What makes WHM special? Nothing anymore.

[winsock]

This is vastly oversimplifying, in theory it sounds great, in reality this is not what happens. AST has 6 cards, if three of them are desirable and three undesirable. Then having an 87.5% chance to get a favorable result means the inverse is true giving me an 87.5% chance of not getting the card I want. So the reality being that its just as likely to gain a favorable outcome as an unfavorable one, it therefore follows that believing anything else to be true is gamblers fallacy.

This all still is off the original topic.

This is what happens in reality.
The desired result is for the coin to be heads at least 1 time when making 3 attempts. The inverse would be the coin never landing on heads. The likelihood of that happening is 1/8 or 12.5% because there is only one outcome "TTT" that did not contain any heads.

If you dont want it simplified, I'll unsimplify it. Let's use a 6 sided die as the AST deck has 6 cards. There are 3 even numbers and 3 odd numbers just like in the scenario of 3 desired and 3 undesired cards. You roll it twice. What is the probability of rolling an even number at least once?
There are 36 possible outcomes (6x6).
27 of said possible outcomes will contain at least one even number:
2,1 2,2 2,3 2,4 2,5 2,6
4,1 4,2 4,3 4,4 4,5 4,6
6,1 6,2 6,3 6,4 6,5 6,6
1,2 1,4 1,6
3,2 3,4 3,6
5,2 5,4 5,6

27/36 = 75% chance

[J-Dax]

Snip

Explaining why the probability is 1/2 for a fair coin
We can see from the above that, if one flips a fair coin 21 times, then the probability of 21 heads is 1 in 2,097,152. However, the probability of flipping a head after having already flipped 20 heads in a row is simply 1⁄2. This is an application of Bayes' theorem.

This can also be seen without knowing that 20 heads have occurred for certain (without applying of Bayes' theorem). Consider the following two probabilities, assuming a fair coin:

probability of 20 heads, then 1 tail = 0.520 × 0.5 = 0.521
probability of 20 heads, then 1 head = 0.520 × 0.5 = 0.521
The probability of getting 20 heads then 1 tail, and the probability of getting 20 heads then another head are both 1 in 2,097,152. Therefore, it is equally likely to flip 21 heads as it is to flip 20 heads and then 1 tail when flipping a fair coin 21 times. Furthermore, these two probabilities are equally as likely as any other 21-flip combinations that can be obtained (there are 2,097,152 total); all 21-flip combinations will have probabilities equal to 0.521, or 1 in 2,097,152. From these observations, there is no reason to assume at any point that a change of luck is warranted based on prior trials (flips), because every outcome observed will always have been as likely as the other outcomes that were not observed for that particular trial, given a fair coin. Therefore, just as Bayes' theorem shows, the result of each trial comes down to the base probability of the fair coin: 1⁄2.

https://en.wikipedia.org/wiki/Gambler%27s_fallacy