Poke Probability-"whats luck got to do with it?*"

[Nizolka33]

So I know for a fact we have some very smart people on these forums. I want to make a forum in which people can ask questions about probability relating to the game.
I'll go first:
-If I run 4 of a card, what's the probability of drawing it in my starting hand (7 cards) out of my 60 card deck?
-^this, but with 3 copies of the card?
So yeah, if you want to know attack probability (like Strip Bare with Flipitini) or just drawing probability like the above, you can ask here.
Please help with these questions if you can as well.
*Mods, please move this if you have to.

 

[Zero]

Or you can just look up probabilities yourself. Fliptini's success rate is p + p(1-p) when p is the probability of the innitial success (.5 in the case of heads tails or .25 in the case of two heads no tails). As far as drawing cards go, I'd highly recommend you all look up nPr and nCr. The proofs and mathematics would be too painful to look it up here. I may release a little java program I made a while ago to help people with their draw calculations.

 

[Glace]

-If I run 4 of a card, what's the probability of drawing it in my starting hand (7 cards) out of my 60 card deck?
-^this, but with 3 copies of the card?

4 copys.

One out of 15 cards is that card, so there is a 466666667% chance of starting with it.

3 copys

One out of 20 cards, 35% chance.

 

[Jalorda]

3 copys

One out of 20 cards, 35% chance.

Not quite how it works. In order to calculate the probability that you'll draw at least one of those cards, you need to have the probability that you'll be drawing exclusively from the remaining 57 cards, and then subtract that from one.

To get that, you get C(57,7) / C(60,7) (where C(a,b) is the combination function, the nCr thing that Zero was talking about) which is about 68.5%.

Then, the probability of drawing at least one of those cards is about 32.5%.

4 copys.

One out of 15 cards is that card, so there is a 466666667% chance of starting with it.

Sure you didn't miss a decimal point somewhere? Anyway, the process is similar to above, and you need 1 - C(56,7) / C(60,7), which is about 39.95%.

You see why your formula is incorrect, right? Suppose you had 9 copies of a card (I know that's illegal, but suppose it's energy). Then, by your calculations, the probability that that card is drawn in your hand is 105%, which is obviously wrong. (the actual probability is more like 70.02%.)

 

[Celebi23]

Here's a tough one:

If I have 4 Pokemon Collector, 3 Pokegear 3.0 and 4 Junk Arm in my deck, what's the probability I hit a Collector T1 provided I use any Junk Arm I have for a Pokegear if the first one misses.

I could probably figure it out myself, but with prizes and Pokegear it's so complicated that I don't want to put the time in.

 

[Jalorda]

What is a collector T1? D:

 

[Futa]

Getting a Pokemon Collector on the first turn (or playing one, should I say).

 

[Nizolka33]

Zero, sure, we could all look it up ourselves, but I think it would prove to be a good, profitable disscusion topic.
What about drawing at least 1 card in your starting hand with 11 copies?