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The forums' hardest game


baltoist

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Time for some more MATH:

 

First off, if you missed my first MATH, you can find it here.

 

Previously, we made the assumption that the game has a 50% chance to be over after the 8th post. Let’s generalize this and assume the game has a 50% chance to be over after the nth post.

 

We follow much the same steps as before. As before, let event D be the game ending after n posts, let event A be the game continuing after the current post, and let event E be the game reaching 50 posts.

 

Since event A needs to occur n times for event D to occur, we have the following relationship between the events:

P(D) = (P(A))^n

 

Rearrange and substitute 0.5 for P(D):

P(A) = 0.5^(1/n)

 

Now that we have the probability of a single post succeeding, we can calculate event E, which is 50 posts occurring:

P(E) = (P(A))^50

Substitute 0.5^(1/n) for P(A):

P(E) = (0.5^(1/n))^50

 

You can rewrite (0.5^(1/n))^50 as (1/(2^50))^(1/n) which I believe is a neater way of expressing it.

 

Why did I do this you ask? For fun!

 

... Actually, I had a different reason this time. Previously, I assumed 8 was a reasonable number for half the games to reach, but the recent games have ended much earlier. Since we just found the probability of winning in terms of the number of posts the game has a 50% chance to be over by (n), we can just substitute in values of n to get different situations, which I’ll list below:

 

If the game has a 50% chance of being over after 1 post, the chance of winning is 0.0000000000000088817% (Requires about 1125899906842624 attempts)

If the game has a 50% chance of being over after 2 posts, the chance of winning is 0.0000029802% (Requires about 33554432 attempts)

3 posts: 0.00096123% (104032 attempts)

4 posts: 0.017263% (5793 attempts)

5 posts: 0.097656% (1024 attempts)

6 posts: 0.31004% (323 attempts)

7 posts: 0.70760% (141 attempts)

8 posts: 1.3139% (76 attempts)

9 posts: 2.1263% (47 attempts)

10 posts: 3.1250% (32 attempts)

11 posts: 4.2823% (23 attempts)

12 posts: 5.5681% (17 attempts)

13 posts: 6.9533% (14 attempts)

14 posts: 8.4119% (12 attempts)

15 posts: 9.9213% (10 attempts)

 

At the moment, it’s looking like we’ll need to try this game at least 1000 times to win now. Great!

 

 

Oh yeah, I have to participate in the game too. 2!

  • Brohoof 1

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My OCs: Aero Wind, Shadowhide, Ebony (WIP)

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To de 2


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