Diablo® III

Solve this math problem and win a prize (expired)


Problem is that your method is not logical and doesnt allow you to come up with a value greater than 50%. But logic dictates that the worst possible outcome is 50%. Worst case scenerio is that your first two portals are the wrong one and you have to open all three portals in the same game giving you a 50% chance. But that is worst case. You chances of getting a drop get better if you get lucky in the first two portals. That alone should tell you that your logic is wrong if it doesnt allow for higher than a 50% chance.


The problem is that you are confusing the best possible outcome with the worst possible outcome.

You say the worst possible outcome is 50%, but I have already proven a scenario where the possible outcome is just 41 and 2/3 %.

The solution WILL be one single sequence, as you have only 3 machines, and you wish to obtain only one organ.

The challenge remains, because if it is possible to create something from nothing, I would like to know!
Edited by littleman#1651 on 7/23/2013 2:17 PM PDT
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Problem is that your method is not logical and doesnt allow you to come up with a value greater than 50%. But logic dictates that the worst possible outcome is 50%. Worst case scenerio is that your first two portals are the wrong one and you have to open all three portals in the same game giving you a 50% chance. But that is worst case. You chances of getting a drop get better if you get lucky in the first two portals. That alone should tell you that your logic is wrong if it doesnt allow for higher than a 50% chance.


The problem is that you are confusing the best possible outcome with the worst possible outcome.

You say the worst possible outcome is 50%, but I have already proven a scenario where the possible outcome is just 41 and 2/3 %.

The solution WILL be one single sequence, as you have only 3 machines, and you wish to obtain only one organ.

The challenge remains, because if it is possible to create something from nothing, I would like to know!


Again you are using backward logic trying to calculate in the odds of an event happening after it has already happened. And you dont even do it consistently throughout your method. You failed to calculate in the odds of getting the wrong portal on the second try which affects the odds of getting the portal on the third.
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So what are the odds,if you have 3 machines, to open the same portal that you need. Now if you are indeed lucky enough for your 3 machines to open the same portal shouldnt that increase your odds?
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DuckOfDeath,

why are you so sure of yourself now? You didn't seem to be very sure at the beginning of your thread? Bandwagon much?

Get on the right train, man. I have provided a very simple method to prove me wrong and I have offered a prize that could be worth as much as 2 - 4 billion gold.

The odds of getting the right portal on the second try are 1/2, as I have previously stated.
The only impact that a previously failed portal attempt has on the next cast is that it removes one of the realms from the odds of the next cast.

I am calculating the odds of an event happening AS it happens, and that is the only number that matters. Other's are calculating the odds of every possible event and summing them, but every possible event cannot occur over the limitation of three machines. You cannot succeed on the first try, and then continue onto the second. That is the flaw you are unwilling to recognize.
Edited by littleman#1651 on 7/23/2013 2:36 PM PDT
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07/23/2013 02:31 PMPosted by Knightmaster
So what are the odds,if you have 3 machines, to open the same portal that you need. Now if you are indeed lucky enough for your 3 machines to open the same portal shouldnt that increase your odds?


You have to factor in the odds of being lucky. If it's the second portal, your odds of being lucky are 1/2. If it is the first portal, your odds are 1/3.
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07/23/2013 02:31 PMPosted by Knightmaster
So what are the odds,if you have 3 machines, to open the same portal that you need. Now if you are indeed lucky enough for your 3 machines to open the same portal shouldnt that increase your odds?


The odds of opening a particular portal three times in three tries is 1/27 or about 3.7%. If that event were to occur the odds of you getting an organ would be 87.5%.
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Problem is that your method is not logical and doesnt allow you to come up with a value greater than 50%. But logic dictates that the worst possible outcome is 50%. Worst case scenerio is that your first two portals are the wrong one and you have to open all three portals in the same game giving you a 50% chance. But that is worst case. You chances of getting a drop get better if you get lucky in the first two portals. That alone should tell you that your logic is wrong if it doesnt allow for higher than a 50% chance.


The problem is that you are confusing the best possible outcome with the worst possible outcome.

You say the worst possible outcome is 50%, but I have already proven a scenario where the possible outcome is just 41 and 2/3 %.

