WoT RU: How many boxes do you need to guarantee a WT E 100?

The Waffentrager is the eleventh tank in the boxes.

To be guaranteed to receive WT E 100, you need to get 10 tanks and the eleventh will be the ‘WT, provided that you do not have a single tank in your garage. Every 50th box is a guaranteed tank, which means to guarantee a Waffentrager you need-

50*11=550 boxes.
On pre-order (84+12) = 96 containers cost 6552 rubles, which means
the minimum cost of WTE100 is 6552/96*550 = 37537.5 rubles,
BUT
The probability that you will receive all 11 tanks as guaranteed after 49 unsuccessful attempts 11 times in a row is total
(0.976)^245*(0.98)^294 = 0.002601*0.002633 = 0.00000685 = 0.0007%
This means that only 7 people out of a million (those who buy 550 containers) will receive WTE100 as guaranteed reward. The rest will receive the coveted prize for the LESS number of boxes.

Next comes the casino. Anyone who wants to take a risk must determine the level of risk, or the probability of their victory. You can answer, for example, the following question:
“How many boxes do you need to buy to have a 50%, 67%, 75%, 90%, 95% or 99% chance of winning WTE100?”
However, you need to understand that even a 99% chance does not guarantee anything.

This is what I propose to calculate below.

Gold WT E 100 “Squire”

The probability of receiving is unknown – this is a jackpot. But it can fall out to anyone even from one box.

Probabilities and boxes

Vehicle drop probability

Due to the new rules for dropping vehicles, namely for the first five vehicles the chance of dropping is 2.4%, for the remaining six – 2%
The graphs are built on the assumption that not a single tank from the boxes is in the hangar.
The leftmost blue line is the probability of not winning a single tank from the boxes; obviously, for >50 boxes this probability is zero.
The following lines are the probabilities of getting at least N(1, 2 … 11) tanks. For example, the red line is a chance to get at least one (and possibly two, three, etc.) tanks, and the last (rightmost) green line is a chance to knock out at least 11 tanks from boxes, i.e. actually get WT E 100.

Another interesting graph is the average number of dropped tanks versus the number of boxes:

Graph with a break on a 50 container

An interesting consequence of the rule of guaranteed reward. Roughly speaking, this rule increases the effective chance of winning. It is because of this that in all previous containers, the actual observed drop rate of tanks was higher than stated. For current containers, the “actual” chance of getting a tank is about 3.16%, instead of the stated 2.0..2.4%.

The graph also shows that on average 11 tanks (read WTE100) drop out of 345-350 containers, i.e. For Lesta, the cost of one WTE100 is approximately
(6552/96)*347 = 23680 rubles (262 USD)

It will be interesting to see how many WTE100 players will pull out of the boxes.

Now a couple of graphs for those for whom theory is not an empty phrase or a curse…

Probability distribution density to win WTE100

It can be seen that the maximum lies in the region of 345-350 containers.

Probability distribution function to win WTE100

This is actually a more detailed version of the probability graph of getting at least 11 tanks presented at the beginning along with the rest.
Looking at this graph, you can answer the question posed at the beginning of the article:
“ How many boxes do you need to buy to have a 50%, 67%, 75%, 90%, 95% or 99% chance of winning WTE100? ”

50% – 340 boxes = 23205 rubles. (257 USD)
67% – 365 boxes = 24911 rubles. (276 USD)
75% – 380 boxes = 25935 rubles. (287 USD)
90% – 415 boxes = 28324 rubles. (314 USD)
95% – 435 boxes = 29,689 rubles. (329 USD)
99% – 470 boxes = 32078 rubles. (355 USD)

From these numbers and the cost of containers, you can decide for yourself which risk (chance of not winning) to choose and how much it will cost.

Summary:

Paying more than 23 thousand rubles for the opportunity to flip a coin is a little expensive. With 32 thousand the chance of winning is 90%.

In the end, everyone decides for themselves

source