What is expected value (EV)?

Expected value is the average outcome you'd get if you repeated an action infinitely. For loot boxes, it's the average value of items received per box opened. If EV is less than box cost, you're losing money on average.

Are loot boxes gambling?

Many experts and lawmakers consider loot boxes a form of gambling because they involve paying money for a random outcome of varying value. Several countries (Belgium, Netherlands) have banned or restricted them. Others require odds disclosure.

What are gacha systems?

Gacha is the Japanese term for randomized reward systems, popular in mobile games like Genshin Impact and Fate/Grand Order. They work similarly to loot boxes but often include pity systems that guarantee rare items after a certain number of pulls.

Do pity systems make gacha fair?

Pity systems improve the worst-case scenario but don't make the expected value positive. In Genshin Impact, for example, the pity system guarantees a 5-star character within 90 pulls ($180-270), which is still expensive for a single character.

How do I find loot box drop rates?

Many countries require publishers to disclose drop rates. In-game, look for a "rates" or "details" button on the loot box screen. For games that don't disclose, community websites track thousands of openings to estimate probabilities.

Is it ever worth buying loot boxes?

Mathematically, no — the expected value is always negative. The only scenario where it makes sense is if you enjoy the opening experience itself and treat the cost as entertainment, not investment. Set a budget and don't expect to come out ahead.

Loot Box Expected Value Calculator

Calculate the expected value of loot boxes by weighing item values against drop probabilities. See if opening loot boxes is worth the cost on average.

Avg Item Value

Drop Probability

Box / Pull Cost

Spending Budget

Pity Guarantee (0 = none)

Duplicate Rate

Expected Value / Box

$3.75

Average return each time you open a box

Net EV / Box

-$1.25

Negative EV -- you lose money on average

House Edge

25.0%

Percentage the system keeps per box

Boxes to Win Target

Statistical average: 1 / 15%

Cost to Win Target

$35.00

7 boxes at $5.00 each

ROI on Budget

-25.0%

Budget yields negative value

Items from Budget

3.0

2.1 unique, 0.9 dupes

Boxes in Budget

$100.00 / $5.00 per box

Value Gauge

EV/Cost

0.75%

Rarity Tier Comparison

Tier	Value	Drop %	EV/Box	Net EV	Avg Cost to Get
Common Skin	$5.00	60%	$3.00	$0.50	$5.00
Rare Weapon	$25.00	15%	$3.75	-$1.25	$35.00
Epic Mount	$80.00	5%	$4.00	-$1.00	$100.00
Legendary Item	$200.00	1%	$2.00	-$3.00	$500.00
Mythic Drop	$500.00	0.2%	$1.00	-$9.00	$5,000.00

Probability Milestones

Boxes Opened	Total Cost	Chance of At Least 1	Expected Hits
10	$50.00	80.31%	1.5
25	$125.00	98.28%	3.75
50	$250.00	99.97%	7.5
100	$500.00	100%	15

Budget Spending Analysis

Budget	Boxes	Expected Items	Unique Items	Value Received	Net Gain/Loss
$25.00	5	0.8	0.5	$18.75	-$6.25
$50.00	10	1.5	1.1	$37.50	-$12.50
$100.00	20	3.0	2.1	$75.00	-$25.00
$250.00	50	7.5	5.3	$187.50	-$62.50
$500.00	100	15.0	10.5	$375.00	-$125.00

Planning notes, formulas, and examples

About the Loot Box Expected Value Calculator

Loot boxes and gacha systems are randomized purchases where you pay a fixed amount but receive a random item of varying value. Some items are worth far more than the box price, while common drops are worth far less. The expected value tells you the average outcome per box.

This calculator computes the expected value (EV) of a loot box by multiplying each possible item's value by its drop probability and summing the results. If the EV is less than the box cost, you're losing money on average — which is the case for almost every loot box system.

Understanding expected value is crucial because loot boxes rely on rare, exciting wins to mask consistent losses. The math always favors the house, just like casino games. This calculator makes the real odds transparent.

Use the estimate as a planning baseline and adjust it once you have real session data from the game you are playing.

When This Page Helps

Loot box systems are deliberately opaque about true value. Flashy animations and rare drop showcases create an illusion of good odds. This calculator cuts through the psychology and shows you the cold math: on average, every loot box costs you more than you receive in value.

How to Use the Inputs

Enter the average value of items you could receive from the loot box.
Enter the average probability of getting a valuable item (as a percentage).
Enter the cost of one loot box.
Review the expected value per box opening.
Compare EV to box cost to see if it's worth it.

Formula used

expected_value = avg_item_value × (probability / 100)
net_ev = expected_value - box_cost

Where:
  avg_item_value = weighted average value of possible rewards
  probability = chance of getting that average value (%)
  box_cost = price of one loot box

Example Calculation

Result: -$2.00 per box (negative EV)

With items averaging $15 value and a 20% chance of getting them, the expected value per box is $3.00 (15 × 0.20). Since the box costs $5, you lose $2.00 on average per box opened. You'd need to open many boxes to occasionally profit.

Tips & Best Practices

Almost every loot box system has negative expected value — the house always wins.
Drop rates are published by law in many countries — look them up before buying.
The "pity system" in gacha games guarantees a rare after X pulls but the EV is still negative.
Buying the item directly (if possible) is almost always cheaper than gambling on boxes.
Set a strict budget for loot boxes and stop when you hit it, regardless of results.
Treat loot box spending as entertainment cost, not investment.

The Math Behind Loot Boxes

Every loot box system is designed so the average box returns less value than it costs. This is how the developer profits. A box costing $3 might contain items ranging from $0.10 to $50, but the probability-weighted average is always below $3. Rare items create the illusion of value.

Disclosure Laws

China, Japan, South Korea, Belgium, and the Netherlands all have regulations requiring loot box odds disclosure or outright banning them. Apple and Google require odds disclosure for all in-app loot box purchases. This transparency reveals that most rare items have 0.5-3% drop rates.

Safer Alternatives

If you want a specific item, compare the expected cost via loot boxes (box price × 1/probability) to directly purchasing it. A $5 item with a 2% drop rate costs $250 on average through boxes. Direct purchase is almost always cheaper and guaranteed.

Sources & Methodology

Last updated: February 10, 2026

Frequently Asked Questions

Expected value is the average outcome you'd get if you repeated an action infinitely. For loot boxes, it's the average value of items received per box opened. If EV is less than box cost, you're losing money on average.