at home; they had absconded to make merry in honour of the time. I had told them that I should not return until the morning, and had given them explicit orders not to stir from the house. These orders were sufficient, I well knew, to insure their immediate disappearance, one and all, as soon as my back was turned.

Thus, Montresor uses reverse psychology on his servants.  He knows that if he tells them not to leave the house when he really wants them to, that they will disobey him because he has "leaked" the information that he will not be home to verify if they are there.  In setting up this scenario, he provides himself with an alibi because the attendants will tell those who ask that their master was out of the house and will, of course, tell no one that they were not there in order to cover their disobedience.  Additionally, Montresor is free to kill Fortunato with no witnesses.

In "The Cask of Amontillado," Montressor, the narrator, explains:

There were no attendants at home; they had absconded to make merry in honour of the time.  I had told them that I should not return until the morning and had given them explicit orders not to stir from the house. These orders were sufficient, I well knew, to insure their immediate disappearance, one and all, as soon as my back was turned.

This, of course, assures that there will be no servants in the palazzo when Montressor arrives with Fortunato. It also shows that Montressor employs disobedient servants who have no respect for him.

The fact that Montresor was only concerned about getting rid of the servants that night, in addition to the fact that the palazzo appears to be empty when he and Fortunato arrive, is a subtle way of indicating Montresor's loneliness. He doesn't have to worry about encountering any family members because there are no family members. Any family he may have had at one time would be among the skeletons lining the walls of the catacombs below his palazzo.

When they are underground, Montresor tells his intended victim:

"You are rich, respected, admired, beloved; you are happy as once I was. You are a man to be missed. For me it is no matter."

This may be indicating that Montresor is not rich, is not respected (even by his servants), is not admired, is not beloved. Montresor is not a man to be missed because there is nobody at home to miss him. His large, possibly decaying palazzo is nearly empty.

Why does he keep such a large house and a staff of servants, however disrespectful and unreliable? Venice is a decaying city. The palazzos may be relics of the city's past glory. Montresor indicates that his palazzo is situated at some distance from the city and that the catacombs are under the river--probably the Po River.