The solution WILL be one single sequence, as you have only 3 machines, and you wish to obtain only one organ.

The challenge remains, because if it is possible to create something from nothing, I would like to know!

portal 1 correct organ 1/3 * 1/2
portal 1 incorrect portal 2 correct organ 2/3 * 1/2 * 1/2
portal 1 incorrect portal 2 incorrect portal 3 correct organ 2/3 * 1/2 * 1/2
1/6 + 1/6 + 1/6 = 1/2

What you are forgetting:
portal 1 correct no organ portal 1 correct organ 1/3 * 1/2 * 1/3 * 1/2
portal 1 correct no organ portal 1 correct no organ portal 1 correct organ 1/3 * 1/2 * 1/3 * 1/2 * 1/3 * 1/2
portal 1 correct no organ portal 1 incorrect portal 2 correct organ 1/3 * 1/2 * 2/3 * 1/2 * 1/2
portal 1 incorrect portal 2 correct no organ portal 1 correct organ 2/3 * 1/2 * 1/2 * 1/3 * 1/2
Edited by RulerEric#1854 on 7/23/2013 2:41 PM PDT
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The odds of opening a particular portal three times in three tries is 1/27 or about 3.7%. If that event were to occur the odds of you getting an organ would be 87.5%.


Now you are claiming that the best odds are FAR ABOVE 56.8%
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The odds of opening a particular portal three times in three tries is 1/27 or about 3.7%. If that event were to occur the odds of you getting an organ would be 87.5%.


Now you are claiming that the best odds are FAR ABOVE 56.8%

average is 0.5879629629629629,
worse case portals give us 1 organ roll thus .5 organ chance. best case portals give us 3 organ rolls for a .875 chance
Edited by RulerEric#1854 on 7/23/2013 2:45 PM PDT
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Blizzard Employee
Posts: 1,449
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.

At MP5 (50%) drop-rate, what are the chances that he will get that particular drop?

There is obviously three possible portals, and a 50/50 drop rate once the correct portal opens - so even if he ends up using all three machines (the last used opening the correct portal), the worst the odds can be is 50/50. But the correct portal could theoretically be opened three times (all on the first try, albeit in different games).

So, what are the odds that three Infernal Machines will be parlayed into the last required organ?

There is an algebraic solution. Show your work.
I stepped into this thread, completely at the ready to unsheathe my ban hammer and redirect this to a more appropriate forum, and instead.... well, I wish you the best in your hellish calculations. ;)

As a side note: according to another set of player calculations, did you know that there are over 3.4 trillion possible builds with Elective mode enabled in Diablo III? See for yourself.
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What you are forgetting:
portal 1 correct no organ portal 1 correct organ 1/3 * 1/2 * 1/3 * 1/2
portal 1 correct no organ portal 1 correct no organ portal 1 correct organ 1/3 * 1/2 * 1/3 * 1/2 * 1/3 * 1/2
portal 1 correct no organ portal 1 incorrect portal 2 correct organ 1/3 * 1/2 * 2/3 * 1/2 * 1/2
... ETC


Please try to hear me out.

Portal 1 correct no organ portal 1 correct organ is:

1/3 * 1/2 + 1/3 * 1/2 = 2/3 or 33%

You guys are insisting on multiplying all these possibilities and then doing a summation and thats simply not the way to solve this problem. Your 33% chance does not improve the following odds just because it does or doesn't happen …

its like this (3 * 5) + .5 = 15.5
3*(5+.5) = 16.5

There's an order of operations when it comes to mathematics, and they are being neglected.
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500 mill please
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07/23/2013 02:45 PMPosted by Knightmaster
500 mill please


Sorry, no gold!

You said if you are lucky enough for all 3 machines to open your portal doesn't that increase your odds?

Incredibly, it doesn't.

the odds of doing it with one machine are 1/3*1/2 = 1/6
1/6 + 1/6 + 1/6 = 1/2 = 50%

You maintain your odd's, IF you are lucky enough to do it all with one machine.
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DuckOfDeath,

why are you so sure of yourself now? You didn't seem to be very sure at the beginning of your thread? Bandwagon much?

Get on the right train, man. I have provided a very simple method to prove me wrong and I have offered a prize that could be worth as much as 2 - 4 billion gold.

