Diablo® III

Solve this math problem and win a prize (expired)

nice thx
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Posts: 47
First Portal

Drops 1/3(1/2) = 1/6

No drop = 1/3*1/2 = 1/6

incorrect portal = 2/3

Second Portal - 1st portal right no drop (1/6)

right portal drops = 1/6(1/3)(1/2) = 1/36

right portal no drop = 1/6(1/3)(1/2) =1/36

wrong portal = (1/6)(2/3) = 1/9

Second Portal - 1st portal wrong - 2/3

right portal drops = 2/3(1/3)(1/2) = 1/9

right portal no drop = 2/3(1/3)(1/2) =1/9

wrong portal = (2/3)(2/3) = 4/9

Third Portal - 2nd portal right no drop (1/9)

right portal drops = 1/9(1/3)(1/2) = 1/54

right portal no drop = 1/9(1/3)(1/2) =1/54

wrong portal = (1/9)(2/3) = 2/27

Third Portal - 2nd portal wrong - 4/9

right portal drops = 4/9(1/3)(1/2) = 2/27

right portal no drop = 4/9(1/3)(1/2) =2/27

wrong portal = (4/9)(2/3) = 8/27
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Azaroth got the prize. /thread
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Posts: 47
07/22/2013 07:54 AMPosted by Darkul
Azaroth got the prize. /thread


well !@#$ this then
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I actually had it right first lol.
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Answer is RNG
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I wouldn't have a clue, I am not good at Math. All I can say is that last week, I wanted a couple more spines and a couple more fangs. I had an oversupply of eyes. So I opened two portals in two games and got exactly what I wanted in each game. This was on MP8 by the way.

As the odds on MP8 are better than on MP5, I would have expected some success, but 100% drop rate was good, and the fact that the portals I wanted opened on each occasion was incredible.
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0% because he played the Auction House instead and found a better ring.
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nevermind. answered already
Edited by MadMonk#1407 on 7/22/2013 11:25 AM PDT
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OK so everyone is incorrect.
This can be solved using bernoulli's trial
let
p= probability of success
q=probability of failure
n=number of trials
k=needed number of success

P(k)= (n choose k) * p^k * q^(n-k)

k=1
p=1/2
q=1-p=1/2
n=3

P(1)=(3 choose 1) * 1/2 ^ 1 * 1/2 ^2 = .375 * 100 = 37.5%

http://www.calcul.com/bernoulli-trials?nt=3&ns=1&ps=.5&op=Calculate&form_build_id=form-4531874526db7f269de99da6d48968bc&form_id=calc_main_form

Masters in statistical analysis...
Give me money !@#$%^s
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Using all 3 portals in a single game gets you to the 50% drop rate at mp5. This means the correct answer is at least 50% and yours was less...
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you cant argue with math....
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07/22/2013 07:54 AMPosted by Darkul
Azaroth got the prize. /thread


Except his math was wrong
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07/22/2013 12:31 PMPosted by shindog3
you cant argue with math....


The math is right. Its just that you are using the wrong math. That formula is the odds of having EXACTLY 1 success in 3 tries. The odds of you getting any number of successes in 3 tries is a different formula and the outcome would be higher.
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hmm i think i see how u look at it

doing it in 1 Portal he has a chance of 50%.

doing it in 2 Portal he has a chance of 50% in the first portal, and 25% (50% of a 50% chance) in for the second portal. so -> 75%

doing it in 3 Portals means: 50% + 25% + 12.5%. so the one with 87.5% was right


This is not correct. For starters the odds of getting it on one portal is not 50%. You have to account for the odds of it being the right portal. Thus the odds are 1/3 (odds of being the right portal with no incorrect portals open) x 1/2 (odds of getting the drop) which = 1/6 or 16.67% (rounding to two decimal places due to repeating 6).
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This is not correct. For starters the odds of getting it on one portal is not 50%. You have to account for the odds of it being the right portal. Thus the odds are 1/3 (odds of being the right portal with no incorrect portals open) x 1/2 (odds of getting the drop) which = 1/6 or 16.67% (rounding to two decimal places due to repeating 6).


Yeah, DivineChief has the math right above, although he never totaled up all the possible "good" outcomes to give the final answer.

EDIT: Even he did it wrong, looking it over even more closer

I was hoping there was a nifty formula for it all instead of his brute-force method. Unfortunately, I've forgotten most of what I learned in discrete math class... even though I was a TA for it :(
Edited by Getch#1848 on 7/22/2013 1:21 PM PDT
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Or, you could learn math first:

So, I don't know yet how these portals and organs work but I'll make some assumptions about them and back it up with very basic math. The math is of course correct, but my assumptions on how the game works might not be so please feel free to correct me.

So, the chance of getting the correct portal on the first try is 1/3 right?

So it goes:
Correct Portal
Success / Failure
Wrong Portal
Failure / Failure
Wrong Portal
Failure / Failure

So far the success rate is 1/6th.

Now 5/6ths the time, another portal will be needed.

Since two possible results are left for the portal to be right or wrong it goes:
Correct Portal
Success/ Failure
Wrong Portal
Failure / Failure

This is a 1/4th of 5/6th of the time success rate for a total success rate (so far) of 5/24 + 4/24 = 9/24 = 3/8ths.

But 3/4ths of this 5/6ths of the time, another portal will still be needed.
It must be the correct portal and has a 50/50 chance:
Correct Portal
Success / Failure

This is an added success rate of 15/48ths.
15/48 + 10/48 + 8/48 = 33/48ths

There is a 68.75% chance that player will succeed according to the assumptions I made. I don't want the prize because I am self found and I don't know if my assumptions about the game are correct anyway. I just wanted to help walk people through the math of how a problem like this should be solved. There are equations to get to the same answer more quickly that you can look up. But this is the way to step through this type of problem and I think 68.75 is the correct % answer.

Have a great day folks and thanks for posting a math thread. Math is cool.

~Philoi.
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07/22/2013 01:16 PMPosted by Philoi
Since two possible results are left for the portal to be right or wrong it goes:


You're wrong here. One failure is that it was the wrong portal, which means it's 50/50 for the next portal to be correct. The other failure was that it was the right portal but the item didn't drop, meaning you need to start a new game and it's a 1/3 chance that the next portal is correct.
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Brute force, of all possible outcomes. "Good" results in bold:

1st portal, correct, drops: 1/6

1st portal, correct, no drop: 1/6
- 2nd portal correct, drops: 1/6 * 1/3 * 1/2 = 1/36
- 2nd portal correct, no drop: 1/6 * 1/3 * 1/2 = 1/36
- - 3rd portal correct, drops: 1/36 * 1/3 * 1/2 = 1/216
- 2nd portal incorrect: 1/6 * 2/3 = 1/9
- - 3rd portal correct, drops, 1/9 * 1/2 * 1/2 = 1/36

1st portal incorrect : 2/3
- 2nd portal correct, drops: 2/3 * 1/2 * 1/2 = 1/6
- 2nd portal correct, no drop: 2/3 * 1/2 * 1/2 = 1/6
- - 3rd portal correct, drops: 1/6 * 1/3 * 1/2 = 1/36
- 2nd portal incorrect: 2/3 * 1/2 = 1/3
- - 3rd portal correct, drops: 1/3 * 1/2 = 1/6

1/6 + 1/36 * 1/216 + 1/36 + 1/6 + 1/36 + 1/6 = 127/216 = 58.8%
Edited by Getch#1848 on 7/22/2013 1:32 PM PDT
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