How long would it take to get a Synchronise Abra of every nature?

Question

I know that you can use the ability Synchronize to get the nature you want for each Pokemon with 50%, if I were to get say 25 different 'abra' with different nature's, would it take long to catch each Pokémen with the right nature and is it worth it?

Comments

One thing is you can do is count out the natures with no effect, since you’ll never intentionally be using them on a set.
I have attempted this before but stopped after getting Adamant, Jolly, Timid and Modest since I use those the most. Main recommendation is Quick Ball.

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Which game are you asking about?

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This isn't a full answer, but I recommend breeding. If you have a Talonflame in your party, eggs will hatch rather quickly. You could also do wild enocunters, but it is not guaranteed you find Abra in the wild, there are other Pokémon that can appear instead.

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double out = 0;
       
for(int i = 25; i > 0; i --) {
    out += 25.0 / i;
}
       
System.out.print(out);
According to that piece of code, you would need to encounter, on average, 95.398954443837684 synchronize Abras to find one of each nature. How long that takes depends on what game you're playing.

Answer 1

Unless you have a bunch of BP for Ability Capsules, you'll probably want to have a low-level Pokemon with Fake Out to assist in this hunt. Low enough level that it doesn't OHKO the Abras, at least. If you're not SOS chaining, Abra can either have Synchronize or Inner Focus, and the nice thing about Inner Focus is it will immediately tell you "you don't want this one" by not flinching on your Fake Out and teleporting away. If it does flinch, then you know it's Synchronize and you can throw a ball. You already used up turn 1 on Fake Out, so Quick Ball isn't in play, but Nest Ball should give you a 100% catch rate against a partially damaged Abra. If the Abra manages to call for help on turn 1, Teleport will at least fail as long as there are two Pokemon on the field, so what you want to do in that case is use Toxic on the second one so you don't risk giving the first Abra an opportunity to successfully teleport, then throw a ball the turn after it faints from poison damage.

Beyond that, the quest for "getting every nature" is an instance of something called the coupon collector's problem; the existing literature provides methods to estimate how many duplicate natures you'll have to put up with before achieving your goal.

Comments

imo, breeding Elgem in S/M/US/UM specifically is better than catching/breeding Abra; They can only have Synchronize (unless you have HA), and hatch relatively quickly (in about a minute) with the Roto Hatch Boost and a Flame Body Pokemon (Magby). I already have Elgem of all natures, and I wonder traded the repeated natures.

Answer 2

The thing about Synchronize Abras is that it isn't like you never get repeats, making it a bit more difficult to calculate then people might think. Here's my thought process:

1.) So first of all, there's a 50% chance the Abra you find will have Inner Focus
2.) You can get repeats
3.) In route 2, on the southern area, the chance of finding an Abra is unknown at the moment (we will solve for it later)

Now that we know all this, let's take this one step at a time and solve for 1, which is really easy. The answer is 50%, or 1/2. Number 2 isn't really a problem, so we can just go straight to 3. So in order to find the exact encounter rate of an Abra, we need to find it's "encounter rate" (50%), which isn't Abra's REAL encounter rate, just the chances of finding an Abra if the only Pokemon you could find is an Abra and a Dratini or something. See, percentages are all parts of a whole, so obviously is there's 6 Pokemon with a 50% encounter rate, something's wrong. So, we can sort this out comparatively by using these pieces of information:

• Smeargle has a 2/4 encounter rate
• Drowzee has a 2/4 encounter rate
• Abra has a 2/4 encounter rate
• Meowth-Alola has a 3/4 encounter rate
• Yungoos/Ratatta-Alola has a 2/4 encounter rate (you can find them on different times of day, making it impossible to find both at the same time, so they count as one Pokemon.)

I put their encounter rates as fractions to make it easier to calculate and decrease my chances of making a mistake. From this we can tell that Abra has 1/5.5 chance of being found. (About 15%)

1/5.5 to the power of 25 = 0.00003960212

Then, we cut this number in half because the Abras found may have Inner Focus, which would be 0.00001980106

So there's a 0.00001980106 chance that you will find 25 Synchronize Abras of different natures consecutively.

Assuming it takes you 20 seconds to find a new encounter, we can use the equation 20 x 1980106, because 190106 is statically the number of times you need to find 25 synchronize Abras of different natures.

1980106 x 20 = 39602120 seconds

39602120 divided by 60 = 660035 minutes and 20 seconds (660035.33333333333...)

660035.3333333333333... divided by 60 = 11000.5888833 hours. (About 11,000 hours and 45 minutes)

CONCLUSIONS: So, the chances of you finding 25 synchronize abras in a row, all with different natures = 0.00001980106. In other words, you need to find 1,980,106 Pokemon in order to find 25 synchronize abras of different natures.

The amount of time needed (about) is 11,000 hours and 45 minutes

You might as well SR for a shiny groudon in OR/AS than look for this, and Groudon is shiny locked lmao

Comments

This is not how math works. In particular, you do not need to find all 25 Abras consecutively (such that a non-Abra encounter or one with a duplicate nature would force you to start over), and even if you did, handling Inner Focus would require dividing by 2^25, not just 2 (since it can apply to each encounter separately). You can build up a growing series of workable natures over time, regardless of what intervening encounters may come in between.

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actually, 1/5.5^25 is  3.09693979e-19

look it up on Google

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Good mathz, but there is NO WAY it takes 11,000 hours to find 25 different natured Syncronise Abras. 11000 hours is 458 days. That would be over a year of playing time.

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That is not math, i know math. looks like someone has the probability failure sickness. You can't multiply probability by number of events, time, etc, because it is random :P

Also, your time math made no sense, as did your finding abra's encounter rate was shady...

Hope I didn't offend you, just saying your math doesn't make sense. :/

Answer 3

It really depends on the parent(s) held items, if the mother holds a destiny knot, its guaranteed to have the nature of the parent. You could also buy a bunch of quick balls to catch and pray. I personally just breed 2 Alakazams because Synchronize isn't that hard to get (correct me if I'm wrong)

Comments

I won’t downvote but this adds nothing to SadisticMystic’s answer, or mine, but apparently my answer is literally factually incorrect, so I might hide it later anyways.