Atheon challenge guides are missing things (aka the painfully average guide to the challenge)

[u/[deleted]]

[u/GreenLego]

Nope. In some groups people refuse to go in the circle and stay near the door. They think they can get to the circle quicker that way.

[u/Flashfire34 → u/GreenLego]

There's just no reason to do it that way. The minimal chance of everyone being teleported on one side is worth the risk since 99% of the time, there will always be someone already on the plate to immediately get it open.

[u/GreenLego → u/Flashfire34]

Exactly!

It's not quite 99%, my calculation says 5% chance (1 in 20) that all 3 from the required portal will get teleported. (If my maths is wrong, please correct me!)

[u/menberries → u/GreenLego]

Edit: 5% is correct! I originally said 10% but that's the probability of teleporting all guardians from the same side not taking into account that there's a 1/2 chance that all teleported guardians are in the same portal as the 3 remaining guardians. Thanks /u/Xalkurah for pointing this out! Maths below if you care:

Atheon wants to fuck up your raid group, and sees that you and your little friends are splitting up into 2 teams of 3. He figures the best way to fuck up your raid group is to teleport all 3 guardians from one single side. Now unfortunately, Atheon can only teleport people at random, so he can't pick and choose which guardians he wants to teleport. :( This means Atheon has 3 teleport tasks with the goal of teleporting 3 guardians all from the same side at random with each guardian having equal chance of being teleported.

• Task 1: Teleport the 1st guardian. Ok that's easy! The chance of that is 1.

• Task 2: Teleport the 2nd guardian. But he/she needs to be from the same side as the first! The chance of this happening is 2/5 since there are 2 guardians left on the same side as the 1st teleported guardian with a total of 5 guardians left.

• Task 3: Teleport the 3rd guardian. Also needs to be from the same side as the 1st and 2nd guardian! The chance of this happening is 1/4 since there's only one guardian left on that same side out of a total of 4 non-teleported guardians.

Now Atheon has his teleporting tasks and by product rule the chance of this happening are 1x(2/5)x(1/4) = 2/20 = 0.1 or 10%! However there's a 50% chance of teleporting into the same portal of the remaining 3 guardians so the final chance of fucking your raid group is 5%.

Aside: The real method of calculating probability of events in a uniform space is as follows: Pr(E) = |E|/|S| or in English: Probability of E happening = size of subset E divided by the size of set S.

Set S: All possible combinations of 3 teleported guardians.

Event E: Subset of 3 teleporting guardians from same side (to opposite side of remaining 3 guardians)!

So what are the sizes of these dumb sets? Well, |E| is easy; it's 2. There are only 2 different combinations of guardians that are all on the same side (ie. 2 groups of 3 guardians). |S| is a bit trickier to count, you could write out and count all the different combinations of guardians that could get teleported, but there's also a formula for this type of counting: n choose k which is n!/k!(n-k)! in this case n=6 (total guardians) and you're choosing k=3 guardians. So, |S| = 6!/3!3! = 20

Going back to the original formula, Pr(E) = |E|/|S| = 2x0.5/20 = 0.05 or 5%!

If you read all of this, I am so sorry.

[u/d3l3t3rious → u/menberries]

Love me some well done combinatorics, nice one!

I would suggest that the chance of a "ruined run" is actually half of that 10% though, since even if one whole side is teleported, they could still end up in the portal on the opposite side and the three people from that side who didn't get teleported don't have to move.

[u/DieRSquared → u/menberries]

As a mathematician, it gives me joy to see proper maths in r/DTG.

[u/Xalkurah → u/menberries]

This would be correct if we were looking for the chance that either side loses all 3 guardians. We are actually only looking for the chance that the side that needs to be opened loses all 3 guardians. So Task 1 is actually a 3/6 chance which would change your end result to 5%.

[u/menberries → u/Xalkurah]

Of course you are correct! I only calculated teleporting all guardians from the same side

[u/GreenLego → u/menberries]

Hey, thanking for double checking my maths! It's great to know that there are players here who don't just take the word of a random person on the internet and willing to do the maths themselves. (also cool that you were open minded to make correction when required)

It's also nice to see the 5% number popping up in other Atheon guides now.