Tutorials/Horses

Because of the way new horses are created, it becomes increasingly harder to breed better horses as the horses get better.

Breeding difficulty
Horses are created by averaging the parents' stats with a fully random non-existent horse, and all three stats are independent of each other. With that known, it becomes logical that it is impossible to breed the perfect horse from two non-perfect horses. Even if the random horse is perfect, the parents will have to be perfect as well in order to get a perfect average.

For example, if two parents are 5.5-block jumpers (assuming this is the exact maximum), and the random horse is a 5.5 block jumper, the average((5.5+5.5+5.5)/3) will be 5.5, a perfect horse. But, if maybe one of the parents is a 5.49 block jumper, the average will be 5.49666..., even if the random horse was perfect. As a result, it is mathematically impossible to breed two imperfect horses into a perfect horse. Theoretically, 15-heart horses are always natural.

Because the range of horses that are better than a given horse gets narrower as the horse gets better, the likelihood of breeding a horse in that range of better horses also gets linearly narrower as the horse gets better, and as a result, the actual number of breed attempts necessary to likely get a better horse increases hyperbolically, until it reaches impossibility at perfection.

This graph shows what jump strength a player should expect their best horse to have after repeatedly breeding their two best horses together up to 1,000 times. The blue line shows the average jump strength of the best horse and the chances of the horse's jump strength being within the red lines is 95%.



Average Breeding Scheme
Although all stats apply, jumping is most easily measurable (excluding health), so use it for this example. If you started with two 1-block jumping horses, and bred them over and over until you got two horses that are better than them, killed them, and replaced them with the two better horses, this would happen if you got the average better horse every time you got a better horse:

If you started with two 1 block horses, and bred them ~2.4 times, you would roll a random horse between 1 and 5.5 twice. Assume that you happened to get a 3.25 random roll, halfway in between this range of betterness, twice, you would get two 1.75 block jumpers to replace the 1 block jumpers.

If you breed them ~2.93 times (now at a total of ~5.33 "breeds"), and got a half-way roll (median in a sense) roll, you now have two 2.375 jumpers.

If you breed those ~3.52 times (now at a total of ~8.85 breeds), and ..., you would have two ~2.89 block jumpers.

... ~4.224 times (... ~13 breeds), ..., ... two ~3.32 block jumpers.

... ~5.068 times (... ~18.14 breeds), ..., ... two ~3.69 block jumpers.

... ~6.082 times (... ~24 breeds), ..., ... two ~3.99 block jumpers.

... ~7.299 times (... ~31.52 breeds), ..., ... two ~4.2441 block jumpers. You have now made a 4 block jumper in around 32 horse "breeds".

87 more breed attempts later....

... ~21.794 times (... ~118.54 breeds), ..., ... two ~5.079 block jumpers. You have now made a 5 block jumper.

1427941 more breed attempts later...

Okay now breed your two 5.49995 block jumping horses 238011 times, for a grand total of 1428059 breed attempts, and you now have two 5.49996 block jumper.

64270535 more breed attempts later (~611 nonstop years of your real life)...

Breed those 10949770 times to get.................. and you have transformed the two 5.49998 block jumpers into two 5.49999 block jumpers!!