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).

He's not right.

The answer is 50%....even though Azaroth didnt word it clearly.

Paraphrasing Azaroth - the chance of opening the correct portal is 100%. Would have been different if you specifically asked, say, what are the odds opening it on the 2nd machine. But you didnt. You asked what are the odds of opening the machine. It's 100% since you have 3 machines.

So the odds of getting the organ to drop is 50%.

Dont let Cyberbeni's diagrams and number crunching confuse you.

This is only true if you open all 3 portals in the same game no matter what. But that is hardly the optimal strategy. =)

1/2*1/2*1/2 = 1/8

I did my analysis this way:

Chance of winning on first try = chance of getting right portal * chance of getting the drop

= 1/3 * 1/2 = 1/6. Since we'll be dealing with lots of 1/3 and 1/2, let's use a common denominator of 216 (6^3) so this is 36/216.

Chance of winning on second try is complicated. You have a 2/3 chance of having gotten the wrong portal on the first try, followed by a 50% chance of getting the right portal on the second try (you've already eliminated one of the wrong choices so your chance of getting the right portal is better after a "wrong portal"), followed by a 50% chance of getting the drop which is 2/3*1/2*1/2 = 2/12 = 1/6 = 36/216.

But, you also had a 1/6 chance of getting the right portal on the first try, but not getting the drop, then quitting the game and restarting, then having a 1/3 chance of getting the right portal on the second try and a 1/2 chance of getting the drop for 1/6*1/3*1/2 = 1/36 = 6/216.

It gets complicated on missing it twice and winning on the third try. You have the following list of possibilities. I'll rewrite the "win in 1" and "win in 2" cases here for consistency:

Y = got right portal and got organ

n = got right portal and did not get organ

a = got wrong portal #1

b = got wrong portal #2

win in 1:

Y = (1/3 * 1/2) = 1/6 = 36/216

win in 2:

a Y = 1/3 * (1/2 * 1/2) = 1/12 = 18/216

b Y = 18/216

n Y = (1/3 * 1/2) * (1/3 * 1/2) = 1/36 = 6/216

win in 3:

a b Y = 1/3 * 1/2 * (1 * 1/2) = 1/12 = 18/216

b a Y = 1/3 * 1/2 * (1 * 1/2) = 18/216

a n Y = 1/3 * (1/2 * 1/2) * (1/3 * 1/2) = 1/72 = 3/216

b n Y = 3/216

n a Y = (1/3 * 1/2) * 1/3 * (1/2 * 1/2) = 1/72 = 3/216

n b Y = 3/216

n n Y = 1/6 * 1/6 * 1/6 = 1/216

Sum = (36 + 18+18+6 + 18+18+3+3+3+3+1)/216

= (36 + 42 + 49)/216

= 127/216

= 0.587962962962963

To verify empirically, the chances of winning are .5879 according to a test program I just wrote.

I did my analysis this way:

Chance of winning on first try = chance of getting right portal * chance of getting the drop

= 1/3 * 1/2 = 1/6. Since we'll be dealing with lots of 1/3 and 1/2, let's use a common denominator of 216 (6^3) so this is 36/216.

Chance of winning on second try is complicated. You have a 2/3 chance of having gotten the wrong portal on the first try, followed by a 50% chance of getting the right portal on the second try (you've already eliminated one of the wrong choices so your chance of getting the right portal is better after a "wrong portal"), followed by a 50% chance of getting the drop which is 2/3*1/2*1/2 = 2/12 = 1/6 = 36/216.

But, you also had a 1/6 chance of getting the right portal on the first try, but not getting the drop, then quitting the game and restarting, then having a 1/3 chance of getting the right portal on the second try and a 1/2 chance of getting the drop for 1/6*1/3*1/2 = 1/36 = 6/216.

