#### Analyzing the chance of Wally fainting the Ralts in Generation III

Posted by: Torchickens

Date: 2016-06-13 16:07:10

In the Generation III games, it is possible for the capture tutorial to end with Ralts fainting. This can only happen if Zigzagoon is generated with 11 Attack, and the wild Ralts has a Nature that lowers Defense, an IV of 3 or less in HP, and 5 or less in Defense. With all this, Zigzagoon can do a maximum of 10 damage with its first Tackle, and after Growl is used on it, 7 with its second. This makes for a total of 17 damage, just enough to knock out Ralts. However, the game continues on as if it had been caught. The probability of this occurring is (182/800)*(4/25)*(4/32)*(6/32)*(5/16)*(7/16), or about 1 in 8574.

A video of Wally fainting the Ralts can be found here:

[youtube]https://www.youtube.com/watch?v=xERTYBk3Txk[/youtube]

Somebody asked me a good question and wondered where the probabilities came from, so I took a guess at working that out.

Hi. I looked into this for you but I don't know the full answer sadly. That's OK, your English is good.

Bulbapedia says the Zigzagoon must be made with 11 Attack, Ralts must have a nature that lowers Defense, an IV of 3 or less in HP, and 5 or less in Defense and the probabilities are (182/800)*(4/25)*(4/32)*(6/32)*(5/16)*(7/16), or about 1 in 8574.

When we work out the probabilities of multiple events occurring, we use multiplication.

The first event 182/800, I'm unsure why this might be.

The second event is 4/25 because there are four natures that lower Defense, Lonely, Hasty, Mild and Gentle.

The third event is 4/32 because every IV including HP takes up four bits (2^4=32). It might be 4/32 and not 3/32 because 0 is a possible Defense IV.

The fourth event is 6/32 for the same reason (there are six possible Defense IVs that will work; 0, 1, 2, 3, 4 and 5.

I'm unsure why the fifth event is 5/16 and the last event is 7/16.

I don't know if this is a valid approach. However, there are 14/32 (which can be simplified as 7/16) possibilities for exactly 11 Attack for a Zigzagoon at a +Attack nature, plus 6/32 possibilities for 12 Attack at a +Attack nature. There are also 6/32 possibilities for a neutral Attack nature Zigzagoon to have 11 Attack (it cannot have 12).

For Zigzagoon to have an Attack of 11 or 12 at level 7, it must have an Attack IV of at least 12 at a +Attack nature, or at least 26 at a nature which doesn't boost Attack. The chances of this might be ((4/25) [positive Attack nature amount]+(17/25) [all neutral Attack natures]))*((20/32) [the total of positive nature IV possibilities for 11+ Attack])+ (6/32) [the total of neutral nature IV possibilities for 11+ Attack] = 0.6825 (273/400).

(4/25)*(4/32)*(6/32)*(273/400)=0.16*0.125*0.1875*0.6825=0.002559375. This is actually 1 in 390.72 (we can round this up to 391), so there is the possibility that Wally fainting the Ralts is more likely than previously thought, but my math may be incorrect.

I worked out the number of viable IVs for a level 7 Zigzagoon with 11 and 12 Attack using the save file editor "A-Save". It's likely that I made an error because I don't consider myself to be very good at maths. However, there could also be an error with A-Save, or my logic, or my calculation method.

Edit: I didn't consider that the damage Ralts takes in battle might vary, even when both Pokémon have the same stats.