First Time Long Time - Diminishing Returns question

OK, I have a question of probability that I hope will improve my math skills and it has a real life application :D This question involves gambling, but in a different format than you might expect, so I figure it makes a good work problem.

I got stumped trying to make a chart for myself, and I immediately thought of the old-school Wizard of Odds Q&A site. Now I see there is a spiffy new site, so good luck to everybody here! Without further ado:

Part I

OK, I am looking for the probability that a NEW random prize will be found in a box of items.

For example, a set of 60 collectible figurines are released by a game company in random boxes, each containing 5 figures.

I want to find the point at which it is no longer profitable to buy blind boxes to complete the set.

Now, I know that when I purchase box #1, the odds are 100% that at least one figure will be new to me. If I designate the number of figures already collected as f, then I know I need a formula where I divide (60-f)/60 to get the percentage chance that the next box I purchase will contain at least one new figure.

Question: Does the amount of figures in a box affect this equation, or am I OK using it the way I wrote it?

Part II

Now, this gets more complex. The 60 figures are different rarities. So if I have 59 out of 60, I need to know the odds I can get a given figure. I think to do that I must create a new dividend/divisor based upon my estimation of the MOST rare figures' rarity. For example, if Figure A is 5 times more rare than the most common figures, I believe I can find the odds by assigning a rarity value to the figures I already have collected and divide them by (5*60)=300. So, if I assign the value of the rarity value of all the figures I own added together as 'r' my equation now looks like this, correct? (300-r)/300

Part III

Lets ratchet this up even more. The whole point of this exercise is to find the point of diminishing returns, at which I should stop purchasing boxes of figures and instead collect individuals to fill the holes in my collection. I know that if I spend $10 on my first random box that I have a 100% chance of being pleased. I also know that if I own 59 out of 60 pieces I would have to be an idiot to buy another blind box expecting to see something new. But how do I graph the exact point where the switch occurs? I would like to use an equation that allows me to find the value of a booster, or V.

So, let us assume that when these boxes are sold they cost $10 a piece. On the secondary market (eBay) each piece sells for $3 for a common piece (rarity 1/5th of Figure A). Therefore it makes much more sense to purchase the blind boxes than individuals at first. But eventually I have most of the set, and the more rare pieces sell for far more than their rarity would suggest. So let us say that I have 45 out of 60 figures, but three of the ones I am missing cost $20, $30, and $60, respectively. If I gamble and buy a blind booster that has the $60 figure then I would win, but if luck is not with me I will be looking at a bunch of duplicate common figures.

Part IV

As these sets go out of production, sometimes the blind boxes themselves raise in price. But I think I can still find the value of any given set just by changing the $10 part of the equation, once I understand Part III better.



What would the Wizard do if he was speculating in this market?! Hepl, pls :-)

Alright, brushing off obviously rusty math abilities here...

Part I I have figured out the answer to.

If I have all but 2 figures of a 60 figure set, and if there are 5 figures per box, then I must simply multiply each number by 5 and divide the result. So, (2*5)/(60*5)=10/300= 3.333% chance . Since this is the same odds as 2/60 I can stick with my original formula of (60-f)/60.