Victini Maths Question

[baby mario]

OK, this is a lot more complicated than it seemed. Some people on here are good at maths so I thought I'd see if they could help.

(Translations by PokeBeach)

Suppose I play this Victini and use V-Blast

Victini – Psychic – HP60
Basic Pokemon

[P] V-Blast: 120 damage. Flip 2 coins, if even 1 is tails, this attack fails.

Weakness: Psychic (x2)
Resistance: none
Retreat: 1

I think that my odds of getting 2 heads are 1 in 4. Correct?

Now, supposing I fail, but have this Victini on the Bench to help me out

Victini – Fire – HP60
Basic Pokemon

Ability: Victory Star
You can use this when one of your Pokemon flips coins as part of its attack. Ignore all results of those coin flips and reflip from the beginning. You can only use Victory Star 1 time during your turn, even if you have multiple Victini in play.

[R][C] Assist Power: 30 damage. Move all Energy attached to this Pokemon to 1 of your Benched Pokemon.

Weakness: Water (x2)
Resistance: none
Retreat: 1

I now get to re-flip the coins and try again.

So, my question is: what are the combined odds of me hitting the two heads over the two separate events?

In other words, how much does having Victory Star Victini out increase my chances of a successful V-Blast? Or to put it in yet another way, is the second Victini worth playing?

Again, I know the maths is a lot harder than it looks, so I'd really appreciate the help.

[nnaann]

Since you get two attempts at it, both which have 1/4 odds of hitting 2 heads, you just need to double your odds - 1/4 + 1/4 = 1/2. It's definitely worth playing the Basic Victini, but it's still not completely reliable.

[Pajamas]

Originally Posted by nnaann

Since you get two attempts at it, both which have 1/4 odds of hitting 2 heads, you just need to double your odds - 1/4 + 1/4 = 1/2. It's definitely worth playing the Basic Victini, but it's still not completely reliable.

That's not how conditional probability works.

Imagine that you could use multiple Victory Stars per turn. If you had three out, would you have a 1/4+1/4+1/4+1/4 = 1 chance of hitting double heads? Of course not. There's always a chance that you'll never flip two heads in a row, even if you flip 1000 coins.

Now, for the real answer. You have a 1/4 chance of hitting double heads on your first try. Thus, you have a 3/4 chance of having to use Victory Star and try again. 1/4 of the time when you try again you'll hit double heads, so the overall odds are 1/4 + (3/4 * 1/4) = 7/16, or 43.75%.

[baby mario]

I knew it wasn't as straightforward as it looked (50%).

Thanks for the helpful explanation.

[Pajamas]

Incidentally, if you were allowed to use three Victory Stars, your odds only improve to about 68.4%. The law of diminishing returns is a nasty one. Wikipedia has a much more formal explanation of how to do this kind of stuff: http://en.wikipedia.org/wiki/Binomial_distribution

[nnaann]

Originally Posted by Pajamas

That's not how conditional probability works.

Imagine that you could use multiple Victory Stars per turn. If you had three out, would you have a 1/4+1/4+1/4+1/4 = 1 chance of hitting double heads? Of course not. There's always a chance that you'll never flip two heads in a row, even if you flip 1000 coins.

Now, for the real answer. You have a 1/4 chance of hitting double heads on your first try. Thus, you have a 3/4 chance of having to use Victory Star and try again. 1/4 of the time when you try again you'll hit double heads, so the overall odds are 1/4 + (3/4 * 1/4) = 7/16, or 43.75%.

Completely forgot about conditional probability, good explanation.

[dogma]

...or you can just draw a probability tree diagram. I'm guessing thats easier for people who haven't really done any probability before :)

[Nintendan]

Originally Posted by dogma

...or you can just draw a probability tree diagram. I'm guessing thats easier for people who haven't really done any probability before :)

Yeah. These help me a lot. :D Tree Diagrams ftw!

[eriknance]

Ability Victini... so good...

[NoPoke]

Originally Posted by eriknance

Ability Victini... so good...

Agrees. It is far too good and if there weren't already enough reasons why Gust-of-wind will be everywhere the Victini would be reason enough on its own.

There have to be bad cards in order for there to be good cards. But just why do we have to have awesome cards?

[eriknance]

Originally Posted by NoPoke

Agrees. It is far too good and if there weren't already enough reasons why Gust-of-wind will be everywhere the Victini would be reason enough on its own.

There have to be bad cards in order for there to be good cards. But just why do we have to have awesome cards?

Well, the thing I like about Ability Victini is that it pulls up the usefulness of soo many "bad" cards. Cards like TR Sharpedo, TR Magmortar, UL Politoed, etc. instantly get a second look. Think about all those otherwise worthless rares that now look pretty good (even anything with an Agility-like attack starts looking decent, haha).

As for Pokemon Catcher, I think it should be released (to make sure we're in line with what Japan's doing), but I really, really don't want it to.

[NoPoke]

.mostly I like it with the 50% paralysis attacks or 50% agility. It does make sharpedo more interesting though I'm not sure it makes it playable. Magmortar and Politoed aren't really improved by Victini.

[bullados]

Magmortar kinda has to be improved with Victini. 50% chance of milling for consecutive turns vs 75% of the same. And it fits into the theme of the deck just being a Fire type. Not saying that it'll be a 4-of in the deck. But it'll be a Shuckle-level tech card in a Emboar deck with a coin flipper.

[NoPoke]

milling the opponents deck is nice but at one or two cards per turn it isn't going to be long before the Magmortar is knocked out. To make the mill effective it has to be combined with some kind of lock or with massive energy recovery from the discard and multiple attach each turn. Even then decking the opponent has to be the hardest way to win in a format where games will probably last fewer than 15 turns each.

[bullados]

Originally Posted by NoPoke

milling the opponents deck is nice but at one or two cards per turn it isn't going to be long before the Magmortar is knocked out. To make the mill effective it has to be combined with some kind of lock or with massive energy recovery from the discard and multiple attach each turn. Even then decking the opponent has to be the hardest way to win in a format where games will probably last fewer than 15 turns each.

What are you talking about? 10-12 card mills every single turn! The only problem with Magmortar is that it isn't known whether those 10-12 energy will stick around for the next turn. So, we hedge the bets.

[dark wobbuffet]

flippy stuff suddenly seems like an advantage. If only you could still use dusclops from sandstorm...

[bullados]

EX: Deoxys.

You're welcome.

[bullados]

Platinum: Arceus

[Nintendan]

This suddenly opens a door to many decks with potential that just didn't see the light of day due to their flips. This might make the format a bit more red face powder-y.

[Yoshi-]

For stuff like this drawing a tree really helps and is pretty easy. This is how I learned it back when I was calculating odds of YGO opening hands :D

[Regis_Neo]

I must admit, I'm still not sold on Victini; there's still the fact that it deals both with flips and inconsistency. In the end of the day, decks that work consistently instead of relying on flip effects will take the format imo. Sure, this opens up the door for more fun ideas and I like fun ideas, but from a competitive perspective, that doesn't always translate into winning.