I tend to disagree with the advantages of a "slurry" (mix of starch and water) over a
roux.
There is a time to use one, and a time to use the other.
A
roux can be used to add body and flavor to a sauce. Also roux thickening is near instant while starches take a bit of time to bind a sauce together. A roux will also add an
opaque quality to your
sauce, which is sometimes desired. Roux-thickened sauces are excellent for dishes with rich flavors (red meat, salmon, etc..)
A
slurry is
excellent when you want a clear or
translucent sauce. Also they can be used in sauces which have a very delicate balance of flavor that may be disrupted by a roux (
cornstarch,
arrowroot and
potato starch have very little flavor on their own). Chinese cooking uses this technique, and the high-heat nature of chinese cooking takes away the slurry disadvantage of slow thickening times.
Well this node is about deglazing, and it's an excellent technique to use when making a sauce, although I discourage the use of water for this practice. Wine is common, but stock (or broth) can also be used, and add more flavor to the dish. Really almost any
liquid will do, it really depends on what the end flavor you want is.