Teacher instructions

Work through this resource material in the following sequence:

10 minutes

Tune in: What is a loot box?

20 minutes

Find out: Calculating loot box chances - How many for a set?

30 minutes

Take action: Design your own loot box

Tune in: What is a loot box?

Step 1.

Arrange your students into groups of three, ensuring that each group contains at least one person who knows what loot boxes are. Have those students describe them to the others, and answer any questions they may have.

Step 2.

As a class, create a word wall on the board of other terms students associate with loot boxes. This may include gambling, fun, chance, games, and real money.

Step 3.

Settle on a definition of a loot box. Write this up on the board.

Step 4.

Watch:

What are video game loot boxes and do they encourage gambling? | ABC News (https://www.youtube.com/watch?v=jh4UYz9apNk)

Step 5.

In their groups, ask students to answer the question: do you think loot boxes are a form of gambling?

Step 6.

After a few minutes of discussion, invite some students to volunteer the perspectives of the group, and discuss these as a whole class.

Step 7.

Consider whether there are any terms students want to add to the word wall, or whether they want to alter their definition of a loot box.

Step 8.

Explain to students that for this task they will invent a computer game that uses loot boxes, and calculate how many loot boxes a player would need to purchase (on average) in order to complete a full set of items, such as a suit of armour.

Step 9.

Independently, or in small groups, students design a basic concept for a video game.

First, students take a sheet of A3 paper and map out some of their ideas.

Remember that the game has to include some form of a set of collectibles. In our example, we’ll be using a suit of medieval armour in a fantasy type game, since that concept and the individual pieces required by the set are easy for everyone to grasp. However, creative students might adapt the set to, for example, a complete outfit for a model (clothes, shoes, hat, accessory), a set of furniture for a room in a house (bed, lamp, desk, wardrobe), or different parts of a spaceship (engines, cargo bay, weapons, shields).

Step 10.

Students write a brief description of their game, such as something that might be included on the back of a box or in a magazine advertisement.

It should also detail all the components required to assemble the whole set. Recommend students come up with between five and ten different pieces.

Students also need to set a price for each loot box.

For example:

Squadron of Supers is an online (fictitious) game where you play a superhero. These heroes roam a digital world, fighting baddies and rescuing cats stuck in trees. Your particular character is Sir Gwent the Adamant, a superhero whose power comes from a magical suit of medieval armour. You get a standard set of armour for free, but to maximise Sir Gwent’s potential he really needs the complete, eight-piece set known as Righteous Protection. The problem is, to obtain the complete set you must purchase loot boxes as the Righteous Protection items cannot be found elsewhere. Each loot box will contain one randomly chosen item from the set. For example, your first loot box might give you the Breastplate of Truth, and in the next you find the Helm of Vision and so on. A single loot box will cost a player $4.99.

Find out: Calculating loot box chances - How many for a set?

Step 1.

Ask your class: how many loot boxes would you need to get the full set?

They should realise that you will need at least eight - but that’s a best case scenario, and highly unlikely!

Step 2.

Ask students to calculate what is the chance that you open 8 boxes in a row and immediately get the 8 items you want?

Step 3.

In reality it will be much more, since you’re not guaranteed to get the exact item you want every time.

So, how do we calculate this?

Let’s start by thinking about the very first box. Ask students:

What are the chances that your first loot box will contain a unique (one that you don’t already have) item? As you don’t have any items yet, the probability is 1, or 100%. There is absolutely no doubt it will definitely give you an item you don’t already have. We can think of this as ‘unique item number one’. It doesn’t really matter which item it is, specifically, as both the Breastplate and Helm would be unique to our collection at this stage.

We can express this with the equation:

P(box one containing a new item) = 1.

Step 4.

Now ask students:

How many ‘box number ones’ do I need to purchase to ensure it will contain a unique item? In this case the answer is pretty simple: one. Buying just one loot box will get us an item we don’t already own.

Step 5.

So we’ve got one item. Fantastic! Now let’s consider the second box. Ask students:

As there are eight items in total in the set, and you already have one of them, what is the chance of this box containing something new?

This can be expressed as:

P(box two containing a new item) = 7/8.

(with P(box two containing an item you already have) = 1/8.)

Step 6.

Explain to students that the amount of ‘box number twos’ you’d need to purchase to ensure the ‘box number two’ will contain an item I do not already have is (on average) equal to the reciprocal of the probability of that box containing a new item.

In other words, you would need to purchase (on average):

8/7 ≈ 1.1429 boxes.

