Mine a Mountain Warmth vs Pickaxe vs Backpack Optimizer

The Mine a Mountain Upgrade Path Optimizer is the second of the three wikis calculators. Where the Time-to-Target Calculator asks “how long to the next goal?”, this one asks “which upgrade is worth the next dollar?”. It compares Warmth, Carry Weight, and pickaxe upgrades side-by-side using your measured route, and ranks them by projected payback hours.

Why a tool for upgrades at all

The beginner guide introduces the bottleneck rule: buy whichever stat ends your last run. That rule is correct on average. It is not correct for every player.

• Some players die to cold once per hour; Carry Weight buys nothing because the bag never fills.
• Some players are ready to grind the next pickaxe tier but the missing piece is a single Warmth upgrade to reach a richer altitude band.
• Some players need a specific pickaxe to break a boulder (Mossite, Voltite, Gildrite, Rimeveil, Nocturnite) — that’s a hard unlock, not a rate decision.

A tier list cannot capture any of that. The optimizer does: it takes your current route’s Cash rate (q$), collection rate (qm), Warmth window (W), and travel time (D), then projects each candidate and ranks the result.

Inputs the optimizer needs

Current route calibration

Candidate upgrades — at minimum:

• A Carry candidate (cost Cb, new capacity B').
• A Warmth candidate (cost Wb, new warmth window W', optional richer-band rate q$').
• A Pickaxe candidate (cost Pp, new power P', new mine size M').
• (Optional) Boulder unlock — forces the optimizer to pick a specific pickaxe.

The optimizer reads these as inputs you supply; it never invents a price for an upgrade the wiki has not verified.

The math, simplified

For the current state, the optimizer runs:

time_to_fill [s] = B / qm
mining_time [s]  = min(time_to_fill, W)
cycle_time [s]   = mining_time + D
cash_per_cycle   = q$ × mining_time
rate_per_hour    = cash_per_cycle / cycle_time × 3600

The bottleneck is whichever limit is closest to firing:

(The 5s tolerance and the 30% travel threshold are product heuristics, not in-game constants.)

Each candidate is then re-evaluated against the same formula with the candidate’s inputs swapped in. The incremental rate, payback hours, and efficiency score are derived per candidate:

incremental_rate [$/h] = projected_rate − current_rate
payback [h]            = cost / incremental_rate
efficiency              = incremental_rate / cost

A candidate with zero or negative incremental gain surfaces a “no modeled gain” note instead of a negative payback duration. The optimizer never returns a negative hour.

Hard-unlock handling

Boulders each require a specific pickaxe. The optimizer treats those as hard unlocks rather than a rate improvement: if you specify a boulder for a candidate, the optimizer forces that candidate into the recommendation, regardless of its payback ranking, and surfaces it as a boulder unlock. Right now, five boulders are documented:

If the candidate pickaxe stats are unknown (for Eclipse Fang, Voidreign, The Terminus), the optimizer prompts for manual entry and refuses to extrapolate the verified Power-doubling pattern.

Pickaxe proxy mode

When you have only stats and not a measured rate for the new pickaxe, the optimizer uses a proxy:

proxy_ratio = (P' × M') / (current P × current M)

Three scenario bands (conservative α=0.35 β=0.20, base α=0.50 β=0.30, optimistic α=0.75 β=0.50) adjust the projected qm and q$. None of these exponents are verified game code — they are scenario controls. The optimizer labels every proxy-derived projection as “Scenario estimate, not official DPS”, and recommends a 60-second before/after sample to replace the proxy with a measured value.

Gamepass mapping

The 13 gamepasses the live Roblox API returned alter different variables, not a single catch-all multiplier. The optimizer’s gamepass axis map aligns each documented pass with the variable it touches (x4 CARRY KG to Carry, INSTANT Mine and Fast Dig to mining speed, x8 Power to pickaxe Power, x2 Crystals to spawn count, VIP to a user-entered custom multiplier, x2 Coins to sale value). Only one axis at a time.

Budget path

The optimizer runs a greedy iterative spend loop:

1. Project the current state.
2. Find the candidate with the shortest positive payback that is also within budget.
3. Apply it as state changes (new capacity / new warmth window / new pickaxe stats).
4. Re-project the remaining candidates — bottlenecks shift as soon as Carry changes.
5. Stop when no candidate is affordable or no candidate improves the rate.

This is a heuristic, not a proof of optimum. The bottleneck-rule-based first upgrade is usually the right first spend; the optimizer’s value is in the second upgrade and onward, when bottleneck interactions get non-obvious.

Edge cases and what the optimizer refuses

• Zero collection rate. If qm or q$ is 0, the optimizer returns “no ranking” rather than projecting zeros across every candidate.
• Negative payback denominator. Displayed as “no modeled gain”, never a negative duration.
• Carry while warmth-limited. Zero incremental gain and an explanation of why (the run ends on cold before the bag matters).
• Warmth while bag-limited. Zero incremental gain unless Carry also changes.
• Unknown later pickaxe. Manual entry required; no extrapolation.
• Robux budget. Out of scope — the optimizer works in $. Cash and Robux never auto-convert.
• Rebirth. Out of scope — no documented rebirth mechanic.

Inputs the wiki cannot safely default

Some upgrades have a documented curve, others do not. The optimizer never invents:

• The exact Warmth upgrade cost curve at each tier (community notes vary).
• The exact Carry Weight upgrade cost curve at each tier.
• The exact cold-drain formula (dW/dt).
• The exact final crystal value function (tier_base × weight × mutation × sell_mult).

Each of these goes into the optimizer as a player-entered scenario. The optimizer encourages a measured 60-second before/after sample for every upgrade you record, and stamps every projection with the date it ran.

How to use it

1. Run a full loop. Record cash and seconds (the Time-to-Target Calculator is the place to log it).
2. Backpack B and Warmth window W come straight from your current HUD.
3. Crystal mass qm = total crystal kg collected / mining seconds.
4. Cash rate q$ = total $ earned / mining seconds.
5. Round-trip D = travel-to-base + Crystal Buyer time + climb-back-to-altitude (use a stopwatch; the beginner guide suggests a guided stopwatch flow).

Type the cost of each candidate upgrade and let the optimizer rank. Run it again after any pickaxe change — bottleneck shifts are common.

FAQ

Can the optimizer recommend a bomb? No. Bombs run through the Bomb ROI Lab. Bombs are spend events, not sustainable upgrades.

What if my next pickaxe is unverified? Type the cash cost and override the power/mine-size values manually. The wiki never extrapolates beyond the July 9 documented lineup.

Why is the warm or cold result zero? Either your sample is too short, or the route actually is the bottleneck. Add another sample to confirm before committing cash.

Sources

• All Things How — new player starting path (community) — checked 2026-07-30
• Earnaldo — free Robux / upgrade strategy (community) — checked 2026-07-30
• All Things How — pickaxe stats (community) — checked 2026-07-30
• Mine a Mountain Fandom — Boulders (community) — checked 2026-07-30
• Mine a Mountain Tools Design Spec — Upgrade Path Optimizer (this wiki) — current revision