The odds of getting the right portal on the second try are 1/2, as I have previously stated.
The only impact that a previously failed portal attempt has on the next cast is that it removes one of the realms from the odds of the next cast.

I am calculating the odds of an event happening AS it happens, and that is the only number that matters. Other's are calculating the odds of every possible event and summing them, but every possible event cannot occur over the limitation of three machines. You cannot succeed on the first try, and then continue onto the second. That is the flaw you are unwilling to recognize.


Please post a quote of mine showing that I was not sure of the solution. Pretty sure every single post I have made has been against the people saying its 50% or some other number that is not 58.8%.

Again you are wrong. The odds of getting the portal on the second try relies on the odds of you getting the wrong portal on the first try. The odds of you getting the wrong portal on the first try is 2/3 that is then multiplied by the odds of getting the right portal on the second try 1/2 and the odds of the drop 1/2 for a 1/6 chance.

You are not calculating them as they happen. You are doing it after they happen. You are saying this is what happened and these are the odds of that happening. In process you are throwing out all the other possibilities which add up to the true odds before they happen. They are all possibilities that give you a chance until it happens.
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I stepped into this thread, completely at the ready to unsheathe my ban hammer and redirect this to a more appropriate forum, and instead.... well, I wish you the best in your hellish calculations. ;)As a side note: according to another set of player calculations, did you know that there are over 3.4 trillion possible builds with Elective mode enabled in Diablo III? See for yourself.


lord god i wish we could thumbs down blizz posts.
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Fine if you dont like the word lucky how about if the "odds" are in your favor and your three machines open the same portal your odds increase. No? then why not and prove it please. because logic suggest that it will increase your odds. Doesnt it?

500 mill please
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The odds of opening a particular portal three times in three tries is 1/27 or about 3.7%. If that event were to occur the odds of you getting an organ would be 87.5%.


Now you are claiming that the best odds are FAR ABOVE 56.8%


You do realize I state that if that particular event were to occur the odds would be 87.5%. That clearly doesnt represent the odds of getting an organ on three tries considering it would be diminished by the odds of that even occuring which is a mere 3.7%. And this is the problem with the way you look at things. You are apparently not understanding what the values I offer represent. If you calculate all the possibe outcomes and multiply them by the chances for each outcome to occur and then add them up you get the overall chances for any of those outcomes to happen thus giving you your odds. All you are calculating is each individual event after they occur.
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there is no odds to luck!
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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.

At MP5 (50%) drop-rate, what are the chances that he will get that particular drop?

There is obviously three possible portals, and a 50/50 drop rate once the correct portal opens - so even if he ends up using all three machines (the last used opening the correct portal), the worst the odds can be is 50/50. But the correct portal could theoretically be opened three times (all on the first try, albeit in different games).

So, what are the odds that three Infernal Machines will be parlayed into the last required organ?

There is an algebraic solution. Show your work.
I stepped into this thread, completely at the ready to unsheathe my ban hammer and redirect this to a more appropriate forum, and instead.... well, I wish you the best in your hellish calculations. ;)

As a side note: according to another set of player calculations, did you know that there are over 3.4 trillion possible builds with Elective mode enabled in Diablo III? [url="http://www.gosugamers.net/diablo/news/19357-doing-the-math-diablo-3-with-3-4-trillion-builds-in-total"]See for yourself.[/url]


I don't feel like doing the math myself but just looking at the numbers it looks like whoever did didn't take into account skills that could not be used together such as monk mantras.
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I will offer an award of 500 million gold to anyone that can successfully and logically present each step, in words, so that the end result offers an opportunity above 50% to receive an organ on mp5 within the limits of 3 machines or less.


Getting the exact figure of 127/216 is a bit involved, but I think I can reasonably explain in words why it must be greater than 50%:

If you open all three portals in one game you are guaranteed a 50% chance.

However, if the correct portal comes up early, then you have an immediate 50% chance plus a nonzero chance by creating a new game.

So sometimes you have a 50% chance and sometimes you have a >50% chance. Together these two cases give a >50% chance.
Edited by DrPotato#1345 on 7/23/2013 3:31 PM PDT
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