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The templates {{Required trials}} and {{Required trials percent}} calculate the number $ n $ of Bernoulli trials required to achieve at least one success with a given minimum probability.
The only difference between the two is that {{Required trials}} works with probabilities from 0 to 1, while {{Required trials percent}} works with probabilities from 0 % to 100 %.
The formula is
 $ n \ge \frac{\ln(1 \mathrm P_{min})}{\ln(1p)} $
 $ \mathrm P_{min} $: desired minimum probability of at least one success
$ p $: probability of success
Usage
{{required trials  pmin =  p =  format}}
or
{{required trials percent  pmin =  p =  format}}
Parameters
pmin
 Desired minimum probability $ \mathrm P_{min} $ of at least one success
 Required.
 {{Required trials}}: Number between 0 and 1.
 {{Required trials percent}}: Number between 0 % and 100 %, with or without percent sign.
p
 Probability $ p $ of success
 Required.
 {{Required trials}}: Number between 0 and 1.
 {{Required trials percent}}: Number between 0 % and 100 %, with or without percent sign.
format
 Display options for $ n $
 Optional. One of the following texts:

ceil
– Displays the ceiling $ \lceil n \rceil $ instead of an unrounded $ n $.
As there are no "partial" trials, it is usually recommended to useceil
instead ofround
. 
round x
– Rounds $ n $ tox
trailing digits.

Examples
Standard
Given a probability $ p $ = 1.88 % = 0.0188 of obtaining a V8 Engine from a Pro Kit Box, the number of cards required to get at least one V8 Engine with a probability of 90 % = 0.9 is:
 Unformatted

{{required trials  p=0.0188  pmin=0.9}}
→ 121.32299622997  Rounded to 3 digits

{{required trials  p=0.0188  pmin=0.9  round 3}}
→ 121.323  Ceiling

{{required trials  p=0.0188  pmin=0.9  ceil}}
→ 122
Percentages
Technically, {{Required trials percent}} simply calls {{Required trials}} with pmin
and p
divided by 100.
Percent signs and spaces are removed, so it doesn't matter if parameters are provided as 90 %, 90% or 90.
 Unformatted

{{required trials percent  p=1.88 %  pmin=90 %}}
→ 121.32299622997  Rounded to 3 digits

{{required trials percent  p=1.88%  pmin=90%  round 3}}
→ 121.323  Ceiling

{{required trials percent  p=1.88  pmin=90  ceil}}
→ 122
Extracted values from Pro Kit Box templates
{{Required trials percent}} is particularly useful for statistical values extracted from Pro Kit Box templates via the #
parameter, as these values are always given in percent.
For example, {{Finish Line Box#sv82}}
delivers 2.13, the average percentage of V8 Engines in Finish Line Boxes. See {{A8boxmeta}} for an overview of statistics parameters.
Cards needed for at least one ...
 V8 Engine from Finish Line Boxes

{{required trials percent  p={{Finish Line Box#sv82}}  pmin=90  ceil}}
→ 107  Tech card from Ultra Boxes

{{required trials percent  p={{Ultra Box#stech2}}  pmin=90  ceil}}
→ 37  Tech card from Engine Boxes (impossible)

{{required trials percent  p={{Engine Box 15#stech2}}  pmin=90  ceil}}
→ $ \infty $
Extreme values
Extreme parameter values would lead to errors like division by zero or invalid arguments for the logarithm. These values are handled as follows:
p

p = 0
: success is impossible, $ \infty $ is displayed (an infinite number of trials is required). 
p = 1
: success is sure, 1 is displayed (only one trial is required).
pmin
(if 0 < p < 1
)

pmin = 0
: A desired 0 % probability of having at least one success is achievable with any probability of success, 1 is displayed (only one trial is required). 
pmin = 1
: A desired 100 % probability of having at least one success is impossible if success is not sure, $ \infty $ is displayed (an infinite number of trials is required).
The percent values 0 % and 100 % work accordingly.

{{required trials  p=0  pmin=0.9}}
→ $ \infty $ 
{{required trials  p=0  pmin=0}}
→ $ \infty $ 
{{required trials  p=0  pmin=1}}
→ $ \infty $

{{required trials  p=1  pmin=0.9}}
→ 1 
{{required trials  p=1  pmin=0}}
→ 1 
{{required trials  p=1  pmin=1}}
→ 1

{{required trials  p=0.2  pmin=0}}
→ 1 
{{required trials  p=0.2  pmin=1}}
→ $ \infty $
Technical details
If the infinity sign is displayed, the template adds an invisible leading <div>
tag:
<div style="display:none;">9999999999999999999</div><math>\infty</math>
This is to ensure that $ \infty $ is sorted after all numbers in tables, for example in Pro Kit Box statistics: minimum card requirements.