Minecraft, 358 293 277 276 bytes
Implementing Minceraft in Minecraft
Should be run as a set of commands in game. Should be run on a fresh superflat (redstone ready) world.
Byte count is the amount of characters you need to type, including newlines.
/scoreboard objectives add s dummy
/summon bat
/execute as @e[type=bat] store result score o s run data get entity @s UUID[1]
/scoreboard players set c s 2147054151
/execute if score o s < c s run tellraw @s "Minecraft"
/execute if score o s >= c s run tellraw @s "Minceraft"
The UUID of an entity is (mostly) randomly generated and stored as four signed 32 bit integers. One of the integers is compared with 2147054151
which is one ten thousandth of the way between 2^31
and -2^31
.
Previous solution because it was so high effort and I'm not deleting it:
Minecraft, 293 bytes
/scoreboard objectives add s dummy
/summon horse
/execute as @e[type=horse] store result score o s run data get entity @s Attributes[1].Base 100000
/scoreboard players set c s 11883
/execute if score o s >= c s run tellraw @s "Minecraft"
/execute if score o s < c s run tellraw @s "Minceraft"
How does it work?
In Minecraft, there are only a limited amount of sources of reliable randomness usable in commands. In Minecraft Functions you can use predicates with specific random chances, but that requires multiple files and submitting that as a zipped data pack would be at least 1 KB.
To avoid this and have it run solely from commands a player can type in, this uses horses as a random source. When a horse is spawned, it is assigned a random speed between 0.1125 and 0.3375 (the units are arbitrary). The random speed calculation is as follows:
$$0.25(0.45 + 0.3x + 0.3y + 0.3z)$$
Where x, y, and z are uniform independent random variables [0, 1). If you find the cumulative density function by convolving the distribution functions (to get the PDF) and then integrating, you will end up with the following piecewise function:
$$
f(x)=\begin{cases}-\frac{9}{16}+15x-\frac{400x^{2}}{3}+\frac{32000x^{3}}{81}&\frac{9}{80}\le x<\frac{3}{16}\\
\frac{29}{4}-110x+\frac{1600x^{2}}{3}-\frac{64000x^{3}}{81}&\frac{3}{16}\le x<\frac{21}{80}\\
-\frac{227}{16}+135x-400x^{2}+\frac{32000x^{3}}{81}&\frac{21}{80}\le x<\frac{27}{80}
\end{cases}
$$
We need to find the horse speed where the probability of a horse with that speed or lower spawning is one in ten thousand or 0.0001. This can be done by solving the first equation:
$$-\frac{9}{16}+15x-\frac{400x^{2}}{3}+\frac{32000x^{3}}{81} = 0.0001\\
f^{-1}(0.0001)\simeq0.11882574$$
This results in the horse speed being multiplied by 100,000 (because scoreboard values must be integers) and compared with 11883 in the code.
The precision is currently 1.00202 in 10,000. Two bytes can be added or removed for approximately each order of magnitude required. Two additional bytes will make it 1.00012 in 10,000.