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The real odds against pulling a perfect
Yes, whoever corrected me about what the average number of packs you need to get to receive a perfect card was right. It's one in 200. But sometimes you pull more than one of them in 200 packs; to balance that out somebody else has to get none in their 200 packs.
Here are the odds on pulling a perfect for some random numbers of packs.
1 - 199:1
2 - 99:1
3 - 66:1
Just what you thought, right?
5 - 39.5:1
10 - 19.5:1
20 - 10.5:1
30 - 6.18:1
We're starting to see the effects of having to balance out the lucky so and so who pulls 2 in that number of packs.
40 - 4.5:1
50 - 3.5:1
75 - 2.2:1
100 - 1.54:1
How many packs do you have to have to have a 50/50 chance to pull a perfect? Between 138 and 139.
200 - about a 63% chance to get one
300 - 77.7%
400 - 86.5%
500 - 91.8%
600 - 95%
And you all thought that 600 packs was enough to be sure you'd get 3. Not even close, one time in 20 you will draw a blank.
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