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Old December 5, 2012, 08:26:22 PM
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Default Egg-stavagent Breeding

Time for something different! We're going to assume "classic" methods of obtaining Pokémon, meaning no Power items, no Everstone, no specialized breeding, no Masuda Method, and no charms.

Odds of getting the right nature (reduced if multiple natures, n, are fine), where C(n) is the count of acceptable natures:
1 in 24 or C(n) in 24

Odds of getting a given stat range, where C(I) represents the count of acceptable IV values:
C(I) in 32

Odds of getting a great stat (75th percentile, or above 23), for each stat:
8 in 32 = 1 in 4

Odds of getting five excellent stats (it's rare to have all six stats matter):
1 in 4^5 = 1 in 1,024

Odds of getting the right ability, where C(a) represents the count of abilities the Pokémon can obtain randomly, excluding hidden abilities; always 1 or 2:
1 in C(a)

Odds of getting the right ability, assuming two different abilities:
1 in 2

Odds of getting a shiny without induction:
1 in 8,192

Odds of getting the right gender:
Varies by Pokémon

Odds of receiving an egg:
Due to the St. Peterburg paradox, it is impossible to determine the amount of time it should take to receive an egg. It can take 255 steps when not induced (due to effects from a previous egg), but if it comes up false every time, it may easily take thousands of steps.

Odds of an egg hatching:
There are no "odds" to this, just the number of cycles (again 255 steps per cycle) when not induced.

===================

So, let's take a typical batch of five of a given starter Pokémon, bred with Ditto, both obtained in the same game:

It will take 21 egg cycles, or 5,355 steps, to hatch one egg. This number reduces by 1 cycle (or 255 steps) every time an egg hatches or is received.

Let's assume an egg is obtained (at 19.8% per cycle) after an "average" of 8 times, as the odds for getting through that many times without an egg (watch out for the Gambler's fallacy if any cycles have already passed!) are about 17.12% (jeez, that's still high). So, let's say every 2,040 steps, you get one egg, but note that subsequent attempts will have one extra cycle run, so let's assume for the sake of simplicity that that adjusts the "odds" such that only 7 cycles + 1 step are required, so 1,786 steps for the first few subsequent eggs.

Every time an egg is received or an egg hatches, the cycle counter reduces.

Check back later to see the calculations!

Last edited by Cat333Pokémon; December 6, 2012 at 07:35:50 PM. Reason: Typo
  #2  
Old December 6, 2012, 04:08:58 AM
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All that calculation mess makes me glad that there are a lot of methods starting from Emerald that allows you to fudge a lot of calculations there, and I especially like how a lot of breeding mechanics are tweaked so that there is now some absolute certainty in the important things in B2W2.
 
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