How pack expected value is actually calculated

Every pack on a case-opening site has a published odds table: a list of items, each with a probability and a market value. Expected value — EV — is the single number that table collapses to. It tells you what one open is worth on average, and it is the only figure that matters when you are comparing packs.

The arithmetic is not complicated. What makes it feel complicated is that the answer is almost always "less than you paid", and most write-ups avoid saying that plainly. This one does not.

The formula

Multiply each item's value by its probability, then add up the results:

EV = Σ (probability of item × value of item)

That is the whole thing. Here is a simplified five-item pack priced at $10.00:

Add the contributions: 2.80 + 2.64 + 2.40 + 1.62 + 2.40 = $11.86. That would be a positive-EV pack, which is why you will not find one. Change the Legendary odds to 0.05% — a change most people would not notice in the table — and its contribution drops from $2.40 to $0.60. EV falls to $10.06. Shave the Rare down too and you land in the $8.50–$9.20 range, which is roughly where real packs sit.

Return to player

Divide EV by price and you get RTP:

RTP = EV ÷ price. A pack with $9.00 EV at a $10.00 price has 90% RTP and a 10% house edge.

Ten percent is your cost of playing. Over 100 opens at $10 each you have wagered $1,000 and the expected outcome is finishing $100 down. Not a possible outcome — the expected one.

Three things the table does not tell you

1. "Value" is not "what you can sell it for"

Item values on case sites are usually reference prices, not guaranteed buybacks. If the site's own buyback is 85% of listed value, then a $40 Rare is really $34 to you unless you want the item itself. Recompute the table with buyback prices and the EV drops again. Always ask which number the odds table is using.

2. The top line carries most of the EV — and you will almost never hit it

In the first table above, the Legendary at 0.20% supplies $2.40 of $11.86 — about a fifth of the total EV. Your median result contains none of it. At 0.20%, there is roughly a 37% chance of not seeing a single Legendary in 500 opens (0.998^500 ≈ 0.37). The average is dragged upward by an outcome most players never experience, so the typical return is meaningfully worse than the EV suggests.

3. Variance decides what actually happens to you

EV is a long-run average. Over 100 opens you are nowhere near the long run. The distribution of your results is wide and lumpy, and the lumpiness increases the more of the EV sits in rare items. Two players with identical odds and identical spend can finish a session hundreds of dollars apart, and neither result says anything about whether the pack was "hot" or "cold".

Where the code fits

A 5% deposit boost does not change the odds table and does not make a negative-EV pack positive. What it does is reduce your effective cost of the same activity. If you deposit $100 and receive $105 of play, then at 90% RTP your expected return moves from $90 to $94.50. Still negative. Just less negative.

That is the honest framing for every reward on this site: leaderboard prizes, the raffle, and the boost give back a slice of what the edge takes. They do not invert it. Anyone telling you a code makes case opening profitable is selling something.

A checklist before you open

• Find the published odds table. If a pack does not have one, that is your answer.
• Compute EV yourself, using buyback values rather than listed values.
• Check what fraction of EV sits in items rarer than 1%. The higher that fraction, the further your realistic outcome sits below the average.
• Decide your total spend before you start, and treat it as the price of entertainment rather than an investment.