appraise
To carefully judge how valuable or good something is.
To appraise something means to carefully examine it to determine its value, quality, or condition. When an art expert appraises a painting, she studies it closely to figure out how much it's worth. When a jeweler appraises a diamond ring, he looks at the stone's size, clarity, and quality to set a price.
The word suggests a thoughtful, expert judgment rather than a quick guess. A professional appraiser might spend hours examining an antique chair, checking for signatures, looking at the wood and craftsmanship, and comparing it to similar pieces before deciding what it's worth.
You can also appraise situations, not just objects. A chess player might appraise the board, studying each piece's position to figure out her best move. A hiker might appraise the trail ahead, looking at the terrain and weather to decide whether to continue. When you appraise something, you're gathering information and making an informed judgment about it.
Don't confuse appraise with apprise, which means to inform someone. You might apprise your parents of your day, but you appraise the value of your baseball card collection.