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## How to Breed Gretchen

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### Expected Time

The "Expected" is short term of Expected Average Breeding Time. This is the estimate time of a specific combination to get the desired results, after an average fail times. In other words, this time is used for comparing between combinations. The lesser the time is, the faster the combination will give you the right monster. There is also the Breeding Statistic Percent, which is a bar with the percentage. This indicates how fast does it take to breed a X monster between different combinations.

### How do we calculate the "Expected Time"?

First, every combination has specific results with correspond chances. It's not difficult to calculate a Average Fail Breeding Time from the given combination. (Please note that Average Fail Breeding Time is different from Expected Average Breeding Time!).

Average Fail Breeding Time = Sum of all (chance * breeding time of single result), exclude the target monster.

This value indicates that the average time used for each breeding.

Chance of the desired monster: When the combination has X chance for the monster M, you have to breed about (average) 1/X times to get the monster M, statistically! If nothing got wrong, you will have that monster on the 1/X try. Therefore, you will have to "used" (1/X - 1) times for failing, the expected time will be Expected Average Breeding Time = Average Fail Breeding Time * (1/X - 1).

### Example: Firesaur (F) + Treezard (N) versus Firesaur (F) + Greenasaur (F,N)

Firesaur (F) + Treezard (N) gives 30% Pandaken (N,F) and 70% Greenasaur (F,N)

The breeding time of Pandaken and Greenasaur are 30 seconds and 30 seconds.

The AFBT = (0.7 * 30) / (0.7) = 30

The X chance to get Pandaken is 0.3, so the EABT = AFBT * (1 / 0.3 - 1) = 70 seconds

Do the same steps, we got EABT of Firesaur + Greenasaur = 1m 53s.

Now, you will see the first combination gives Pandaken faster (or more efficient) than the second one, in a same period of time. That's what Expected Average Breeding Time is used for.

### Breeding Statistic (Percentage Bar)

This metric is only used for comparing Avg. Time between the combinations. The fastest (least time) combination will be base as 100%. Other combinations if slower (longer time) will be decreased below 100%, depends on how much it is longer.