In my run, I'm getting the copper axe upgraded on day 3 (this is hard)
To my knowledge, the only way to upgrade the pickaxe on Spring 3 is to use 25 copper gathered from random fishing chests (and potentially with a few coming from Artifact Spots). That isn't possible without resetting your day over and over, which is considered to be cheating - see appendix A of the guide.
If you allow resetting the day over and over, then my whole route isn't applicable at all. You would instead use RNG manipulation to get around 6000g on the first day with clay + artifacts + geodes + etc., and end up in Skull Caverns a lot earlier using no pickaxe at all and just using explosive ammo.
So, if you wanted to do a route that upgraded the pickaxe on Spring 3 without cheating, you would have to grind runs over and over starting from day 1 and hope for insane fishing chest luck. If you want to do that, go for it, but the point of the guide is to provide a consistent strategy. Thus, the guide recommends to start to upgrade the Copper Pickaxe on Spring 5, which is when the mines open, and the first reasonable day that you can get 25 copper.
Thus:
- Upgrade to Copper Pickaxe on Spring 5
- Get Copper Pickaxe back on Spring 7.
- Upgrade to Steel Pickaxe on Spring 7.
- Get Steel Pickaxe back on Spring 9.
- Upgrade to the Gold Pickaxe on Spring 9.
- Get the Gold Pickaxe back on Spring 11.
- Finish mines ASAP, all time in mines is spent "optimally" because you can do it twice as fast with Gold Pickaxe as you would with a Copper/Steel Pickaxe
- Get to bottom of mines around Spring 14, depending on luck
- Skull Caverns on Spring 15
doing a lot of mining, farming part of day 7 and upgrading to steel on day 8. Then mining down some more and doing the next upgrade on day 12 (I'm upgrading the axe when I'm not upgrading the pick, which may be a mistake, I'm not sure). I'd then expect to be able to reach bottom on 14 or 15 and start skull from 15 or 16. This seems in line with your guide -- am I mistaken? It seems to me that the extra money spent on gold ore -- 10k -- delays the vault by at least a day itself.
Your route doesn't seem to make sense to me.
First, you don't have enough money to upgrade the Axe until you are already in Skull Caverns. Otherwise you would be delaying completing the Vault + buying the level 2 backpack, which is suboptimal.
Second, you only have one Furnace. Are you proposing that you make more? That would take farming 80 copper. (Call that A hours.)
Third, you would have to wait for the gold to smelt. (5 hours with 5 Furnaces, or 25 hours with 1 Furnace.)
Forth, you lose the marginal advantage of the Gold Pickaxe when clearing mines floors. The earliest floor that you can farm gold is floor 81. Doing the mines from floor 20 to floor 80 is 60 floors. (Call that B hours.)
Fifth, you lose the time of farming the 25 gold from floor 81. (Call that C hours.)
If M is the hourly rate of return from fishing at the mountain lake, then A+5+B+C would have to be <= 10,000g / M.
Making some assumptions:
For A, it might be 5 copper per hour = 16 hours.
For B, if on average it takes 3 days to get to the bottom of the mines, then that is (120 - 20) / 3 = 33.3 floors per day = 1.7 floors per hour = 102 hours.
Then, we use a penalty factor of say 0.5x (for marginal cost), which gives us 51 hours.
For C, it might be 5 gold per hour = 5 hours.
A+5+B+C = 77 hours.
I don't know what M is but it would have to be lower than 129.9 gold / per hour.
Feel free to experiment and refine these numbers if you'd like.
Finally, another thing not represented in these numbers is that the more that you defer mining, the greater the chances that you will get either a
Neptune's Glaive or a
Broken Trident from fishing chests, which obviously vastly outperform the Rusty Sword and any other weapons that you will get prior to the Obsidian Edge. You would want to account for that by increasing the penalty factor by an arbitrary amount.