How Dota 2 Treasure Odds Work
Find the treasure’s reward rules first, then pick the right probability formula.
Project editor:GrassKnuckles
There is no single drop rate for all Dota 2 treasures. Find the exact treasure’s edition, then separate the ordinary reward, any bonus rewards and odds that change with earlier openings. With fixed odds, the chance of at least one hit in n openings is 1 − (1 − p)n, which the next section works through.
Ten attempts at 2% are not a 20% promise
Take a fixed, independent 2% chance at a target item. The probability of at least one target in n openings is 1 − (1 − 0.02)n. Ten openings give about 18.3%; fifty give about 63.6%. That leaves roughly 36.4% of fifty-opening runs without the target. Multiplying 2% by fifty to “reach 100%” double-counts overlapping successes.
The average wait is 1 ÷ 0.02 = 50 attempts, but success has no deadline. With fixed odds, a failed opening leaves the next attempt at 2%.
Rising odds need a chance for each attempt
Now take a different example: the chance is 1%, then 2%, then 4% after successive misses. The chance of at least one success in three attempts is 1 − 0.99 × 0.98 × 0.96 = 6.8608%. Applying the final 4% to all three attempts would give 11.5264%, which overstates it. To go further, you need the counter’s rule after a reward: does it reset or carry on?
Bonus rewards are a separate calculation
The 2015 Compendium describes one past structure with an ordinary reward plus a bonus. Other editions have their own rules. In this example, an ordinary item worth $1 plus a bonus worth $20 with a 2% chance has a gross expected value of $1 + 0.02 × $20 = $1.40. If you treat the bonus as replacing the ordinary reward, you answer a different question.
Expected value is the average across the outcomes you specify. It predicts neither your next reward nor the money you can withdraw. Transfer restrictions, missing prices, selling fees and the opening cost all still matter.
What to enter in the treasure calculator
In the treasure calculator, choose Your own chances and enter each outcome’s value and percentage. The outcomes must exclude one another and total 100%. The calculator has no built-in treasure odds and no equal-chance or weight mode; if you assume equal chances or weights, convert them to percentages yourself. The after-fee option uses the site’s Steam fee formula, so check the current fee on the marketplace before relying on it.
The calculator can’t read your escalating counter or model how it changes. Record the edition, the rule and the starting counter first. For extra bonus rolls, define the combined outcomes instead of entering the bonus as a replacement reward. If you don’t know the real odds, don’t guess them. Compare the cost of opening with the cost of buying the item you want, as in the opening-cost comparison.