The comedies are the best
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Shakespeare's comedies are the most diverse and complex group of his plays
Many of Shakespeare's comedies defy easy genre classification because they so deftly mix comedy, tragedy and biting social and personal commentary. This huge variety and complexity is distinctive and makes them perhaps the most richly rewarding of Shakespeare's works both to perform and to study.
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Shakespeare's plays are usually categorised according to the traditional Elizabethan system of comedies, tragedies and histories, but for a modern audience, these categories are much more blurred, especially for the plays we typically consider comedies. For example, several of Shakespeare's plays which, although ostensibly comic in structure, contain deeply moving, even tragic, emotional scenes. These problem plays present characters as scarred by their experiences throughout the play.
Although several of Shakespeare's comedies are straightforward romantic comedies (e.g. 'Much Ado About Nothing'), some are much more complex and have more twists than his tragedies and histories. Some of the comedies shift between dark and comedic themes and have been referred to as the "problem plays" by academics due to the difficulty in categorising them.  For example, both 'The Merchant of Venice' and 'Measure for Measure' are in the comedy section of the First Folio. Both end with marriage (or celebration of marriage) as is typical of comedies, but both have dark themes which are more suited to tragedy. 'The Merchant of Venice' deals with issues of greed, Anti Semitism, and revenge, while 'Measure for Measure' covers sexual coercion, execution, and atonement. Some characters in 'Measure for Measure' are not given the happy endings usually afforded in comedies. This manipulation of theme indicates the complexity of Shakespearean comedy. They can range from simple romantic comedies to dark, multi-layered plays that blend elements of comedy and tragedy. These plays suggest that Shakespeare's comedies have more thematic complexity than the other genres, making them richly rewarding to perform and study.
Although several of the 'problem plays' are traditionally considered comedies, not all of them are. 'Troilus and Cressida' and 'Timon of Athens', both problem plays, are firmly tragic in scope (their 'problem' comes from speculation that they could perhaps be history plays), suggesting that comedies are not unique in their ability to incorporate elements of many genres. Additionally, Shakespeare's tragic work redefined the meaning of tragedy in Elizabethan theatre and expanded the scope of events that audiences considered tragic. To suggest his comedies are the best for their complexity ignores the fact that all of Shakespeare's plays are thematically complex and provide much material for study and discussion.
Several of Shakespeare's so-called comedies are considered "problem plays" because their themes and plots don't fit neatly into Elizabethan categories. This displays that Shakespeare's use of comedy was innovative and complex, and suggests that comedies in particular are able to be adapted to include many themes.
Rejecting the premises
Not all of the problem plays are comedies. Shakespeare's tragic work is just as innovative and complex as his comic work, suggesting that comedy is not inherently more able to deal with a variety of themes.