Is it worthwhile to collect gold?
Solution 1:
Math is not necessary - there are three reasons that gold is not worthwhile to go out of your way for:
- Most of your gear comes from boss runs and player trades, not gold.
- Almost no players with good gear will trade it for your gold.
- Very rarely can exceptional gear can be bought from shops (source).
Given the above points, it's pretty clear gold isn't enough to get great gear.
However, gold is useful for repairing items and reviving henchmen. You will learn how much that costs when you get there, and you'll see that exhaustively exploring dungeons for gold is not necessary to provide you with repair and revive gold.
If you do really want gold, however, there is a guide especially geared towards finding lots of gold quickly (source). The gear required is pretty tough to get (Enigma among other things) so it will be a while before you can get to that stage, but nonetheless it's possible to farm gold in an extremely efficient way, I suggest you read the guide to find out more.
Diablo is more of a speed run game more than an explore and collect game. The reason for this is that your gold does very little to advance you further in the game - leveling is the most effective way to advance. There are efficient ways to level and acquire good gear, and exploring everything while picking up every piece of gold is not one of them.
What you should do is focus on leveling quickly, and with that you will have access to higher difficulties and tougher bosses, which is turn gives much more gold and gear for the time spent than exploring dungeons bit by bit. For example, Baal runs (the final boss in the Diablo 2 expansion) are very juicy for collecting xp and gold, and in almost every leveling and farming guide you will see that most of your time is spent killing Baal. Pros who get to the top of their ladder kill Baal thousands of times!
There are many guides on leveling fast in Diablo 2, and a side effect of you leveling fast is that with xp comes lots of gold and gear. These guides are focused on maximizing gains for time spent, and effectively executed you can hit level 75 in under a week with decent gear. Here's a guide I highly recommend to give you a perspective on the game, it's the story of a pro hitting level 99 first with his character. There are others you should take a look at that are specific to your character class.
Sorry for the lack of math, but Diablo is played the way I explained for a reason: acquiring gold in no way can measure up to the value of leveling quickly. Only collect enough gold to purchase potions and scrolls, repair you items, and revive henchmen, and you will usually get enough as a side effect of simply speed running the game.
Solution 2:
Gold can be extremely useful; however, it's not worth going out of your way to pick it up unless your character is wearing a large amount of gold find, since the time/reward ratio is very low for picking up piles of 4-5 gold. Piles of 4000-5000 gold, on the other hand, are worth the trip.
Most players need gold for two reasons: reviving mercenaries (especially sorceresses with Insight or Infinity mercenaries, who lose effectiveness when their mercenary dies), and repairing weapons and armor (mostly for melee characters).
There is, however, a valuable use for gold if you can get it in large quantities: gambling for rare circlets and amulets.
Necromancers will often find themselves automatically building up gold in quantity, because they don't have a gold sink, but the most effective purpose-built gold farmers are said to be barbarians encrusted with Lem runes, running the council and horking dead bodies with find item. Council runs are also known to be one of the best sources of runes, producing many more high runes per unit time than Countess runs.
Several of the best items in the game can be gotten by gold farming and gambling, in particular +2 class skills circlets with 20% faster cast rate (particularly valuable with faster hit recovery, good resists, and/or dual sockets). Because circlets, coronets, tiaras and diadems give a boost to the item's magic level, gambling for them has a decent chance of creating good items even for mid-level characters.
Some of the magical (blue) circlets can also be quite valuable; for example, the highest magic find helm is an extremely rare magical tiara/diadem with three sockets (from a specific prefix) and 35% magic find (the maximum possible for the best suffix), fitted with three ist runes, and the best chance of finding one is from gambling.
High level characters (level 86 to have a chance, level 95 for the maximum chance) can also gamble for +2 class skills rare amulets with 10% faster cast rate and other bonuses, which can have very high trade value, partly because reaching a good level to gamble for them is extremely tedious. (Crafted caster amulets with 15-20% fcr are more valuable, but good rares with more affixes than crafted amulets are often better for characters that reach their target fcr with only 10% from the amulet.)