You bought a chance, not a prize
- 2 dollarsA chestThe rare skin1 in 100
A chest in the shop costs 2 dollars. Inside is one of fifty items, picked at random. The one you want, the rare skin, is in 1 chest in every 100. You did not buy the skin. You bought a chance at it.
- Common70 in 100 chests · 70%
- Uncommon25 in 100 chests · 25%
- Rare4 in 100 chests · 4%
- The top one1 in 100 chests · 1%
A typical shape; the real list is printed in each game. Since 2017 the big app stores make games print the odds. Odds just means how often a thing happens out of a hundred tries. A typical list looks like this: most chests hold a common item, a few hold a rare one, and one in a hundred holds the top one.
- A chanceThe rare skinAny item you choose
What do the 2 dollars buy?
A choice of any item in the list.
Not yet. Nothing in a chest is chosen. The whole point of the chest is that the game picks, not you.A chance. The chest might hold the skin, and usually does not.
Right. Ninety-nine times in a hundred the 2 dollars buys something else. That is not a fault in the chest; it is what a chest is.The rare skin. Two dollars is its price.
Not yet. If 2 dollars bought the skin, the shop would sell the skin for 2 dollars. It sells a chest instead, because a chest can be sold a hundred times to one person. - After 1 chest1 in 100 who have itAfter 2 chests2 in 100 who have itAfter 10 chests10 in 100 who have it
Rounded. After 10 it is just under 10. Two chests do not give you 2 in 100. Each chest is its own draw, and it does not remember the last one. After two chests the chance you still have nothing is 99 in 100 of 99 in 100, which is about 98 in 100. The chance creeps up slowly.
Move the control to set how many chests a player opens. Each chest holds the rare item 1 time in 100, and the sums are exact.
Players in 100 who have it10 in 100Players in 100 who still do not90 in 10010 chestsAfter 10 chests at 1 in 100 each, about 10 players in 100 have the rare item and 90 still do not. Every chest was its own draw.
Players in 100 who have it39 in 100Players in 100 who still do not61 in 10050 chestsAfter 50 chests at 1 in 100 each, about 39 players in 100 have the rare item and 61 still do not. Every chest was its own draw.
Players in 100 who have it63 in 100Players in 100 who still do not37 in 100100 chestsAfter 100 chests at 1 in 100 each, about 63 players in 100 have the rare item and 37 still do not. Every chest was its own draw.
Players in 100 who have it95 in 100Players in 100 who still do not5 in 100300 chestsAfter 300 chests at 1 in 100 each, about 95 players in 100 have the rare item and 5 still do not. Every chest was its own draw.
Players in 100 who have it99 in 100Players in 100 who still do not1 in 100500 chestsAfter 500 chests at 1 in 100 each, about 99 players in 100 have the rare item and 1 still do not. Every chest was its own draw.
A player opens 100 chests at 1 in 100 each. What is the chance they have the rare item?
About 63 in 100. More than a third of players who open 100 chests still have nothing.
Right. A hundred tries at 1 in 100 does not add up to certain. It never does. Some players open 300 and are still waiting, and the game has taken 600 dollars from each of them.Still 1 in 100. The odds never change.
Not yet. The odds of each chest never change. The chance that at least one of a hundred chests lands is a different number, and it grows with every chest.Certain. A hundred tries at 1 in 100 must land once.
Not yet. Each chest forgets the last. A hundred misses in a row is unlikely, but it happens to 37 players in 100, and the chest owes them nothing.Move the control.
- 0.6 in 100Each pullpull 90Promised byabout 225 dollars90 pulls
Real numbers. In one big game, each pull has a 0.6 in 100 chance of a top character. The game promises one by the 90th pull. A pull costs about two and a half dollars at the biggest bundle. So a promised top character can cost about 225 dollars.
- 6,480 coinsBundle160 coinsOne pull
In that game a pull costs 160 of its coins. The biggest bundle sells 6,480 coins. How many full pulls is that?
pullsRight. Forty pulls, with 80 coins left over. The bundle is 99.99 dollars, and forty pulls is less than half the ninety the promise needs. Two bundles and a bit is what a promised character costs. - Chest 11 in 100Chest 501 in 100Chest 1001 in 100
A player has opened 99 chests and never got the rare item. What is the chance the 100th chest holds it?
Less than 1 in 100. This player is unlucky.
Not yet. Luck is not a property of a player. The same 1 in 100 applies to everyone on every chest, however the last ninety-nine went.1 in 100, the same as the first chest.
Right. The chest has no memory. Ninety-nine misses do not make the hundredth more likely, however much it feels that way, and that feeling sells the hundredth chest.Nearly certain. After 99 misses it is due.
Not yet. Nothing is due. The draw is made fresh each time, and the 99 chests already opened have no say in it. - 25 dollars25 packsEach pack4 in 100The top card
A card game sells packs for 1 dollar. Each pack has a 4 in 100 chance of the top card. A player spends 25 dollars. Do they get the top card?
Probably, but not certainly: about 64 players in 100 who spend 25 dollars get it.
Right. Twenty-five draws at 4 in 100 leave about 36 in 100 players empty-handed. About a third of players spend 25 dollars and get a stack of common cards.Certainly. Twenty-five packs at 4 in 100 adds up to 100 in 100.
Not yet. Chances do not add like that. Each pack forgets the last, and the chance of at least one hit after 25 packs is about 64 in 100, not 100.No more likely than with one pack. It is 4 in 100 whatever you do.
Not yet. Each pack is 4 in 100. The chance that at least one of 25 packs lands is much higher, and it is that chance the 25 dollars buys.
Lesson complete
A paid chest sells a chance, each chest is its own draw, and many chests still promise nothing.