Help me calculate the odds

Some recent Doctor Strange collectible non-sports cards were released in extremely limited editions and I was wondering if there was some way to mathematically calculate the odds of collecting the following:

Above is a photo of 20 cards featuring all 4 of the 2013 Marvel Fleer Retro Precious Gem Doctor Strange cards (top row), the Rittenhouse Marvel 75th Anniversary Dr. Strange card (top row far right), as well as every form of the three Doctor Strange cards and one Dormammu card from the 2014 Rittenhouse Marvel Universe set (these are seen in the 4 rows below).

Of these 20...

There were only 10 made of 4 of them. (The Fleer Green Precious Gem (top row, second card from right) and the 3 Rittenhouse Diamond Parallel cards. You can see these on the far right on rows 2 - 4.

There were only 50 made of 4 of them. (The Fleer Blue Precious Gem and the 3 Rittenhouse Ruby Parallel cards)

There were only 75 made of 1 of them. (The Rittenhouse 75th Anniversary card seen on the far right in the first row)

There were only 100 made of 4 of them. (The Fleer Red Precious Gem and the 3 Rittenhouse Emerald Parallel cards)

The rest of the 7 cards are commons. The Rittenhouse set has a gold base set along with a blue "Sapphire Parallel" base set, so that makes 6 total in that run. The common one from the Marvel Fleer Retro set is top row left.

These cards are distributed to a few hundred stores and private collections around the world.

How do I calculate the odds of having been able to find them all?

To determine the odds you would need to determine the probability first, which would require knowing a few vital pieces of information:

1. Approximately how many people collect these things? This would be the variable that determines the demand.
2. How many cases of each card set were made in total? This would determine total supply.
3. How many of each card are currently available on eBay (or elsewhere online)? This would determine the variable of 99% certainty that you could currently obtain an item if you had enough money.
4. The probability that the rare items are still available in unopened packages and have not all already been accounted for.

Once you have these figures (or an educated guess for each) you can use a mathematical formula to work out the probability and determine the odds of all of them ever coming together as they have in the picture above.

ADDITIONAL INFORMATION:

2013 FLEER MARVEL RETRO CARD LINE
20 packs per box, 5 cards per pack
Mini boxes have 10 packs per box, 5 cards per pack.
6 boxes per case.
Approximately 500-600 cases made

2014 RITTENHOUSE MARVEL
24 packs per box. 5 cards per pack.
12 boxes per case.
Approximately 500-600 cases made

2013 Fleer Marvel Retro Cases currently available online for sale (as of 5/3/14): 10
2013 Fleer Marvel Retro Boxes currently available online for sale (as of 5/3/14): 50
2013 Fleer Marvel Retro Mini Boxes currently available online for sale (as of 5/3/14): 7

2014 Rittenhouse Marvel Cases currently available online for sale (as of 5/3/14): 3
2014 Rittenhouse Marvel Boxes currently available online for sale (as of 5/3/14): 40

From top left to right
Card #1 Fleer Dr. Strange: 11 Available on eBay (as of 5/3/14)
Card #2 Fleer Dr. Strange Precious Metal Gem Red: 3 available on eBay (as of 5/3/14)
Card #3 Fleer Dr. Strange Precious Metal Gem Blue: 2 available on eBay (as of 5/3/14)
Card #4 Fleer Dr. Strange Precious Metal Gem Green: 0 available on eBay (as of 5/3/14)
Card #5 Rittenhouse 75th Anniversary Dr. Strange Card: 1 available on eBay (as of 5/3/14)
Card #6 Rittenhouse #3 Dormammu Gold Base card: 13 available on eBay (as of 5/3/14)
Card #7 Rittenhouse #3 Dormammu Sapphire Parallel card: 37 available on eBay (as of 5/3/14)
Card #8 Rittenhouse #3 Dormammu Ruby Parallel card: 1 available on eBay (as of 5/3/14)
Card #9 Rittenhouse #3 Dormammu Emerald Parallel card: 1 available on eBay (as of 5/3/14)
Card #10 Rittenhouse #3 Dormammu Diamond Parallel card: 2 available on eBay (as of 5/3/14)
Card #11 Rittenhouse #6 Dr. Strange Gold Base card: 12 available on eBay (as of 5/3/14)
Card #12 Rittenhouse #6 Dr. Strange Sapphire Parallel card: 1 available on eBay (as of 5/3/14)
Card #13 Rittenhouse #6 Dr. Strange Ruby Parallel card: 2 available on eBay (as of 5/3/14)
Card #14 Rittenhouse #6 Dr. Strange Emerald Parallel card: 1 available on eBay (as of 5/3/14)
Card #15 Rittenhouse #6 Dr. Strange Diamond Parallel card: 1 available on eBay (as of 5/3/14)
Card #16 Rittenhouse #53 Dr. Strange Gold base card: 12 available on eBay (as of 5/3/14)
Card #17 Rittenhouse #53 Dr. Strange Sapphire Parallel card: 1 available on eBay (as of 5/3/14)
Card #18 Rittenhouse #53 Dr. Strange Emerald Parallel card: 1 available on eBay (as of 5/3/14)
Card #19 Rittenhouse #53 Dr. Strange Ruby Parallel card: 1 available on eBay (as of 5/3/14)
Card #20 Rittenhouse #53 Dr. Strange Diamond Parallel card: 0 available on eBay (as of 5/3/14)

Out of the 20, 2 cards are not currently available for sale online unless you find them in a case or box and they have not already been accounted for.

Completed auctions for those 2 cards:
1 Fleer 2013 Green Precious Gem card was ever up for sale on eBay.
1 Rittenhouse 2014 Diamond Parallel card #53 was ever up for sale on eBay.

So those 2 by default are the rarest… AT THE MOMENT.

Calculations would be appreciated in the comments. Thanks!