Solve this math problem and win a prize (expired)

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What the !@#$? Only retards here? Not even the person who asked the question knows the right answer? I drew some %^-* to explain the math:
http://i.imgur.com/FSRQ0Xv.png
red circle: right portal
black circle: wrong portal
number next to circle: chance to get to that portal from the previous step
numbers in red circles are the outcomes how he could get the organ
chances:
1: (1/3*1/2)
2: (1/3*1/2)*(1/3*1/2)
3: (1/3*1/2)*(1/3*1/2)*(1/3*1/2)
4: (1/3*1/2)*(2/3)*(1/2*1/2)
5: (2/3)*(1/2*1/2)
6: (2/3)*(1/2*1/2)*(1/3*1/2)
7: (2/3)*(1/2)*(1*1/2)
so the total chance is 127/216=~56.8%
Damn Getch, you're right.

Add me and tomorrow morning (when I am back online) and I will give you something else (already gave away the other stuff).
Damn Getch, you're right.

Add me and tomorrow morning (when I am back online) and I will give you something else (already gave away the other stuff).


LOL, I appreciate the offer but I respectfully decline. The thread was amusement enough.


so the total chance is 127/216=~56.8%


Black flagged on the last lap. Check your calculator :). Extra points for a picture though.
07/22/2013 01:45 PMPosted by Cyberbeni
What the !@#$? Only retards here? Not even the person who asked the question knows the right answer?


No, I knew it was greater than 50/50 odds. I wasn't sure on the exact figure (which is why I asked people to show their work), but I knew it was greater than 50/50 because of the extra variables.

It was when everyone started saying 50% that I started second guessing myself, lol.
I haven't done the math out, but the 87.5% answer is almost certainly wrong. I think the answer is 56ish%, but it's pretty terrible either way that the thread is this wrong and no one agrees with me (and I don't agree with anyone else).
07/22/2013 01:54 PMPosted by Getch
Check your calculator


yeah, it's 11PM here, and pretty dark... 127/216 is ~58,8%, not 56,8%
07/22/2013 01:45 PMPosted by Cyberbeni
What the !@#$? Only retards here?


Just because I didnt give an answer doesnt mean I didnt know the answer. Wasnt interested in the prize and wanted to see if someone would come up with the right answer to claim the prize. Just wanted to point out to the OP that he was giving the prize to someone with the wrong answer. And to make fun of the guy that claimed he had a masters and still got it wrong. =p
I think getting a masters in statistical analysis makes you more likely to get it wrong.
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.


Getch, would you explain that again in better detail? I only know the math, I haven't gotten to Ubers yet in Diablo 3. So I didn't know if I was assuming the correct order and mechanics to everything. ~Philoi.
07/22/2013 02:13 PMPosted by Philoi
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.


Can you explain that again in better detail? I only know the math, I haven't gotten to Ubers yet in Diablo 3. ~Philoi.


The way ubers work is that there are 3 portals that open in random order. If you stay in a game you are guaranteed to get all three in three tries. So if the first isnt the right portal you would stay and open another then another. Thus the odds of it being the right portal the first time is 1/3, 1/2 for the second portal, and 1/1 for the last portal. But if the portal was the correct one and you didnt get the drop then you wouldnt want to stay in the game since you are guaranteed to get the wrong portal. So you make a new game and you once again have a 1/3 chance of getting the right portal.

EDIT: Oh and just to be clear each portal has a specific drop people are looking for and the OP said he has two of them and looking for the third which is why he needs to find the correct portal. Its not that only one portal has something. Also the drop chance is determined by MP level. Each level equals a 10% chance to drop. Thus the OP said MP5 which is a 50% chance to drop.
the worst odds is
0% he forgot to get the 5 stack...

the best odds is
1/3 = 33.33% open the portal he needs and gets the organ in 1 go.

1/3 x 3 x 1/2 = 50% the odds of him failing to get the machine is 50%, given that he only have 3 machine.
Guys

The first person to solve this problem will win a decent Uhkapian Serpent (5 million gold value), a nice wand (5 million gold value), and 1 million in gold.

Sam wants to craft a Hellfire ring. He has three Infernal Machines, and only needs one more organ to craft it.


This is telling you something important. The only drop rate that matters is the drop rate coming from the portal of the organ he needs. Lets say the organs are A,B,C. If he only needs one more organ, WLOG let him have organs A,B.
In MP5, the portal for C will drop C at 50%. He has three machines. HE HAS THREE MACHINES. THAT MEANS HE CAN OPEN EVERY PORTAL IN ONE GAME.
Boom - opens a portal. Is it the one for organ C? No? Then drop rate is completely irrelevant, he DOES NOT NEED IT. Who CARES if this organ (A or B) drops or doesn't. It is completely irrelevant.

