What are the chances of breeding a type of dragon?

Solution 1:

Rare dragons are certainly less likely to be bred when they're an option. It's all a matter of chance, though there's been some unproven theories that the dragon you put on the left side of the breeding menu determines the order of elements of the egg. It doesn't seem to hold true.

Generally assume the breed will yield a random possible combination, and note that rare dragons are very rare, I'd say maybe less than a 10% chance. I don't think there's any formal numbers. From experience only Rare dragons have a different breeding chance, everything else, assume an even chance of all other possible results. If there is a difference, it's not large enough to fuss over.

Special Event dragons also tend to be "Rare" at approximately the same rate as the Sun/Moon/Rainbow dragons. Generally you'll want to stop everything and start trying to breed time-limited dragons immediately until you get one, or two if you want a breeding pair.

Note the Epic Breeding Island advertises that you have a higher chance of rares. It doesn't seem extremely significant; rare dragons are still rare on the breeding island. In fact I haven't noticed a perceptible difference, but if you're trying to breed for rares you might as well try the island first.

Also note that breeding two dragons always gives you that same dragon (best I can tell), so breeding two Rare Rainbow dragons has a 100% chance of giving a rainbow dragon.

Solution 2:

There is a chance for breeding any dragon that fits the combanation, just as flipping a coin can get you heads or tails. For the coin, 50/50, that doesn't mean out of 50 times you'll get an even amount of heads and tails. The same is with breeding the dragons, you don't really know what you're going to get in the end. If you're really lucky you'll get rare ones on every breed, if you're not getting anything good at all then bad luck. Then according to mathematics if you get normal most of the time and rare occasionally, you're on the right track. Think of Punnett squares.