What a sure thing costs
- 1 in 100Odds100Chests on average200 dollarsAt 2 dollars each
A 1 in 100 chance takes 100 tries on average. Some players get it on the third chest, some on the four-hundredth. Across everyone, it comes out at about 100. At 2 dollars a chest, that is 200 dollars for one rare item, on average.
- A label nobody would pay200 dollarsThe label on the chest2 dollars
That average is the real price. Nobody would pay 200 dollars for a picture of a hat if the label said 200. So the label says 2, and the 200 arrives as a hundred small yeses, each one easy.
- 2 dollarsA chest1 in 100The rare item
The rare item is in 1 chest in 100, and a chest costs 2 dollars. On average, what does the rare item cost?
100 dollars. One in 100 means 100.
Not yet. A hundred is the number of chests, not the number of dollars. Each of those hundred chests costs 2.About 200 dollars.
Right. A hundred chests at 2 dollars. The player who gets it on the first chest paid 2; the one who needed 300 paid 600. The shop is paid by both.2 dollars. That is what the chest costs.
Not yet. Two dollars is what one chest costs, and one chest almost never holds it. The price of the item is the price of all the chests it takes. - Odds halvedTwice as many chestsTwice the money
The game's makers can turn two dials. The odds, and the price of a chest. Halve the odds and the average doubles. Double the chest price and it doubles again. That is how they set the price of a rare thing without ever printing it.
Set the odds of the rare item and the price of a chest. The average cost is the chest price times the average number of chests, worked out exactly.
Average cost of one rare item200 dollarsA full-price 60-dollar game, for size60 dollars1 in 200 · 1 dollarAt 1 in 200, a player needs 200 chests on average. At 1 dollar a chest, that is 200 dollars on average for one rare item.
Average cost of one rare item400 dollarsA full-price 60-dollar game, for size60 dollars1 in 200 · 2 dollarsAt 1 in 200, a player needs 200 chests on average. At 2 dollars a chest, that is 400 dollars on average for one rare item.
Average cost of one rare item1,000 dollarsA full-price 60-dollar game, for size60 dollars1 in 200 · 5 dollarsAt 1 in 200, a player needs 200 chests on average. At 5 dollars a chest, that is 1,000 dollars on average for one rare item.
Average cost of one rare item100 dollarsA full-price 60-dollar game, for size60 dollars1 in 100 · 1 dollarAt 1 in 100, a player needs 100 chests on average. At 1 dollar a chest, that is 100 dollars on average for one rare item.
Average cost of one rare item200 dollarsA full-price 60-dollar game, for size60 dollars1 in 100 · 2 dollarsAt 1 in 100, a player needs 100 chests on average. At 2 dollars a chest, that is 200 dollars on average for one rare item.
Average cost of one rare item500 dollarsA full-price 60-dollar game, for size60 dollars1 in 100 · 5 dollarsAt 1 in 100, a player needs 100 chests on average. At 5 dollars a chest, that is 500 dollars on average for one rare item.
Average cost of one rare item50 dollarsA full-price 60-dollar game, for size60 dollars1 in 50 · 1 dollarAt 1 in 50, a player needs 50 chests on average. At 1 dollar a chest, that is 50 dollars on average for one rare item.
Average cost of one rare item100 dollarsA full-price 60-dollar game, for size60 dollars1 in 50 · 2 dollarsAt 1 in 50, a player needs 50 chests on average. At 2 dollars a chest, that is 100 dollars on average for one rare item.
Average cost of one rare item250 dollarsA full-price 60-dollar game, for size60 dollars1 in 50 · 5 dollarsAt 1 in 50, a player needs 50 chests on average. At 5 dollars a chest, that is 250 dollars on average for one rare item.
Average cost of one rare item20 dollarsA full-price 60-dollar game, for size60 dollars1 in 20 · 1 dollarAt 1 in 20, a player needs 20 chests on average. At 1 dollar a chest, that is 20 dollars on average for one rare item.
Average cost of one rare item40 dollarsA full-price 60-dollar game, for size60 dollars1 in 20 · 2 dollarsAt 1 in 20, a player needs 20 chests on average. At 2 dollars a chest, that is 40 dollars on average for one rare item.
Average cost of one rare item100 dollarsA full-price 60-dollar game, for size60 dollars1 in 20 · 5 dollarsAt 1 in 20, a player needs 20 chests on average. At 5 dollars a chest, that is 100 dollars on average for one rare item.
Which costs more on average: a 1-dollar chest at 1 in 200, or a 5-dollar chest at 1 in 20?
The 5-dollar chest. Five dollars is five times the price.
Not yet. Five times the price, but a tenth of the chests. Twenty chests at 5 dollars is 100 dollars; two hundred at 1 dollar is 200.The 1-dollar chest. Two hundred dollars against a hundred.
Right. The cheap chest with long odds is the dearer item. Cheap is the label; the odds are the price, and a player sees the label.The same. Both come to 100 dollars.
Not yet. They meet only at 1 in 100 for the dollar chest. At 1 in 200 the dollar chest needs two hundred tries, and two hundred dollars is twice the other.Move both controls.
- Card packs29 of every 100 dollars, one year · 29%
- Everything else the company sells71 of every 100 dollars, one year · 71%
Real numbers. One publisher's football game sells card packs with players inside. In one year those packs took in about 1.6 billion dollars, more than a quarter of everything the company earned. The chest is not a side business. For some games it is the business.
- 3 dollarsA chest1 in 40Odds
A chest costs 3 dollars, and the rare item is in 1 chest in 40. On average, how much does the rare item cost?
dollarsRight. Forty chests at 3 dollars each. A game that wanted the item to cost 60 could halve the price or double the odds, and neither change would appear on any label. Of the 100 top-earning phone games on the Android store in 2019, how many sold chests with a chance inside?
Pick one. Nothing is scored.
6 of 10
Of every 10 top-earning games, about 6 sell paid chests
About 60.Most people guess lower because the games they know best are not the ones that earn most. In a 2020 study, 58 of the top 100 earning Android games and 59 of the top 100 iPhone games sold paid chests. The chest is how most of the top earners earn.- up to 10Chests2 dollarsEachpromised by the 10thTop item
A game says: a top item in every tenth chest, guaranteed. A chest costs 2 dollars. What is the most a top item can cost?
No limit. A chance is a chance.
Not yet. A chance alone has no limit; that is why the promise exists. The tenth chest is guaranteed, so nobody pays for an eleventh.20 dollars. The promise sets a top price, and many players pay less.
Right. The promise caps the worst case. Some players get it on the second chest for 4 dollars, so the average is under 20 while the ceiling is exactly 20.2 dollars. It might be in the first chest.
Not yet. It might be, and that player pays 2. The question asks the most it can cost, and the most is ten chests.
Lesson complete
Chest price divided by the odds is the rare item's average price, and the game never prints it.