And patience, experience; and experience, hope:
Note 11 at Ro 5:4: The Greek word used for "experience" here is "DOKIME," and it means "approved character; the quality of being approved as a result of test and trials" ("Linguistic Key to the Greek New Testament" by Fritz Rienecker). Sanday and Headlam also defined this word in this verse as "the temper of the veteran as opposed to that of the raw recruit." Therefore, this verse is speaking of the character that is produced as a result of having fought battles and won.
Note 12 at Ro 5:4: Hope by itself will never give people victory. Many people have hoped for things and yet have never realized those hopes because they never moved into faith. Faith is the victory that causes people to overcome the world (1Jo 5:4), yet faith won't work without hope.
Just as a thermostat activates the power unit on an air conditioner, so hope is what activates our faith. Faith only produces what we hope for (Heb 11:1). Therefore, hope is the first step toward faith.
The word "hope" means "a desire accompanied by confident expectation" (American Heritage Dictionary), so desiring the things of God with some expectation of obtaining them is the first step in walking in faith. Once this hope is present, then faith begins to bring the desired thing into manifestation. If a delay is encountered, patience completes the work (see note 10 at Ro 5:3).
In context, Paul was saying that our experience "worketh" (see note 9 at Ro 5:3) hope. However, he also said in this same epistle (Ro 15:4) that hope comes through the Scriptures. Therefore, it is to be understood that the character that is developed through tribulations just adds to the hope that we have already received through God's Word.