XY Pokémon Probability Math Help Needed!

Sheriff_K

Sheriff_K

Eevee Breeder
Member
I'm not that learnéd in the ways of probability/statistics, calculus is more my cup of tea, so I ask for help from any who is knowledgeable in these matters.

I have 2 inquiries, the first of which is related to the odds of getting X amount of max IVs from a Safari Ditto.
From what I reckon the odds should be something like this, but I may be gravely mistaken, so please correct me if I am:

3 IV Ditto: 1/8
4 IV Ditto: 1/341
5 IV Ditto: 1/16,384
6 IV Ditto: 1/1,048,576

And my other question, is if anyone knows a formula I could use to calculate the probability of getting X number of IVs from Parents with Y and Z IVs when one Holds a Destiny Knot. Most specifically, the odds of getting a 5 IV Baby from Parents with 4 and 5 IVs (none of their IVs are unwanted.)

From what I've heard and understand, the way Destiny Knot works is that it rolls 5 Stats out of the pool of 12, if the same Stat is chosen from both Parents, the highest is chosen, if both are maxed (31), then that is chosen and another Stat is rolled instead. (Though I've heard from some people that it isn't rerolled, so I don't really know who to believe...)

Any input, criticism, or brainstorming is appreciated. Thanks ^.^
 
RE: Pokemon Probability Math Help Needed!

For calculating the odds of ditto IV catches in friend safari you'd do this:

nIVS as 31 = 1 / (32 ^ (n-2) ) . Each IV there is a 1/32 chance of it being 31 since numbers are chosen from 0-31 inclusively. The 2 comes from 2 IVs automatically being perfect. If you want to dive even deeper, the odds of having stat x be a 31 IV it'd look like this:

stat as 31 = ( 2 / 6 ) + ( ( 1 / 32 ) * 4 ) .

There is a 2 out of 6 chance the value will be one of the two values that are guaranteed a 31. There are four remaining stats so the 4 comes from that. 1 out of 32 comes from each IV having a 1 in 32 chance of being perfect.

The breeding part I'm not as sure about.
 
RE: Pokemon Probability Math Help Needed!

That's what I originally thought Arceus, but then I realized that each Stat can roll for 31, so you'd have 4 chances at rolling a 31 to get a 3 IV. So I was thinking something along the lines of:

nIVs@31 = (1/32^(n-2))*(6-n+1)

Which got me my odds in the first post.
 
RE: Pokemon Probability Math Help Needed!

Here's an easy way of thinking about it, keeping algebra to a minimum.

Let A = 1 / 32, B = 31/32 (The chances of a stat being max and non-max, respectively)

For two max IVs (i.e getting no extra 31's from the safari):

Prob = B*B*B*B = 0.88073825836181640625

For three max IVs:

Prob = ABBB + BABB + BBAB + BBBA = 0.113643646240234375

For four max IVs:

Prob = AABB + BAAB + BBAA + ABAB + BABA + ABBA = 0.0054988861083984375

For five max IVs:=

Prob = BAAA + ABAA + AABA + AAAB = 0.000118255615234375 (This is on par with the chances of catching a shiny in the old games)

For six max IVs:

Prob = AAAA = 0.00000095367431640625

Consistency:

These represent all possible scenarios. Add 'em up, and you get a sum total of 1.

I'll mull over the Destiny Knot question, it would be a very useful tool for breeders!
 
RE: Pokemon Probability Math Help Needed!

According to Reddit, the Destiny Knot cannot overlap, such that 2 6 IV Parents always produces a child with no less than 5 IVs, with a 1/6 chance of a Perfect 6/6 child.

And apparently Power Items stack with the Destiny Knot, having a 1/6 chance of overwriting the random Stat not chosen by the Destiny Knot, increasing your chances of getting a Perfect 6/6 child from 1/32 to 1/6. Though do keep in mind getting the correct Nature AND a Perfect 6/6 without an Everstone would then be 1/150.. But it does have its uses, if you want multiple Natured 5s of a single Poke (Eeveelutions), or just want to have a 5-6 IV Parent for Breeding first.

@Bacon,
Fairly similar to what I had, I guess the deviation is because I didn't take into consideration the other 31 possibilities?
Ah, the discrepancy on the 5 IV is due to the lack of permutations. :)
 
RE: Pokemon Probability Math Help Needed!

It's just the way these things work out really!

Like flipping a coin, trying to get N number of heads in a row. If I increase N linearly (1, 2, 3...) probability doesn't increase linearly too, but via a power law (1/2^N). : )

Are you approximating in your answers though? I don't think you can reduce the numerator down to 1.

For example, 3 max IVs:

ABBB + BABB + BBAB + BBBA = 4*ABBB = 4 * (1 * 31 * 31 * 31) / (32 * 32 * 32 * 32) = 29791 / 262144
 
RE: Pokemon Probability Math Help Needed!

All I was doing for the odds was: 1/x
Though the probability of actually getting it in that many tries isn't 100%.

This little formula is for calculating the likelihood of success as your attempts increase: 1-(1-p)^n
(Where p is the probability, in n number of events.)
 
RE: Pokemon Probability Math Help Needed!

I'm currently brainstorming an xls file that allows the user to input some parental parameters and then calculates the odds of the baby having a given set of stats. : )
 
RE: Pokemon Probability Math Help Needed!

I've pretty much got a grasp on the odds involved in Breeding with Destiny Knot now.

One of the odd things though, is that 2 4 IV Parents with the SAME IVs and a 4 IV Parent + a 1 IV Parent with a DIFFERENT IV, have the same exact odds of producing a 5 IV Child... o_0

I've bred probably 500 or so Eevees over the last 3 days (30hours+), but my Eeveelution team is finally complete! AND I got a nearly Flawless Shiny Eevee... :3
 
You must log in or register to reply here.
Back
Top