Out of the three lectures ね is the easiest to predict for me because it is always related to a price as in 値が張る (which is the only place where I would read it ね when alone), this lecture can also be found in 値段 (the more casual word for 価格 (it may be worth noting that the 訓読み of 価 is あたい)), 高値 or 安値.
Things are a little unclear when 値 as the meaning of value. Technically, it should be read as あたい since it is its 訓読み, nevertheless I have heard Xに値{ち}を取る in a probability course and in some other settings I have heard 値 read as ち when isolated.
So I am wondering, how to read 値 when alone, how can I choose between ち and あたい?