It gets complicated on missing it twice and winning on the third try. You have the following list of possibilities. I'll rewrite the "win in 1" and "win in 2" cases here for consistency:

Y = got right portal and got organ

n = got right portal and did not get organ

a = got wrong portal #1

b = got wrong portal #2

win in 1:

Y = (1/3 * 1/2) = 1/6 = 36/216

win in 2:

a Y = 1/3 * (1/2 * 1/2) = 1/12 = 18/216

b Y = 18/216

n Y = (1/3 * 1/2) * (1/3 * 1/2) = 1/36 = 6/216

win in 3:

a b Y = 1/3 * 1/2 * (1 * 1/2) = 1/12 = 18/216

b a Y = 1/3 * 1/2 * (1 * 1/2) = 18/216

a n Y = 1/3 * (1/2 * 1/2) * (1/3 * 1/2) = 1/72 = 3/216

b n Y = 3/216

n a Y = (1/3 * 1/2) * 1/3 * (1/2 * 1/2) = 1/72 = 3/216

n b Y = 3/216

n n Y = 1/6 * 1/6 * 1/6 = 1/216

Sum = (36 + 18+18+6 + 18+18+3+3+3+3+1)/216

= (36 + 42 + 49)/216

= 127/216

= 0.587962962962963

To verify empirically, the chances of winning are .5879 according to a test program I just wrote.

Correct.

Its a binomial distribution.

Find the probability of winning (p)

Find q which is 1 - p

Then use nCr on your calculator to find the probability using the binomial formula

(NCR)(p^r)(q^(n-r))

the quote above is doing it the long way using a tree diagram but same thing.

ALso the original question was not clear. Re-write the question so people know exactly what you are after. (i.e. what probability you are after).

Jul 23, 2013
-1

this thread is still going?

The correct answer to this problem is:

ask someone for an MP10 run

who thinks festavus should have won?

07/23/2013 03:46 AMPosted by Mowzewho thinks festavus should have won?

No, the first correct response is on page two by Getch:

Brute force, of all possible outcomes. "Good" results in bold:

...[snip]...

1/6 + 1/36 * 1/216 + 1/36 + 1/6 + 1/36 + 1/6 = 127/216 = 58.8%

Jul 23, 2013
-1

The simple answer is there is no answer. It all comes down to the simple coin toss, 50/50 chance at getting heads or tails but 10 coin flips in a row could all be tails meaning a 50/50 chance ends in 100% 1 sided result. So basically it comes down to luck, no mathematical work will result in a correct answer no matter how smart you think you are : )

removed

1______1______0.166666667

2______1______0.027777778

2______2______0.027777778

3______1______0.00462963

1______2______0.166666667

2______1______0.027777778

1______3______0.166666667

0.587962963

However instead of doing it on paper or manually. We can do it with a program. A program can produce the result for a variable number of machines. Also we can determine the average organ yield where a user will use all machines in the search to maximize 1 organ type.

source:

