OSRS Barrows EV, Unique Odds & GPH Guide (2025)

→ Unique item rates and Expected Value

Each Barrows chest has an independent chance p_u to roll a Barrows item (your "unique"). Typical routes that kill all six brothers land in the ~5.6–6.0% per-chest range (check current tables and your kill-count setup in the calculator). Let:

• V_u = market value for the item actually rolled (use a weighted mean across pieces)
• V_s = value of secondary loot (runes, bolt racks, coins) conditional on no unique
• p_u = per-chest unique probability

Then Expected Value per chest:

EV_chest = p_u · 𝔼[V_u] + (1 − p_u) · 𝔼[V_s] − Cost_supplies

Use your real prices. Our calculator lets you override item values and supply costs to match your world's market. Price volatility can shift EV by 10-20% depending on which pieces are in demand.

Chest roll model

Barrows "unique vs not" can be treated as a single union event per chest. Internally the table has many items; we aggregate them into one unique bucket for EV and then apply weights for piece distribution when needed. This simplification makes the math tractable while maintaining accuracy for profit planning.

Kill count optimization

Your kill count (KC) affects both unique probability and secondary loot. The sweet spot is typically 88% reward potential by killing all six brothers plus 2-3 skeletons or bloodworms. Going higher adds time without meaningful EV gains.

Why 88% KC is standard

At 88% KC, you maximize rune drops (especially bolt racks and death/blood runes) while keeping run times under 4 minutes. Higher KC only marginally increases unique odds but significantly slows your GPH.

Sample EV calculation

EV_chest ≈ 0.058 × 1,750,000 + 0.942 × 38,000 − 8,500

         ≈ 139,400 + 35,796 − 8,500 ≈ 166,700 gp

Caveats and variability

• EV is an average, not a guarantee. Variance is high because uniques are spiky.
• Secondary loot can shift with rune prices—bolt racks and death runes are particularly volatile.
• If your route skips brothers or uses lower KC, p_u drops—update inputs accordingly.
• Market crashes on specific items (like Karil's coif) can temporarily lower your realized EV even if drop rates stay constant.

Tracking your actual results

Keep a simple spreadsheet: date, chests opened, uniques received, total loot value. After 100+ chests, compare your realized EV against the calculator's prediction. Large deviations suggest either outdated prices or setup differences.

→ Single-run odds

For a single chest:

Pr(any unique) = p_u     and     Pr(no unique) = 1 − p_u

See Glossary – Union probability for the general rule Pr(A∪B) = Pr(A) + Pr(B) − Pr(AB). Here we compress all unique items into a single union event.

→ Multi-run cumulative odds

Over n independent chests with per-chest probability p_u:

Pr(≥1 unique in n) = 1 − (1 − p_u)ⁿ

This comes from the binomial model with X ~ Binomial(n, p_u). See Glossary – Binomial distribution. The formula grows non-linearly—your first 10 chests give far less cumulative probability than chests 40-50.

Worked examples

Using p_u = 0.058:

Link to live math

Open OSRS Barrows Calculator → enter your route time, supply cost, and prices → copy the share link for your clan or friends.

Understanding dry streak probability

Even at 50 chests, you still have a ~6% chance of seeing zero uniques. This is normal statistical variance, not account "bad luck." Plan your bankroll assuming worst-case scenarios, not average outcomes.

→ Time decomposition

Let:

• t_run = seconds per run (dig → kill 6 brothers → finish mound → bank)
• EV_chest from earlier
• c_runs/hr = 3600 / t_run

Then:

GPH = EV_chest × c_runs/hr

EV/hour vs EV/run

• EV/run changes with prices and p_u.
• EV/hour also changes with time; shaving 20–30 seconds per run can beat small EV gains.
• A 3:30 run with 160k EV beats a 5:00 run with 175k EV in terms of GPH.

When to bank and repair

• Repairing on POH or armour stand can batch costs—time it between supply refills.
• If your route time climbs above 5:00+ per run, consider travel optimizations first; EV rarely offsets slow routes.
• Bank every 6-8 runs to keep inventory space for high-value drops and maintain prayer/food reserves.

Brother order and prayer

• Ahrim and Karil can spike supply usage—bring swaps that minimize prayer drain.
• Prioritize reliable specs (e.g., crystal bow, trident setups) to stabilize time.
• Kill Dharok last if possible—his high hits are less dangerous when prayer is already low.

→ Estimating p_u with a binomial proportion CI

If you observe k uniques in n chests, an approximate 95% confidence interval for the true p_u is:

p̂ ± z₀.₉₇₅ √(p̂(1−p̂)/n)     where p̂ = k/n

For small samples, use Wilson/Agresti–Coull intervals. See Glossary – Confidence interval. These corrections prevent CI bounds from going negative or exceeding 1.0 when sample sizes are small.

How many runs do I need?

• To measure p_u ≈ 0.058 within ±1.5 pp (0.015) at 95% CI, you'll need ~240–300 chests.
• For casual validation, even 100 chests narrows noise a lot.
• If testing a new setup (different KC or gear), 50 chests gives a rough signal; 150+ chests gives strong evidence.

Practical recommendations

• Log time per run and whether a chest rolled unique—simple checkboxes suffice.
• Expect dry streaks; binomial variance implies long no-unique stretches are normal.
• Use RuneLite plugins or spreadsheet templates to automate tracking.

Links for deeper reading

• Union probability
• Binomial distribution
• Confidence interval