Friday, October 29, 2010

A small correction... a VERY small correction

In my original Gamma World review, while I was complaining about the booster pack system, I had said there was a better than 50-50 chance of getting a dupe in your third booster pack, and one came with the game.

I have a correction to make ...kind of.

This afternoon, on a whim and to prove myself right about something, I bought two booster packs. The expectation based on my math was that I would have no repeats in the first purchased (the second) booster, and had about a 31% chance of getting a dupe in the second purchased (the third) booster.

As I was inspecting the boosters I had from the first pack, though, I realized that the numbers on the Alpha and Omega cards were all over the place. In the gratis booster, I had Alphas 3, 11, 19, 60, and 99, and Omegas 27, 35, and 72. There was no way to split the deck of 120 cards that those made sense.

So I realized that this had to be a universe of 240 cards, 120 Alphas and 120 Omegas, not just 120 cards split between Alphas and Omegas.

Different numbers? Of course the math is different!

If the universe held 120 cards, and the first booster didn't have a dupe, that would mean I held 16 unique cards, and according to my original calculations would only have a 31.8% chance of getting another dupe-free booster, and the odds would go down on subsequent boosters.

With a universe of 240 cards, you still have a 57.58% chance, better than 50-50, of being dupe-free after your second purchased (third) booster.

But...

Then I opened my boosters.

I got a dupe anyway.

What a shock, right? I mean, there was only a 42.42% chance of that happening!

Your odds of remaining dupe-free per booster:

0100.00%
176.25%
257.58%
343.05%
431.83%
523.26%
616.78%
711.94%
88.36%
95.76%
103.90%
112.59%
121.68%
131.06%
140.65%
150.39%
160.22%
170.12%
180.07%
190.03%
200.02%
210.01%
222.56E-05
238.79E-06
242.56E-06
255.95E-07
269.99E-08
271.00E-08
283.90E-10
291.52E-12

So, yeah, uh, if anyone wants to trade for a Force Axe (Omega 35)...

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