http://pastebin.com/raw.php?i=fmwmBebd

For 1 machines, Chance To Get >=1 Organ

1 / 6 ~= 0.16666666666666666

For 1 machines, Average Organs from spending all machines

1 / 6 ~= 0.16666666666666666

For 2 machines, Chance To Get >=1 Organ

13 / 36 ~= 0.3611111111111111

For 2 machines, Average Organs from spending all machines

7 / 18 ~= 0.3888888888888889

For 3 machines, Chance To Get >=1 Organ

127 / 216 ~= 0.5879629629629629

For 3 machines, Average Organs from spending all machines

37 / 54 ~= 0.6851851851851852

For 4 machines, Chance To Get >=1 Organ

889 / 1296 ~= 0.6859567901234568

For 4 machines, Average Organs from spending all machines

74 / 81 ~= 0.9135802469135802

For 5 machines, Chance To Get >=1 Organ

6007 / 7776 ~= 0.7725051440329218

For 5 machines, Average Organs from spending all machines

565 / 486 ~= 1.162551440329218

For 6 machines, Chance To Get >=1 Organ

39241 / 46656 ~= 0.8410708161865569

For 6 machines, Average Organs from spending all machines

2071 / 1458 ~= 1.4204389574759946

For 7 machines, Chance To Get >=1 Organ

247255 / 279936 ~= 0.8832554583904892

For 7 machines, Average Organs from spending all machines

7285 / 4374 ~= 1.6655235482395976

For 8 machines, Chance To Get >=1 Organ

1538761 / 1679616 ~= 0.916138569768328

For 8 machines, Average Organs from spending all machines

12572 / 6561 ~= 1.91617131534827

For 9 machines, Chance To Get >=1 Organ

9473815 / 10077696 ~= 0.9400774740575624

For 9 machines, Average Organs from spending all machines

85321 / 39366 ~= 2.167377940354621

For 10 machines, Chance To Get >=1 Organ

57840649 / 60466176 ~= 0.95657858370273

For 10 machines, Average Organs from spending all machines

285367 / 118098 ~= 2.416357601314163

For 15 machines, Chance To Get >=1 Organ

466248612439 / 470184984576 ~= 0.9916280352071436

For 15 machines, Average Organs from spending all machines

105225877 / 28697814 ~= 3.6666861455022324

For 20 machines, Chance To Get >=1 Organ

3650240655886153 / 3656158440062976 ~= 0.9983814202054326

For 20 machines, Average Organs from spending all machines

17143360514 / 3486784401 ~= 4.916667778220911

For 25 machines, Chance To Get >=1 Organ

28421393604598182679 / 28430288029929701376 ~= 0.9996871496580634

For 25 machines, Average Organs from spending all machines

10449892698457 / 1694577218886 ~= 6.166666577358255

For 30 machines, Chance To Get >=1 Organ

221060551987010497582729 / 221073919720733357899776 ~= 0.9999395327420811

For 30 machines, Average Organs from spending all machines

3054051791156359 / 411782264189298 ~= 7.416666662827418

For 35 machines, Chance To Get >=1 Organ

1719050708823285319818255319 / 1719070799748422591028658176 ~= 0.9999883129158263

For 35 machines, Average Organs from spending all machines

867213448422599077 / 100063090197999414 ~= 8.66666666706579

For 40 machines, Chance To Get >=1 Organ

13367464343333472198458637923785 / 13367494538843734067838845976576 ~= 0.9999977411241745

For 40 machines, Average Organs from spending all machines

120563515802466689996 / 12157665459056928801 ~= 9.916666666679182

For 45 machines, Chance To Get >=1 Organ

103945592151930507026628494195881111 / 103945637534048876111514866313854976 ~= 0.9999995634052622

For 45 machines, Average Organs from spending all machines

65979650446291639208989 / 5908625413101667397286 ~= 11.166666666664922

For 50 machines, Chance To Get >=1 Organ

808281209258046236569910278620995970313 / 808281277464764060643139600456536293376 ~= 0.999999915615121

For 50 machines, Average Organs from spending all machines

17827800027680952638267623 / 1435795975383705177540498 ~= 12.41666666666663

For 55 machines, Chance To Get >=1 Organ

6285195111055225026007329091629320359394647 / 6285195213566005335561053533150026217291776 ~= 0.9999999836901201

For 55 machines, Average Organs from spending all machines

4768278434249287507399132213 / 348898422018240358142341014 ~= 13.666666666666675

For 60 machines, Chance To Get >=1 Organ

48873677826621441059611310490774565486657545289 / 48873677980689257489322752273774603865660850176 ~= 0.999999996847632

For 60 machines, Average Organs from spending all machines

632334777605308372953355674494 / 42391158275216203514294433201 ~= 14.916666666666666

For 65 machines, Chance To Get >=1 Organ

380041719746284585036848352135758529770884477187607 / 380041719977839666236973721680871319659378770968576 ~= 0.9999999993907114

For 65 machines, Average Organs from spending all machines

333067330568373710361443565523009 / 20602102921755074907947094535686 ~= 16.166666666666664

