searching for etymology of words in a song I heard.
snake baked a ho cake
and set the frog to watch it
the frog fell a dozing
the lizard came and took it
bring back my ho cake
you long tailed nanny-o
bring back my ho cake
you long tailed nanny-o
bring back my ho cake
you long tailed nanny-o
The song is reported to be part of a presumably American folk-game where a circle of children sing the song, while the song is "acted out" by the children. 

I speculate that a child carries a suitable token around a circle, such as a napkin, plate, or other ho-cake proxy. Then he selects a "frog" to guard the cake. Then the snake-player must steal the cake. I'm not able to guess the mechanics there. I wonder if any "skill" is required to steal the "ho-cake". Next a chase could ensue, around the circle. I'm guessing that the "snake" must reach the position vacated by the other actors before being caught. If the snake is caught, perhaps he's eliminated from the game. If the snake fails to steal the cake, he may be eliminate. If the "frog" fails to protect the cake, he may be eliminated. However, I suspect that only one actor is eliminated per episode, and that the circle decreases until only two players remain, who are the winners. This is ALL speculation.

A google search showed that a "ho-cake" is a kind of pancake made mainly with white flour and grease and any other suitable ingredients.
It's said to have been mixed in a washtub for large groups, using a hoe, particularly by slaves in the south.
They're also called "Johnny Cakes" because Johnny Reb also ate them, evidently, in the civil war.
That makes sense, knowing the methods of military mess hall cooking.

I also was intrigued that the thief, evidently an outsider (the lizard CAME and took it) was called nanny-o.
At first I thought that the the snake was a nanny, who took the ho-cake, but that didn't make sense in context.
I searched the web for the etymology and alternate meanings to Nanny, and didn't find anything that seemed to correspond. I'm assuming that the word "nanny-o" is nonsense, and used for it's sound and meter, rather than meaning.

Now the "curious" part. An entry following "nanny" at 
http://www.etymonline.com/index.php?search=nanny&searchmode=none
Nun 
O.E. nunne, from L.L. nonna "nun, tutor," originally (along with masc. nonnus) a term of address to elderly persons, perhaps from children's speech, reminiscent of nana (cf. Skt. nona, Pers. nana "mother," Gk. nanna "aunt," Serbo-Cr. nena "mother," It. nonna, Welsh nain "grandmother;" see nanny). Nunnery, c.1275, originally meant "nunhood." Sense of "house of ill-fame" is first recorded 1593.

It seems our junior/senior high school english teacher was somewhat more reasonable in her Hamlet commentary, and less hysterical than we may have formerly belived. 

I found in the online FAQ: http://www.shakespeare-online.com/faq/hamletfaq.html which give a somewhat un-compelling argument based on the context of the play:

Is 'nunnery' a euphemism for a brothel in Hamlet?

It is true that 'nunnery' had two very different meanings in Tudor England. Modern dictionaries only list one definition of the word, which is, of course, a convent. However, if you look up 'nunnery' in a dictionary of archaic words and uses, you will see that 'nunnery' did mean both a convent and a brothel in Shakespeare's day. Its meaning as a 'brothel' was colloquial, though, even in Tudor England. Despite the use of 'nunnery' as 'house of ill repute' in Shakespearean England, there can be no question that Hamlet is referring to the standard definition of the word -- a house of meditation for women who have devoted themselves to God. Only by entering a nunnery can Ophelia ensure that she will not procreate and become a breeder of sinners. As is pointed out in the Oxford edition of the play, "The injunction makes it clear that nunnery is not being used here in the sense of 'brothel', as it is in 'Christ's Tears' over Jerusalem, for example, where a nunnery is synonymous with a college of courtesans (Nashe, II. 151-2)." (243) Hamlet is indeed disgusted by the behaviour of his mother, and does take his hostility out on innocent Ophelia, but he does not call her a whore in this particular line. 

