The probability that X-Ost missiles will kill X-Dragon

1. A simple probability question

X-Dragon is an interesting neutral creature in the legend of hearth stone. It cannot be a target of spells or hero skills. It has 2 blood and has good viability. The mage has a spell card for the Oracle missile, which is randomly causing damage, so it can cause damage to the X-dragon. So there is an interesting question:

What is the probability that an Austrian missile will kill X-Dragon? (Note: Octa missiles may hit the other hero.) First, the probability is relatively low. It should not exceed 50%.

The situation is still complicated. Let's discuss it slowly: There are three situations:

1. Dragon, face, Dragon 1/2*1/2*1/2 = 1/8

2. Dragon, dragon, face 1/2*1/2 = 1/4

3. Face, dragon, Dragon 1/2*1/2*1/2 = 1/8

So the total probability is 1/8 + 1/4 + 1/8 = 1/2

Let's look at the probability of not killing X-Dragon:

1. face, face, face 1/2*1/2*1/2 = 1/8

2. Trigger only one hit on X-Dragon (in three cases), 1/2*1/2*1/2*3 = 3/8

Therefore, the probability of killing X-Dragon is 1-(1/8 + 3/8) = 1/2, which verifies the above calculation results.

Firestone also has a legend like a dog-headed man, which can increase spell damage. If an oracle missile can cause four points of damage, what is the probability of killing X-Dragon?

We still reverse the computation, which is simpler:

1. face, face 1/2*1/2*1/2*1/2 = 1/16

2. 4. Only 1 hair hits X-Dragon (in four cases), 1/2*1/2*1/2*1/2*4 = 1/4

Therefore, the probability of four O & M missiles killing X-Dragon is 1-(1/16 + 1/4) = 11/16 equals 0.6875, and it is not high.

5. The probability that X-Dragon will be killed by an oracle missile is 1-(1/32 + 1/32*5) = 13/16 or 0.8125.

2. Slightly complicated problems

Assume that the opponent's field has a 2-blood follower and a 1-blood follower. I am a mage and have an oracle missile, which can cause 3 points of damage and 1 point of damage to the mage's hero skill, I want to work with the hero skill to clear the probability of the two followers?

There are two solutions:

1. First Use the hero skill to kill 1 blood, and then use the Oracle missile. After our calculation above, the probability is cleared at 1/2.

2. First Use the Oracle missile, view the results, and then use the hero skill to complete the knife. (Intuition is that this probability is relatively high)

Focus on the second medium case:

We can also calculate it in a reverse way, which is simpler: Calculate the worst case:

1. Face-hitting of all trigger missiles: 1/3*1/3*1/3 = 1/27

2. Only one O & M missile hits the followers of 2 blood, and the other two faces: 1/3*1/3*1/3*3 = 1/9

3. Only the followers of one O & M missile hitting one blood, and the other two faces:

3.1 1st followers: 1/3*1/2*1/2

3.2 2nd followers: 1/3*1/3*1/2

3.3 3rd followers: 1/3*1/3*1/3

The total probability of the other two faces is 19/108.

So the total clearance probability is 1-(1/27 + 1/9 + 19/108) = 73/108 = 0.6759 higher than 0.5

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