[RPG] the DC for Crafting an arrow

Mechanical Trap Minimum Cost

It doesn't look like you're pricing that trap correctly. Here's from the mechanical trap rules:

The base cost of a mechanical trap is 1,000 gp. Apply all the modifiers from Table: Cost Modifiers for Mechanical Traps for the various features you’ve added to the trap to get the modified base cost.

The final cost is equal to (modified base cost × Challenge Rating) + extra costs. The minimum cost for a mechanical trap is (CR × 100) gp.

And from the trap creation rules:

The base CR for a mechanical trap is 0. If your final CR is 0 or lower, add features until you get a CR of 1 or higher.

By the rules, you can't create a trap below CR 1, and the minimum cost is 100g.

Trap Math

Lets look at your costs compared to the rules. The base cost is 1000g.

It is location trigger (no cost)

Correct, this is no change to the base cost.

with repair as a reset (-200gp)

Correct.

there is no bypass

No modification to cost.

the search DC shouldn't be more than 20 (no cost), if not less (-100gp x (20-DC))

Correct, so a search DC of 15 would be a modifier of -500. Total of -700. You have no extra costs, as there's no alchemy involved.

Your cost is calculated as such:

The final cost is equal to (modified base cost × Challenge Rating) + extra costs. The minimum cost for a mechanical trap is (CR × 100) gp.

So you have (1000 - 700) x 1 + 0 = 300g. You could get it down to 100g if you lowered the save DC on the pit to 18 instead of the base 20.

Note that you currently have a CR 0 trap, and the rules require minimum CR of 1. You can get to 1 without increasing the cost by adding average damage (adding 7 average damage increases CR by 1). This would not increase the cost.

What if it really didn't have a cost?

If something really doesn't have a cost, you can make something up. For "digging a hole in the ground", the cost is time. The PCs can do it themselves, or they can hire someone. An untrained labourer costs 1sp per day.

The economy in 3.5 doesn't make a ton of sense, so you can assume the extra cost in a trap vs a hole in the ground is what's required to actually fool anybody into ever falling into it. It's best not to try to expect too much logical consistency on this stuff, becuase unless you use houserules, it doesn't exist.

How Long Does Digging a Hole Take?

Races of the Dragon p.98 has rules for using Profession (Miner) to mine, which you could also use for digging a big hole for your trap. The rules cover how long this would take based on how good a check you can make, with modifiers for different type of ground. You could combine those with the hireling cost to get an idea of what it'd cost to hire a bunch of people in town to dig a 10x10x10' hole.

(Summary version: a medium size miner can empty a 5' cube per day with a DC 15 check. DC 10 would do half of that, and every 5 you beat it over 15 lets you do another 5' cube. Large size works twice as fast, small half as fast. A second medium miner can assist and use aid another to boost the role, while smaller creatures can have more assistance.)

Now that you have your hole, you'd just have to figure out how to conceal it. There's no particular rule for that outside of the trap rules that I know of, but you could make something up.

The alchemist's lab specifically overrides the more general masterwork tool and the masterwork artisan's tools

• Most skills don't need tools. However, a craftsman usually needs different artisan's tools for each Craft skill.
• You can buy a masterwork tool for a skill. The masterwork tool for the skill Craft is masterwork artisan's tools.
• If a specific masterwork tool is available for a skill (and you want that circumstance bonus) you must buy that instead. The specific masterwork tool for the skill Craft (alchemy) is an alchemist's lab.

Below are relevant passages from the Player's Handbook. They don't make a lot of sense when considered individually, which is why I included the above summary.

The Player's Handbook on Favorable and Unfavorable Conditions says

Give the skill user a +2 circumstance bonus to represent conditions that improve performance, such as having the perfect tool for the job, getting help from another character (see Combining Skill Attempts, page 65), or possessing unusually accurate information. (64)

Emphasis mine. The Player's Handbook later describes the masterwork tool as follows:

This well-made item is the perfect tool for the job. It grants a +2 circumstance bonus on a related skill check (if any). Some examples of this sort of item from Table 7–8 include masterwork artisan’s tools, masterwork thieves’ tools, disguise kit, climber’s kit, healer’s kit, and masterwork musical instrument. This entry covers just about anything else. Bonuses provided by multiple masterwork items used toward the same skill check do not stack, so masterwork pitons and a masterwork climber’s kit do not provide a +4 bonus if used together on a Climb check. (130-1)

Emphasis mine. Note that the list of examples isn't exhaustive and that Craft is a skill. The Player's Handbook also describes artisan's tools:

These special tools include the items needed to pursue any craft. Without them, you have to use improvised tools (–2 penalty on Craft checks), if you can do the job at all. (129)

And masterwork artisan's tools:

These tools serve the same purpose as artisan’s tools..., but masterwork artisan’s tools are the perfect tools for the job, so you get a +2 circumstance bonus on Craft checks made with them. (129-30)

Emphasis mine. Finally, the Player's Handbook describes the alchemist's lab, in part, as follows:

This set of equipment includes beakers, bottles, mixing and measuring containers, and a miscellany of chemicals and substances. An alchemist’s lab always has the perfect tool for making alchemical items, so it provides a +2 circumstance bonus on Craft (alchemy) checks. (129)

Emphasis mine. When a skill lacks a specific perfect tool, you buy a generic masterwork tool or, for a Craft skill, generic masterwork artisan's tools for that Craft skill. The skill Craft (alchemy) has a perfect tool available: the alchemist's lab. This makes both a masterwork tool and masterwork artisan's tools unavailable for the skill Craft (alchemy) in the same way you can't buy a masterwork tool for the skill Heal instead of a healer's kit. To get the +2 circumstance bonus for using the perfect tool on Craft (alchemy) skill checks you use an alchemist's lab.