Greg again: as I re-read the act, I find the passage so ambiguous that I now see this as central to both Shakespeare's and Hamlet's purpose. That doesn't to be the accepted academic interpretation, though it is a subject of some controversy. The strongest argument is that if Hamlet had been suggesting only that Ophilia should go to a brothel, then its almost non-sensical to suggest that this avoids breeding sinners. Prostitutes did bear children. On the other hand, prostitutes generally do what they can to avoid bearing children, so it "almost" makes sense. But if this can be overlooked as an asymmetrical "flaw" in an otherwise elegantly ambiguous dialogue, the very ambivalence of the message can be seen as a masterful representation of the crisis in Hamlet's life and the focus of his statements and thoughts about it.

Hamlet is cloaking his meaning in ambiguity to protect himself, but he is also being extremely expressive and articulate and even "frank" if you undershand "where he is coming from" in his degenenerated view of life. I would assert that his ambiguity, ambivilance, and cynicism lie at the core of his message to Ophelia. He says plainly that he, himself, is not an entirely honest man, and will without much resistance subvert truth for the sake of beauty. Plainly, this is a reference to his initial belief in his mother, and in perhaps the "beauty" of the core notion of motherhood. It may also refer to the nature of his public and private relationship with Ophelia. This scene is the only private discussion that they have during the play. This always ambiguous, sometimes sarcastic dual meaning is the natural language of his cynicism and covert intent, and of his own inability to resolve his own dilema. Shakespeare uses it as a device to tell us not only what he thinks, but what he feels, which is double-minded, and about his waivering resolve.

He argues that, in human nature, truth is too easily sacrificed to the seduction of beauty. As a seeker after justice, Hamlet is desperately and dangerously seeking to expose truth. But he's become an extreme cynic. To hold on to her virtue, Ophelia must flee humanity, to a convent, secluded from the temptations of human nature, insofar as possible. On the other hand, even in religious selclusion, human nature is corrupt. Perhaps it's better to satisfy your needs with a fool. This suggestion begins the suggestion of an "inversion" of the concepts which may continue from that point forward in a negative sense. As an extension. in the extreme opposite sense, she could give in to corruption entirely, and thus escape, at least, being dishonest with herself about her own sins. 

His last private words to her are very harsh:
I have heard of your paintings too, well enough. God hath given you
one face, and you make yourselves another. You jig, you amble, and you lisp;
you nickname God's creatures and make your wantonness your ignorance. Go
to, I'll no more on't! it hath made me mad. I say, we will have no moe marriages.
Those that are married already- all but one- shall live; the rest shall keep as they
are. To a nunnery, go.

I don't understand the paintings allusion. Is he perhaps referring to facial make up? I doubt it. You can see that, and don't need to hear about it. Knowing his meaning here might shed considerable light on the meaning of the rest of the dialogue. Perhaps he is merely using the visual imagery of two portraits representing a private and a public persona to heighten the the metaphor of his accusation of her own two-faced nature. 

He accuses her of being two faced, and self-decieved specifically regarding her own wantonness. In the "negative" sense of his double-edged exhortation, he's cynically suggesting that it's more honest to be honestly unfaithful, as a harlot, than to betray marriage vows and love, and become a hypocryte as his mother has done. In his cynicism, he is projecting his own sins, his mother's sins, and Ophelia's to the the extreme, and to the whole human race. On the other hand, since he cannot see himself surviving his crisis, if she wishes to try to keep her decency, without him to make an "honest woman" of her, her only chance is to flee human nature to a convent. This thesis/antithesis is strenghend if they've "consumated their marriage" prior to their wedding. In this moral speculation, the "tokens" Ophelia refers to in her initial lines might be a wedding ring, engagement ring, or some customary token of the time signifying a committment to marry, given as engaged couples sometimes do, in an attempt to avoid or minimize the guilt of their premature actions.

It's in the larger context of the play, not just this scene's ambiguity, where I would argue that the ambiguity is deliciously intentional. Take the preceeding soliquoy, for example. To be, or not to be. He's tempted by the desire to save his life by forsaking his desire for truth and justice, and become corrupt, or to escape the corruption by suicide. But then, there's the afterlife, and the meaning flip-flops. Now he must continue on to confront his mother and the king, and face probable death, even though the couse of action seems suicidal, and condemn him to suffer the humiliation of enduring his fearfulness and live out his probable short life mired in his incapacity to instigate justice. In the end, justice will not be served, he will probably be further corrupted, and his mother's and uncle's sins will be multiplied, and even Ophelia will be mired in the mess. All this comes to pass, and more, as the denoument unfolds as the situation devolves into the tragic and enevitable result of fallen human nature.

