What a clever idea! -- but I do think you have a few mistakes in your doubling for weakness.

I'll confess, I didn't realize you could item find for the MIsty's -- I thought they stayed in play until after the attack, but I just reread the card and I see your point! It doesn't say discard after the attack, as plus powers do. But it does say the 20 is applied AFTER weakness and resistance (I believe the printed rules also specify trainer effects on attacks are calculated AFTER weakness/resistance). 

Also, you can't use Nightly Garbage Runs for  Trainer cards -- oh, but I see the combo with Trash Exchange! The N.G.R.s will keep the discard pile from swelling each time -- you really can get an infinite loop! (see below for a way to work it out -- of course it isn't realistic, but the puzzle allowed you to assume your card draws were as lucky as you needed them to be).

>But since I want
>to submit an answer I will just wrap up The Goldeen would get "heads" when it
>attacks since I am to have 3 "heads" coin flips so damge would be 240 for my
>trainers plus 30 for my attack, 270 times two for weakness to water 480 total
>damage. 

There are two things wrong with this: (1) 480 is 2*240, 2*270 = 540.

(2) Both the plus powers and the effect from Misty are added AFTER applying weakness and resistance -- they are not doubled. So it would only be 30*2 + 240.

Still, I think the general idea could be used quite well -- save the coin flips for Misty's Psyduck as the original proposer's solution had, but use Item Find to get the Mistys played twice each, then Trash Exchange them all back into the deck (Mistys and Item Finders, both!), then use them all twice more,then Trash Exchange to get all 8 (plus the first Trash Exchange, and a professor Oak, etc) back into your deck...[and with one professor oak in your hand to restart the cycle]... Given the magical ability allowed in this problem to have your shuffled deck be just the way you'd like it,  this is an ALMOST infinite loop. The only problem is that your discard pile grows each time you go through the loop and your deck shrinks (aha! THAT'S what you wanted the Nightly Garbage Runs for! So long as the discard pile is at most 12 cards all of whom are garbage-runnable, you can reduce it down to 4.  So the question is, can you find a way to run the entire loop with at most 12 discards (including the NGRs, the trash exchange, etc.)

Here's the loop:

(**) If, after playing your trash exchange, the discard pile contains:

(between 4 and 7) Nightly Garbage Runnable Cards and  (1) trash exchange

and your hand contains (1) Professor Oak, then:

Play your Oak. You magically draw:  1 misty, 1 trash exchange, 4 nightly garbage run, 1 Professor Oak,

Then you play the Misty, the 4 Nightly Garbage Runs (For some of these you will only put one or two cards back in the deck, but you use up all the Nightly-Garbage-Runnable Cards this way).

Now the the discards contain: (1) Trash Exchange (1) Professor Oak, (1) Misty, (4) NIghtly Garbage Runs

And your hand contains: (1) Professor Oak  (1) Trash Exchange.

Playing the Trash Exchange will bring you back to point (**)

 

To get into the loop is even easier,

On the deal you had your Misty's Psyduck (or Misty's Goldeen), plus Water Energy,  Four Plus powers and Professor Oak.

play the pokemon, energy and plus powers, then Oak.

You draw 4 Misty, another Oak,  Trash Exchange  and a Gold Berry and you are on your way. Play the Mistys and the berry, then the trash exchange, and you can go to (**) and begin.

Ted Alper    castma@pacbell.net