l wasn't able to find exact numbers on the increase of Shiny rate the DexNav increases with each chain, so these calculations will be based on [this test l found on Reddit though][1], having a higher chain or higher search level doesn't increase the rate of encountering shiny Pokemon.

The chance of encountering a Shiny Pokemon with DexNav according to the document l found (with an average of **308.3333333 search level** and **95.23188406** chain level) is within the range of 1/308 and 1/512. (this was the only data l could find about this rate)

The probability of encountering a Pokemon with all max IVs naturally is 1/32^(6) or 1/1073741824 however the DexNav is able to leave you to encounter Pokemon with the Potential rating system up to 3 stars (or 3 perfect IVs). l wasn't able to find the rate of getting 0, 1, 2, or 3 stars, but l'm going to base the calculation on the positive side of the spectrum.

Basing this variable on the assumption that this Pokemon will always have 3 stars, will have a rate of getting a Pokemon with all max IVs is 1/32^(6-3) or 1/32768.

The rate of getting a Pokemon with a Hidden Ability according to an observation by Bulbapedia is 23%(23/100) with a search level of 100, and 5%(5/100) with a search level of 10.

Taking this mess of junk and numbers:

The rate of getting a Shiny Pokemon with all Max IVs and Hidden Ability

(with 0 stars of Potential, and Lv 10 search level and using the minimum probability of getting Shiny based on the test 1/512)

1/512 * 1/1073741824 * 5/100(1/20) = **1/10995116000000**

or **9.0949472e-14%** (lol or **0.000000000000090949472%**)

The rate of getting a Shiny Pokemon with all Max IVs and Hidden Ability

(with 3 stars of Potential, and Lv 100 search level, and using the maximum probability of getting Shiny based on the test 1/308)

1/308 * 1/32768 * 23/100 = **23/1009254400**

or **2.27891005e-8%** (**0.00000002.27891005%**)

### The rate of getting a Shiny Pokemon with all Max IVs and Hidden Ability is within 1/10995116000000 and 23/1009254400

*The rate of Hidden Abilities taken from Bulbapedia are not exact values, but based on observation.*

The rate of Shiny rate of the DexNav was based on a research conducted by /u/Galactiiiic and others on Reddit are not exact values, but based on their test.

*All the variables factored in are without the use of Shiny Charm.

Sources:

http://bulbapedia.bulbagarden.net/wiki/Shiny_Pokémon#Generation_VI

http://bulbapedia.bulbagarden.net/wiki/DexNav

Shiny Encounter data provided by/u/Galactiiiic of Reddit.

https://docs.google.com/spreadsheets/d/1wIMVoliCKs4HkDvpgFkPfP5HKxZb0De3cFQidBoYB1c/edit#gid=0

https://docs.google.com/document/d/1e4y6TW21TcUSG_Qe2sKzXoMgkwttLlclzV94_DBpUgU/edit

[1]: https://docs.google.com/document/d/1e4y6TW21TcUSG_Qe2sKzXoMgkwttLlclzV94_DBpUgU/edit

Edit: Fixed 5 IVs to 6 IVs