It's been argued that most people wouldn't have understood the "darker" meaning alluding to a brothel, but I disagree. Slang usage travels quickly, and this usage seems likely to have been common and popular at the time. In asserting that the audience wouldn't "get it", does the critic mean the well educated, read, and traveled people in the good seats, or the worldly, crude and ignoble general admission crowd? My description is my argument that MOST people could understand the ambiguity, if they were sharp enough to see it. Even if they didn't, if they discussed the play, as scholars do now, or as sports fans discuss a game, they would have found that some people assumed convent, and some people assumed brothel, unaware of the other possibility. It may have been debated at many a table following the entertainment.

Hamlet's only plan for survival with honor is to use ambiguity to subliminally communicate his message and evade an overt challange to the throne, until some final revelation, hopefully not directly from himself, unmasks the king and queen's guilt to the court's outrage, resulting in support for his succession to the throne. Thus the play within the play, which backfires. The members of the court may or may not suspect, but the king and queen see the message clearly, and are impelled to retaliatory action.

Back to Hamlet's dilema. Consider some biblical teachings:
Perhaps rhetorically, Jesus suggests plucking out an eye to avoid sin, yet the body is the temple of the the Holy Spirit, and so this would also seem be a desecration in itself. On the other hand, He sacrificed his body also, to remove our sin. But perhaps only HE could do so sinlessly. 
Human nature became corrupt at the Fall, in Eden, and one sin negates all the "righteousness" of a lifetime, making us as unfit for God as a dirty rag. 

Perhaps, then, Hamlet may cynically reason that we are no worse off to admit our fallen nature, and live it out in brothels, to avoid desecrating marriage, which is a holy sacrement intended to be an allegory teaching us and  pointing us forward to our more intimate and important relationship with God. He's fixated on his Mother's betrayal. 

Cynicism is a sin, believing that God's justice and grace do not apply to a situation. A cynic would not have hung on the cross. Only a loving realist, willing to pay an extreme cost for true justice, would endure that sacrifice. A redeemed cynic must deny his nature, pick up his cross, and follow Jesus. He must not hate himself, or humanity, but submit to love and grace, and by faith face the trials in his life regardless of if they lead to martyrdom or spiritual humility, or any other outcome, including any form of failure. The classic tragedy coalesces around a flaw in the protagonist's human nature, and it's the predisposition to sarcasm, ambiguity, indecisiveness and cynicism that precipited his crisis, and furthermore caused a chain of circumstances which lead to his slaying of Ophelia's father, which "sealed" his cathartic doom.

An early heresy was to supposedly increase grace by increasing sin. This is the fault in Hamlet's antithesis. And I believe that he ultimately opts, to the best of his ability, to avoid the "dark side" and do his best to pursue justice. He falls deep into the dark side with killing Ophelia's father, and destroying her. However, he nearly succeeds at the last, not in the sense of surviving, but struggles to preserve what remains of his thoroughly shattered virtue in the final outcome. But he has he named fear as virtue's enemy in his siloquy, so he again succumbs to his fear of his inability to face of his impending death, and drinks from the poisoned wine to evade his prolonged half-hour death, transforming his own murder instead into a cowardly suicide.

It's interesting, on the other hand, that his mother seems to avoid this fate, unknowingly and thus "innocently" drinking wine intended to poison her son. Her actual death, at least, is merely a tragic accident.

The timing of the nunnery/brothel usage is somewhat iffy. Nunnery is first recorded as used for brothel in 1593, and Hamlet was written in 1601. Slang travels quickly. Do we see Shakespeare using it in this sense elsewhere, perhaps earlier? I couldn't find it in my searches, so no conclusion can be reached there. If the specific 1593 useage were mentioned in 1593, we might determine if Shakespeare would have been likely to be aware of it. I'm guessing that as a wordsmith, apt with double-entendre, it's probable that Shakespeare knew the useage, and would not have flinched at ambiguously employing it to heighten the polarization of Hamlet's dilema.