wandlore - What was Dumbledore's plan for the Elder Wand? Why didn't he bequeath it to someone (Harry, Snape...) for safekeeping?

Dumbledore clearly put a good deal of thought into his plans regarding his last will, as well as the circumstances that would surround his demise.

Based on his final gifts, and his conversation with Harry on the matter, he clearly intended for Harry, Hermione, and Ron to discover the Deathly Hallows (albeit only gradually). It also seems that he very much did not want the Elder Wand's power to fall into improper hands. So why did he neither bequeath the Wand to the trio (even in an obscured or protected way, as with the Resurrection Stone) or to a trusted protector?

It would seem that, by not expressly stating a preference for the handling of the wand following his death, he puts its ultimate fate up to a great deal of risk. Why allow that?

Answer

Dumbledore intended for the Elder Wand to go to Snape for safe-keeping.

‘But you expected him to go after the wand?’

‘I have been sure that he would try, ever since your wand beat Voldemort’s in the graveyard of Little Hangleton. At first, he was afraid that you had conquered him by superior skill. Once he had kidnapped Ollivander, however, he discovered the existence of the twin cores. He thought that explained everything. Yet the borrowed wand did no better against yours! So Voldemort, instead of asking himself what quality it was in you that had made your wand so strong, what gift you possessed that he did not, naturally set out to find the one wand that, they said, would beat any other. For him, the Elder Wand has become an obsession to rival his obsession with you. He believes that the Elder Wand removes his last weakness and makes him truly invincible. Poor Severus ...’

‘If you planned your death with Snape, you meant him to end up with the Elder Wand, didn’t you?’

‘I admit that was my intention,’ said Dumbledore, ‘but it did not work as I intended, did it?’

‘No,’ said Harry. ‘That bit didn’t work out.’

Deathly Hallows - Pages 577-578 - British Hardcover - Adult Edition

Dumbledore wanted Snape to keep the Elder Wand safe after Dumbledore's death. However, when Draco Malfoy disarmed Dumbledore at the top of the Astronomy Tower the night Dumbledore died, he unintentionally, and unknowingly to all at that point, became master of the Elder Wand, even though it was Snape who ultimately killed Dumbledore. At the end of Deathly Hallows, with Harry as master of the Elder Wand, Harry plans to put the Elder Wand back with Dumbledore in Dumbledore's tomb:

‘I’m putting the Elder Wand,’ he told Dumbledore, who was watching him with enormous affection and admiration, ‘back where it came from. It can stay there. If I die a natural death like Ignotus, its power will be broken, won’t it? The previous master will never have been defeated. That’ll be the end of it.’

Dumbledore nodded. They smiled at each other.

Deathly Hallows - Page 600 - British Hardcover - Adult Edition

Dumbledore did have a plan; it just didn't work out.