one for the legal experts here. in a case like this where i'm assuming there were no procedural problems (ie mistrial by hung jury), under what circumstances might the state try it again? for instance is it more likely in a murder trial? might they offer a more lenient deal to avoid a trial? and when would they drop the charges altogether?
Pretty much any homicide or heinous sex crime they look into retrying. If they chose not to retry (or try the case at all which happens a lot in the lower courts) they file a nolle prosequi which dismisses the charges gives them right to bring it back out if something changes down the line (i.e. a new witness comes forward). there is also a DWOP (dismissed without prejudice) which has a similar effect but is requested by the defendant (could mean a million things like the Gov. does not want to file a nolle pros but cant get a necessary witness to come to court or on a drug case the evidence was suppressed).
Before i mentioned "no contest" (sometimes called nolo contedre) and Alford pleas -- that's not a "guilty" plea but its an adjudication and firmly closes the book on a case. both sides call this a victory. Time served its pretty much self explanatory. that's why you sometimes see sentences of "215 days HOC deemed served." You may also get offers of a guilty on an amended lesser included offence ("ABDW" is a lesser included of "ABDW causing serious bodily injury") with a split sentence (3 years State Prison, 18 months to serve, balance suspended over five years).
when i was a student ADA in law school (i did not have the right temperament to make a career out it) i never really got to see how the sausage was made for the superior court stuff but based on what ive experenced doing defense i would speculate that They drop the charges after consulting with the family of the alleged vic (who may not want to go through the stress of trial again), they don't have the resources or time to dedicate to another trial, and to some extent whether or not or they think the Defendant is a danger to the community or likely to reoffend.