Guide Accurate Horses

Why I did this

For anyone who can't be bothered to read just look at the bottom and the averages will be listed...
So recently I've been looking at horse percentages trying to work out whether I should buy or bread to get the horse I want , but when ever I look its people using the known percentages (20% Up 30% Down and 50% same) but they have been using 100 or maybe 1000 horses to work it out, although that's pretty accurate its not enough for me and some others , so I've spent the last few hours working it out with 1,000,000, I haven't done white yet because that will take a few hours and my brain is now mush.

The stats!
*just a disclaimer this is with very aggressive breading.

Currently per 1,000,000 brown horses (500,000 breeding operations) horses you should get 166,667 black horses, which is about 1/6 of the starting horses so a 1/3 chance per breeding operation. ( don't forget you can reuse failed horses which is why its above 1/5 and their is no way for it to go down so it stays the same)

Once you have the 166,667 Black horses you can breed for chestnut , you can now go down a horse back to brown the chances will be slightly lower. They come in at 23,900, which is about 1/7 of the starting black horses , which is about 2/7 chance from the 83,333 (since you cant have half a horse).
This means that out of the starting 1,000,000 horses 2.239% will become chestnut which is 4.78% per breeding operation.

So next time you're buying or breeding remember.
1/6 of your total brown horses will become black (1/5.99998) 16.6666666... %

1/7 of your black ones will become chestnut (1/6.973514644) 14.2857.... %

which is 1/42 of your original brown ones ! 2.380952.... %

on average a black horse will cost 144eb (2.25le)

on average a chestnut horse will cost 1008eb (15.75le)

Haven't done white yet.

Algebra !

Brown to Black

Spoiler: The Algebra

X= number of horses owned
Bl = Black horses

an amount bl = X/5
((X*24)-((X - X/5)/2)*24)/(x/10)=144 (average cost for a black horse)

You times X by 24 to convert the answer from terms of X to eb.
You divide XR (the amount of brown horses you have) By 5 to give you how many black horses you will get from that amount since its well known you have a 20% chance to lvl up a horse from breading.
And you divide the final amount by x/10 to make sure that all results are relative.

If you do it correctly no matter what number you use as X you should always get 144 as your answer which means that is the average cost from brown to black by breeding.

Black to Chestnut

Spoiler: More Algebra

X=Number of Black horses owned

Now we have to factor in horses going down a level so the equation consists of one more small equation.

((X*144)-((X/4)*24)+((X*0.15)*24))/(X/10)= 1044
No matter how many horses (X) you will always get 1044 as the average, because it is.

 

Nice, but seems late.
@Yuno F Gasai
https://forums.wynncraft.com/threads/horses-breeding-prices.90224/

 

we were messaging before I made this :)

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Just fixed percentages

 

So you calculated the outcome of breeding a million horses again and again?

@Kepler_17c @Szei @YuuuuSama

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I always like to see new approaches to the math here (and to see if someone can prove me wrong)

 

Is the first message directed at me ?

 

Yup, I just tagged others that calculated horse prices

 

no , I started imagining I bought 1,000,000 horses and did the math to see how far it would get me , so I could calculate percentages and fractions behind it. I only used a million to get a good degree of accuracy.

 

As this stuff gets further and further added up it makes me think people should just get walk speed gear and call it good. (Good thing i got my chestnut horse before they changed the breeding system 2LE Chestnut ftw)

 

They never changed the breeding system

 

Really? I definitely remember ridding around on horses for a long time until I got them max, e.g brown 10/10 then breeding them and my odds were way higher than 20%, got chestnut on first try with two 20/20 black horses.

If it was changed or not I got a Chestnut after only spending a few LE so there's that. This was 2 years ago I believe btw (old profile says I joined 3 years ago so idk)

 

All of this is nice, but you could do also do this with 1 000 000 000 or 1 000 000 000 000, or even 10^100 horses, and it still would never be as accurate as just using algebra to determine the same thing. And the simple algebraic equations are much faster and less time consuming, too.

That said, I like your explanation and I'm amazed at the amount of work you put in to this. This is dedication, Dawg.

 

You just got lucky

That's why my calculations are the correct ones (altho it's nice seeing ithers agree)

 

Agreed , I just though putting it into numbers would please people , has algebra been done ? if not ill happily try it.

 

I've done it with algebra but I'd like to see your version

 

okay, ill add it later.

 

just lost an hour of work on this

 

Rip :(