2
PixelRayn
Yesterday I had a little disagreement with another editor of the minecraft wiki about the "Egg" article. I wanted to know how often a chicken lays an egg, because I was going through some concepts for furnace based XP-grinders and I wanted to know how big a chicken farm would need to be to produce enough raw chicken to cook.
The minecraft wiki pages on the chicken and the egg both state, that a chicken lays an egg every 5 to 10 minutes. This claim is unsourced. I would like to trust this, but I wanted to know it exactly.
If we assume a symmetrical distribution we would expect an average of 0.13333 eggs/minute or 1 egg every 7.5 minutes for every chicken.
Over the course of one hour we can determine the probability for a number of eggs laid using the binomial distribution. Every minute a chicken either lays an egg, or doesn't. (This isn't perfect for multiple reasons, but it's good enough for now.)
https://imgur.com/a/gMF5G6X
In this example we would wait 1 hour and count all eggs laid in that time frame. On the x axis is the number of eggs, on the y axis is the probability for this exact number of eggs laid. If the chickens produced an egg every 5 to 10 minutes they would lay 6 to 12 eggs. This area is marked red on the graph. We can see, that the maximum probability is expected at 8 eggs, which is the expected value for this distribution.
Armed with this knowledge we can resume with the experiment. Each chicken is to be placed in an isolated pod.
https://imgur.com/Ytxr30D
Each chickens is standing on a hopper. These pods are then assembled so that the hoppers all funnel into a storage area.
https://imgur.com/idadxxY
https://imgur.com/7AarT6j
I assembled a total of 400 chickens. Since all chickens operate independently from each other we can treat this as if we had waited 400 times the actual amount. I then positioned the player in the middle of this farm and went for a shower. After 18:50 minutes (7533 chicken-minutes) I disconnected the chest and counted a total of 992 Eggs.
https://imgur.com/T3rgSiA
Please note that at this point the numbers get so large that they break the python float specifications, so I am approximating using the normal distribution.
With sample sizes this large we can easily see, why the specification of 5-10 minutes becomes completely useless. If all chickens laid their eggs every 10 minutes we'd get 753 Eggs, at every 5 minutes 1507 eggs. This is larger then the entire section of the graph I am showing.
The result of 992 eggs is well within the expected window. You can see that the result is close to the expected value, but to judge just how likely this result is, we can calculate, how likely it is to get less:
P(X<992) = 33.463%
This is a very likely result and thus it is safe to assume that a probability of 13.333% for a chicken to lay an egg in any given minute is accurate.
Imgur Link: imgur.com/a/gMF5G6X
The minecraft wiki pages on the chicken and the egg both state, that a chicken lays an egg every 5 to 10 minutes. This claim is unsourced. I would like to trust this, but I wanted to know it exactly.
If we assume a symmetrical distribution we would expect an average of 0.13333 eggs/minute or 1 egg every 7.5 minutes for every chicken.
Over the course of one hour we can determine the probability for a number of eggs laid using the binomial distribution. Every minute a chicken either lays an egg, or doesn't. (This isn't perfect for multiple reasons, but it's good enough for now.)
https://imgur.com/a/gMF5G6X
In this example we would wait 1 hour and count all eggs laid in that time frame. On the x axis is the number of eggs, on the y axis is the probability for this exact number of eggs laid. If the chickens produced an egg every 5 to 10 minutes they would lay 6 to 12 eggs. This area is marked red on the graph. We can see, that the maximum probability is expected at 8 eggs, which is the expected value for this distribution.
Armed with this knowledge we can resume with the experiment. Each chicken is to be placed in an isolated pod.
https://imgur.com/Ytxr30D
Each chickens is standing on a hopper. These pods are then assembled so that the hoppers all funnel into a storage area.
https://imgur.com/idadxxY
https://imgur.com/7AarT6j
I assembled a total of 400 chickens. Since all chickens operate independently from each other we can treat this as if we had waited 400 times the actual amount. I then positioned the player in the middle of this farm and went for a shower. After 18:50 minutes (7533 chicken-minutes) I disconnected the chest and counted a total of 992 Eggs.
https://imgur.com/T3rgSiA
Please note that at this point the numbers get so large that they break the python float specifications, so I am approximating using the normal distribution.
With sample sizes this large we can easily see, why the specification of 5-10 minutes becomes completely useless. If all chickens laid their eggs every 10 minutes we'd get 753 Eggs, at every 5 minutes 1507 eggs. This is larger then the entire section of the graph I am showing.
The result of 992 eggs is well within the expected window. You can see that the result is close to the expected value, but to judge just how likely this result is, we can calculate, how likely it is to get less:
P(X<992) = 33.463%
This is a very likely result and thus it is safe to assume that a probability of 13.333% for a chicken to lay an egg in any given minute is accurate.
Imgur Link: imgur.com/a/gMF5G6X
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