Step 7.

Important! This is not the number of boxes needed altogether! This is just how many ‘box number twos’ you would need in order to get ‘unique item number two’.

Explain to students that in order to secure two of the eight pieces of armour from loot boxes, you would need to purchase (on average)

1 x box number one
1.1429 x box number two

Combined with the first box then, you would need to buy (on average):

1 + 1.1429 = 2.1429 boxes.

This means that if we bought (on average) 2.1429 loot boxes, we’d obtain two unique items out of the set of eight.

Step 8.

Pause for a moment and ask students to discuss how they feel about these chances. It looks pretty good from the outset, right? In fact if we round down, it looks like probability is saying that we purchase two loot boxes for two unique items.

However, is that .1429 worrying any students? Can anyone see a potential pattern emerging, even at this early stage?

Ask students to predict what they think might happen in terms of how many ‘box number eights’ they might have to purchase.

Step 9.

Let’s try one more box before we leap into a spreadsheet to ease our calculations.

Players currently own two unique items, with six from the collection left to collect.

P(box three containing a new item) = 6/8.

Taking the reciprocal of this tells us that on average we would have to purchase

8/6 = 1.333 boxes.

Adding the numbers for each box together gives us:

1 + 1.1429 + 1.333 = 3.4762 boxes.

Purchasing 3.4762 boxes (on average) will reward a player with three unique items.

Not quite three unique items from three loot boxes, is it? Obtaining this full set of armour might be trickier than at first thought…

Take action: Design your own loot box

Step 1.

Independently, students calculate how many loot boxes on average a player of their video game will need to purchase in order to achieve a full set of unique items.

Step 2.

Once all students have finished their calculations, invite some students to share their findings.

On average, to assemble a full set of eight unique items, a player will be required to purchase 21.74 (or rounding up to 22) loot boxes.

If students had a higher number of unique items in their set, the number of loot boxes to be purchased will be even higher.

Important! Explain to students the use of the phrase ‘on average’ throughout this lesson. Probability says that if you purchase 22 loot boxes you should assemble a full set of eight items. However, reality doesn’t always reflect probability. There will be some players who purchase eight loot boxes and receive eight unique items straight away. And there will be other players who purchase fifty loot boxes and still not assemble a set!

Step 3.

Independently, or in their small groups, students write a disclaimer for the box of their video game, explaining the probability of achieving a full set, the cost of purchasing that many loots boxes, and warning players about the potential of spending even more than that if the probability doesn’t pay out as expected.

Step 4.

Students who finish early could draw some cool box art for their game to go alongside their blurb and disclaimer.

Reflection

Ask students to write a short paragraph reflecting on their approach to loot boxes, knowing the probability of winning the items they desire.

How might they feel when they purchase the average amount of loot boxes and don’t complete their set?

What impact might this have on their behaviour? Will they continue to gamble on purchasing loot boxes, or will they realise this might not be a rewarding course of action?

Differentiated Learning

Provisions for learning support:

You may wish to share the following table with students to support them with their calculations, based on the example above.

Box number	Calculation	Number of boxes to be purchased to receive a unique item
Box number one	8/8	1
Box number two	8/7	1.1429
Box number three	8/6	1.333
Box number four	8/5
Box number five	8/4
Box number six	8/3
Box number seven	8/2
Box number eight	8/1
-	-	Total:

Alternatively, if the above task is too difficult, encourage students to create a game with a full set of only five items, remembering that the calculations will change based on the total number of items in the set.

Box number	Calculation	Number of boxes to be purchased to receive a unique item
Box number one	5/5
Box number two	5/4
Box number three	5/3
Box number four	5/2
Box number five	5/1
-	-	Total:

Provisions for extending students:

Encourage students to create a game where a full set is in excess of 10 items.
Some loot boxes contain not one but three or more items. Does this change the probability of receiving a unique item? For better or worse?
Some loot boxes have different rarities of items. For example, the Common Boots of Walking might have a 70% chance of appearing, the Rare Boots of Striding Might have a 20% chance of appearing, and the Ultra Rare Winged Boots of Flight might have only a 10% chance of appearing. Can students design a system which predicts a player’s chance of assembling a full set of Ultra Rare items? Note: This is a thought experiment to challenge students only! The maths starts to get complicated… like third year uni complicated… but students will enjoy puzzling over the challenge!
There are 363 skins in the video game Overwatch - how many boxes do you think you should open to get them all?

Loot Box Chances

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