Build a base RNG Luck & drop-rate calculator — read the formula, stack the multipliers

What the calculator does

The Luck & drop-rate calculator is a player-input tool. You supply a target item (or a custom 1 in N denominator), tick the Skill Tree / consumable / gamepass toggles that match your save file, and the calculator returns:

• The effective 1 in X odds after the math.pow Luck convention is applied.
• The probability of pulling the target at least once in R rolls.
• The expected rolls to first hit (geometric mean).
• The composite L_eff that produced the value.
• A recommendation chip — BUY_LUCK_FIRST / STACK_INDEX_AND_LUCK_II / BANK_FOR_CRAFTING_MACHINE / BALANCED_GRIND — based on whether your current loadout makes the roll you are planning.

Every output is computed in plain JavaScript with Math.pow. There are no hidden constants beyond those declared in the tool’s source.

The math.pow Luck convention

The closed-form Luck multiplier follows the convention documented on the Roblox DevForum:

local roll = math.random()
local rollAfterLuck = math.pow(roll, 1/luck)

The wiki’s calculator uses the equivalent closed form:

p_eff = 1 - (1 - p_base)^L_eff

where p_base = 1 / N_base and L_eff is a composite multiplier you supply by toggling the loadout.

What L_eff actually is

L_eff is the single composite Luck value the engine effectively applies to your roll. It is built from two layers:

1. L_additive — the baseline = 1.0 plus each active source (+0.5 for Luck I, +1.0 for Luck II, +0.5 for Friend Luck I, +1.0 for Group 2x, +0.75 for Luck Potion, +0.09 for Gold Rolls I, +0.005 per percent Index completion, +0.05 per Clover rank).
2. L_multiplicative — multiplicative gates (×2.0 for Group 2x, ×1.5 for Luck Potion).

The final value is L_eff = max(1.0, L_additive × L_multiplicative). The floor at 1.0 makes “no Luck sources” the no-Luck baseline.

What the engine form looks like in practice

A few worked examples from the calculator’s source:

• No Luck, 1 in 100. L_eff = 1.0, p_eff = 0.01, N_eff = 100.
• Luck I + Group 2x, 1 in 150. L_additive = 2.5, L_multiplicative = 2.0, L_eff = 5.0, p_eff ≈ 0.0329, N_eff = 31.
• Wood Block, 1 in 3 with full Luck stack. L_eff can saturate above 6.0, p_eff clamps to 1.0, N_eff = 1 (“guaranteed next roll”).

The DevForum does not state that Build a base RNG uses this exact form internally; the calculator labels the math [INFERRED-FROM-MECHANICS] and the open-questions list tracks that confirmation gap.

The published roll-odds table

Per-item odds come from one community-published source: the allthings.how Build a base RNG guide. No second source corroborates each 1 in N denominator, so the table is tagged [SINGLE-SOURCE] in the research library.

The rarity-tier names (Common / Rare / Legendary) are inferred from the odds, not officially stated by the developer. The calculator labels them [INFERRED-FROM-MECHANICS] and surfaces the disclaimer in the UI.

Variant layer (Shiny / Galaxy passes)

The Shiny Hunter (330 R$) and Galaxy Hunter (640 R$) gamepasses lift variant-tier odds — they do not fold into the headline N_eff. The calculator renders them as a separate row:

• P(variant at least one in R) = 1 - (1 - p_eff × variant_uplift)^R
• variant_uplift = 0.5 per pass (Shiny + Galaxy stacked = 1.0)

The split exists because variant chance is decoupled from base rarity. A shiny Wooden Trap is meaningfully different from a standard Wooden Trap, but the headline drop rate of Wooden Trap itself does not change.

Recommendation engine rules

The CTA chip picks one of four states:

The rule reasons:

• BUY_LUCK_FIRST fires when the roll is dominated by raw tier — your wallet is the bottleneck, your Luck is not.
• STACK_INDEX_AND_LUCK_II fires when you have some Luck but not enough to break into Epic / Legendary territory cheaply.
• BANK_FOR_CRAFTING_MACHINE fires when your Luck is strong enough that you should be parking coins for the 150K Crafting Machine gate, not chasing one more roll.

Edge cases the calculator handles

• R = 0 → clamped to 1, surfaced as “simulate at least one roll” warning.
• Wood Block at full Luck → p_eff saturates at 1.0, surfaced as “guaranteed next roll”.
• R ≥ 100,000 → binomial switches to log-space (1 - exp(R × ln(1 - p_eff))) to avoid pow() numerical underflow.
• index_pct > 100 → clamped to 100, surfaced as warning chip.
• Custom N_base outside [3, 1,000,000] → clamped + warning.
• shiny_hunter_pass or galaxy_hunter_pass → variant row appears separately, main N_eff unchanged.

Source label summary

Related reads

• Beginner guide for the Skill Tree priority that produces useful L_eff values.
• Coin ETA explained for the coin-income side of the same grind.