Excursion into stochastics

Loot boxes, crates, containers - there are many words for a current phenomenon in various online games. We are talking about boxes with randomly distributed content that contain a certain percentage of goods that the buyer would like to have. These boxes are different from many other additional goods that can be bought for the use of real money because they only offer a chance to receive them.

The principle:

If I buy a tank for real money, I know that I will certainly get the desired value for my issue. With crates, however, I buy a lot - no more and no less. So these boxes fall under the category of gambling and I will continue to call it that.

My request:

I do not want to explain in this article whether it makes sense to buy boxes or not. Everyone has to decide for himself. What I would like to do, however, is to clarify about errors that circulate in the calculation of probabilities in the forums and on the Discord servers.

The math:

In the game WoT-Blitz boxes are offered periodically, which contain a certain percentage of a tank. Let's assume in the following that there is a box in the shop which contains a T22 with a probability of 5%, i.e. basically the tanks are distributed in such a way that on average there are 5 tanks in 100 boxes. But this is no guarantee! With a dice the probability is to roll a 6 1/6 = 16.67 %. Nevertheless it is not guaranteed that you roll at least one 6 on all six rolls.

The mistake:

Many players now think: "Cool - the probability is 5%. So I buy myself 20 boxes and then I definitely have him!" – That's not true! It's just probabilities. You can also buy 100 crates and if a Fortuna is not well-disposed towards you, you won't get a tank.

The calculation:

In school mathematics, this experiment is known in stochastics as "pulling out of an urn and putting it back". What does this mean? The probability distribution does not change even if the urn is dragged several times. However, several combinations are possible. Let's look at the picture of the following tree diagram:

Wahrscheinlichkeitsverteilung

The diagram illustrates the combinations when opening a Loot Box four times. The path in the tree on the far right would be four rivets, because no tank is ever pulled. In all other paths at least one tank is drawn. On the paths themselves, the single probabilities are worn out. Since these do not change, it is always 5% for pulling a tank. The single probabilities of a path are now multiplied and give the probability of a single event path.

Short and sweet:

The probability of not getting a tank four times in a row is therefore (0,95*0,95*0,95*0,95)=0,8145=81,45%.

Often, packages of 10 are offered in the shop. A tree for this would have 1024 paths, but the path on which no tank can be pulled is calculated very simply: 0.95^10=0.5987. So even with 10 boxes you would only have a probability of about 40% to pull a tank. Remember that when you buy crates!

Current crates:

There is currently a container collection in the shop. There are 11 crates in this collection, but each crate has a different probability of being used on a selected tank. The range goes from 2.5% to 6%, depending on the type of tank. There's a 65% chance we won't get a tank here! And if you do get one, it's pure coincidence which. It is and remains gambling!

It's not for nothing that gambling can be addictive! And for the money, you'd rather buy your wife / mother a beautiful bouquet of flowers!

Stay clean, your hasso.

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