Loot Box Probability vs Cost Calculator
Plan your loot box spending with realistic probability math. Enter the drop rate, box cost, and your desired confidence level to estimate how much you need to spend.
The stated probability of getting the desired item per box
Price of a single loot box or crate
How confident you want to be (50% = coin flip, 95% = near certainty)
Number of pulls before pity activates
Geometric Distribution:
P(success within N boxes) = 1 - (1 - p)^NBoxes needed for desired confidence:
N = log(1 - D) / log(1 - p)Where p = drop rate per box, D = desired probability
Expected boxes (average case):
E = 1 / pWith Hard Pity at P pulls:
N = min(calculated, P)Note: Without a pity system, there is no guarantee even after thousands of pulls. Each box is an independent trial — past failures do not increase future chances.
Inputs: Drop Rate = 2.5%, Box Cost = $2.99, Desired Probability = 75%
Results:
• Boxes needed for 75% confidence: 55
• Expected cost: $164.45
• Average expected boxes (50%): 40, cost: $119.60
• At average pulls, success rate: 63.6%
• At double average pulls (80), success rate: 86.5%
Warning: 25% of players still will not have the item after 55 boxes due to variance. Budget for the worst case, hope for the best.
What does "desired probability" mean in loot box calculations?
Desired probability is the statistical confidence level you want. At 50% confidence, you have a coin-flip chance of having obtained the item. At 95% confidence, if 100 players each opened that many boxes, 95 would have the item. Higher confidence means more boxes and higher cost. Most players should plan for 75-90% confidence to avoid disappointment.
How do pity and mercy systems affect the math?
Hard pity guarantees the item after a set number of pulls (e.g., 90 for a 5-star in Genshin Impact) — this puts a hard cap on worst-case cost. Soft pity gradually increases drop rate after a threshold, improving odds without a hard guarantee. Without any pity system, there is no upper bound — in theory, you could open thousands of boxes without getting the desired item (though probability becomes very low).
What is the "gambler's fallacy" in loot boxes?
The gambler's fallacy is the mistaken belief that past failures increase future success probability. If a loot box has a 2% drop rate with no pity, each box independently has exactly 2% chance — regardless of how many you have already opened. This calculator uses geometric distribution which correctly models independent trials. Opening 50 dry boxes does not make the 51st any more likely to contain the item without a pity system.
How should I budget for loot boxes?
Set a hard spending limit before you start, and never exceed it. The expected cost (1/drop rate × box price) is the average, but variance is high. A safe approach: budget for 3× the expected cost, which covers roughly 95% of outcomes. Consider the worst case: if getting the item would cost more than buying it directly (via trade, crafting, or in-game currency), do not open boxes — just buy it outright.
🔗 Related Calculators
📐 Formula
Geometric Distribution:
P(success within N boxes) = 1 - (1 - p)^NBoxes needed for desired confidence:
N = log(1 - D) / log(1 - p)Where p = drop rate per box, D = desired probability
Expected boxes (average case):
E = 1 / pWith Hard Pity at P pulls:
N = min(calculated, P)Note: Without a pity system, there is no guarantee even after thousands of pulls. Each box is an independent trial — past failures do not increase future chances.
📝 Example Calculation
Inputs: Drop Rate = 2.5%, Box Cost = $2.99, Desired Probability = 75%
Results:
• Boxes needed for 75% confidence: 55
• Expected cost: $164.45
• Average expected boxes (50%): 40, cost: $119.60
• At average pulls, success rate: 63.6%
• At double average pulls (80), success rate: 86.5%
Warning: 25% of players still will not have the item after 55 boxes due to variance. Budget for the worst case, hope for the best.