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Author Topic: Analyzing the chance of Wally fainting the Ralts in Generation III  (Read 1272 times)

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Evie ✿

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Bulbapedia states:

Quote
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.

Quote
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.
« Last Edit: June 13, 2016, 03:10:53 pm by Torchickens »
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Thank you Aeriixion for the cute sprite above! :) Roelof also made different variations of the sprite (which I animated).

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Háčky

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Re: Analyzing the chance of Wally fainting the Ralts in Generation III
« Reply #1 on: June 13, 2016, 07:41:04 pm »
The 182/800 figure is the probability of Zigzagoon having 11 or 12 Attack. It’s based on the same figures you came up with, but the correct calculation for the probability of Zigzagoon having an Attack-enhancing nature and 12–31 IVs, or an Attack-neutral nature and 26–31 IVs, is (4/25 × 20/32) + (17/25 × 6/32) = 182/800.

The next three figures are the probabilities of Ralts having a Defense-reducing nature, 0–3 HP IVs, and 0–5 Defense IVs. But by my calculations, Ralts can actually have up to 9 Defense IVs and still end up with a Defense stat of 6, so the probability of Ralts being vulnerable to a two-hit KO should be 4/25 × 4/32 × 10/32 = 1/160.

The last two figures are apparently meant to be the probability that the 85%–100% random damage multiplier will be high enough to deal 10 damage on the first attack and 7 on the second. Assuming that Pokémon Showdown’s damage calculator is accurate (is it?), those figures are also wrong: if the damage roll is anything less than 100%, the damage will be rounded down and Zigzagoon will be unable to KO Ralts. The probability of a 100% roll is 1/16, so the probability of two in a row is (1/16)2 = 1/256.

The probability of all these things happening at once would thus be 182/800 × 1/160 × 1/256 = 182/32768000, or about 1 in 180 044.

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Re: Analyzing the chance of Wally fainting the Ralts in Generation III
« Reply #2 on: June 14, 2016, 05:27:21 am »
about 1 in 180044.

and it happened to me once on a real cart...

I think anyway, it's been years.
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Evie ✿

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Re: Analyzing the chance of Wally fainting the Ralts in Generation III
« Reply #3 on: June 14, 2016, 08:04:25 am »
Thanks for the information Háčky!
Hi! I identify as transgender female.  She/her pronouns, please.

Online I most often use the username Torchickens or Chickasaurus.



Thank you Aeriixion for the cute sprite above! :) Roelof also made different variations of the sprite (which I animated).

Contact:

Email Youtube Twitter
Skype: Torchickens
Bulbapedia Starfy Wiki

I like to collect interesting video games.
https://www.vgcollect.com/Torchickens

The psychology of birth (including spiritual birth): pain>acceptance/courage in face of pain>embracement>unconditional love and strength

Beyond all philosophies are the things that go best for you; what makes you feel content. It's important to always follow your heart, so unless you feel perfectly happy about it don't just follow something because it is popular, fits a style or is conventional. Sometimes you may reach a point you're not sure who you are, but as things settle I'm convinced things do work out in time.