Open second portal - is it organ C? Let's assume so. In mp5 it has a 50% drop rate. So the chance to get the organ is 50%.
Suppose the second portal wasn't organ C. Well whatever portal it is, it is not C nor the one before. Does it matter? NO. !@#$%^- IT, NO. He DOES NOT NEED IT. Kill the uber, carry on.

Finally the last portal is guarenteed portal C. 50% drop rate. Done.

The portal does not matter. He has 3 machines. He has entry to each portal in one game. Therefore the drop rate will be 50% for the organ he needs.

This is called the "memoryless" principle. What happened beforehand (which portal opened) is irrelevant when the portal is finally opened, BECAUSE he opens ALL THREE.

Edit: forgot to say therefore the chances are at least 50%. Obviously these aren't optimal. But for anyone who says 50%, no.
The correct answer to this problem is:
ask someone for an MP10 run.
It looks like there are two correct answers so far, sorry Darkul it's not 50%. Indeed it is 127/216 to get at least one of the desired organ if you do three games.

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%


07/22/2013 01:58 PMPosted by Cyberbeni
yeah, it's 11PM here, and pretty dark... 127/216 is ~58,8%, not 56,8%


However, neither of these are optimal. This is because if the first portal is the wrong one, you shouldn't change games. By staying in the same game the new (conditional) probability is 1/4 that you get it, instead of 1/6.

EDIT: I didn't realize that he was taking into account the fact that you stay in the game if you get the wrong portal. I believe this is optimal: 127/216
The highest chance he has is 50% because even though he gets the right portal the 3 times, it is limited by the 50% chance to drop which is randomized. Sorry if i can't explain myself better I'm really tired =)
07/22/2013 03:10 PMPosted by Vivaldi
The highest chance he has is 50% because even though he gets the right portal the 3 times, it is limited by the 50% chance to drop which is randomized. Sorry if i can't explain myself better I'm really tired =)


This isn't true. Say he joined a game, made a portal, and it was the right one. He beats the uber. 50% drop -> failure.
If he used the two machines in the same game, he is capped at 50% because his chance is done.

However if he leaves the game, and uses a portal in a new one, there is a chance to reopen that portal on the first try. This gives him another 50% (assuming the right portal). Therefore he'd have a total 75% (IF the portal rolled right). If he failed again, left, remade, and got the right portal on the last try, its another 50% for a total of 87.5.

This is the absolute best, top chance possible. This assumes he goes into the same portal three times, and that is very rare. So the highest chance in some given scenario is 87.5%, but this scenario is very rare so it is offset.
Thank you DuckOfDeath!

I reread what Getch wrote. I was assuming this was all in one game. Remaking games does alter things a little. I am too tired to check Getch's math but it seemed correct after rereading it and getting how the game works better now. Thanks for the explanation DuckOfDeath.

~Philoi.
Posted by Vivaldi
The highest chance he has is 50% because even though he gets the right portal the 3 times, it is limited by the 50% chance to drop which is randomized. Sorry if i can't explain myself better I'm really tired =)

This isn't true. Say he joined a game, made a portal, and it was the right one. He beats the uber. 50% drop -> failure.
If he used the two machines in the same game, he is capped at 50% because his chance is done.

However if he leaves the game, and uses a portal in a new one, there is a chance to reopen that portal on the first try. This gives him another 50% (assuming the right portal). Therefore he'd have a total 75% (IF the portal rolled right). If he failed again, left, remade, and got the right portal on the last try, its another 50% for a total of 87.5.


I have to disagree, because the first 50% chance is independent from the next ones. Lets say I get the first portal, I have a 50% chance to get it. I open the second one, I still have a 50% chance and since it is "truly" randomized you can't take the first result into count because results are independent from each other.

Edit: grammar
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%


Er, you're not brute forcing an optimal strategy here. Actually, you're not brute forcing anything. I mean look at the middle block - correct portal, no drop. He is going to leave this game, he isn't going to check out the second and third portals and if they will drop. He doesn't care. They don't have the organ he wants. Adding the following chances is meaningless.
What the !@#$? Only retards here? Not even the person who asked the question knows the right answer? I drew some %^-* to explain the math:
http://i.imgur.com/FSRQ0Xv.png
red circle: right portal
black circle: wrong portal
number next to circle: chance to get to that portal from the previous step
numbers in red circles are the outcomes how he could get the organ
chances:
1: (1/3*1/2)
2: (1/3*1/2)*(1/3*1/2)
3: (1/3*1/2)*(1/3*1/2)*(1/3*1/2)
4: (1/3*1/2)*(2/3)*(1/2*1/2)
5: (2/3)*(1/2*1/2)
6: (2/3)*(1/2*1/2)*(1/3*1/2)
7: (2/3)*(1/2)*(1*1/2)
so the total chance is 127/216=~56.8%


Does anyone else hate it when wrong people call others retards?

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