For 70 machines, Chance To Get >=1 Organ

2955204414199667253988670995034753366738871248409031561 / 2955204414547681244658707659790455381671329323051646976 ~= 0.999999999882237

For 70 machines, Average Organs from spending all machines

87193250090597915778581373076618135 / 5006311009986483202631143972171698 ~= 17.416666666666664

For 75 machines, Chance To Get >=1 Organ

22979669526999724314174900030133295952727806488083999792855 / 22979669527522769358466110762530581047876256816049606885376 ~= 0.9999999999772387

For 75 machines, Average Organs from spending all machines

22708626741298687807294063867776251269 / 1216533575426715418239367985237722614 ~= 18.666666666666664

For 80 machines, Chance To Get >=1 Organ

178689910245230947864195115025159271684561039058833158353113801 / 178689910246017054531432477289437798228285773001601743140683776 ~= 0.9999999999956007

For 80 machines, Average Organs from spending all machines

2943859185835722972711901601176431312440 / 147808829414345923316083210206383297601 ~= 19.916666666666664

For 85 machines, Chance To Get >=1 Organ

1389492742071847142855438058262361913913392752242838344357906462615 / 1389492742073028616036418943402668319023150170860455154661957042176 ~= 0.9999999999991497

For 85 machines, Average Organs from spending all machines

1520509428185376513152509655062636473932677 / 71835091095372118731616440160302282634086 ~= 21.166666666666664

For 90 machines, Chance To Get >=1 Organ

10804695562358094831950822343985392873842673139349587960058408190231049 / 10804695562359870518299193703899148848724015728610899282651377959960576 ~= 0.9999999999998358

For 90 machines, Average Organs from spending all machines

391303699969265773760797773574888407606785623 / 17455927136175424851782794958953454680082898 ~= 22.416666666666668

For 95 machines, Chance To Get >=1 Organ

84017312692907684395676524715943347762122344351729656658870896059353972823 / 84017312692910353150294530241519781447677946305678352821897115016653438976 ~= 0.9999999999999681

For 95 machines, Average Organs from spending all machines

100389036960144868322602862882902248395663005909 / 4241790294090628238983219175025689487260144214 ~= 23.666666666666664

For 100 machines, Chance To Get >=1 Organ

653318623500066895111744835624186667667445448787330805035663512014523572535625 / 653318623500070906096690267158057820537143710472954871543071966369497141477376 ~= 0.9999999999999939

For 100 machines, Average Organs from spending all machines

12841489891572615664991823126350166442442489160218 / 515377520732011331036461129765621272702107522001 ~= 24.916666666666668

For 1000 machines, Chance To Get >=1 Organ

14166102623834861723796252524915224416640471830910191322323547432140618947596486436347661333869287260068907949302029484915942402681211620694597762903768493031793437496360887770405170017360367775685180887600222888037722079533459491004747944372063257507753971205889900009748316822012021763199215894753285262008784429860791005107434776049420802546396387214484156773576780563603487216193121989408145776439986674339488257614492579842146276269121340448272733184321294740548634134183983966542587002322710193226457256012433516522674636684321859849905433686605500321425343345293648345146344534788883625829081980922149300258663737339530754547325785844790709651498911546241790096022163928512788463291211005181604538995905550137997898318998598275884992295341662153949271529602704581957807561 / 14166102623834861723796252524915224416640471830910191322323547432140618947596486436347661333869287260068907949302029484915942402681211620694598046617844295512220793103312980549591537160959053027940624117598003417503015722697428176155600362263128567590299511776686592862074376328232990325101248680123776914576482815095784568122986221890411837737570098864613342090972756469661488216176894465388028416768338495326989675118087222767384596111351304957869025273802978281783731929966468210579229830069556698928937342508988340792335737744719376598506908977135291983117722648269177947154657697517074993441515526839887073400191797445153760221695723268255006134044062503100710134200414607696976757837002911389023284338696251543694980946202137938610119300450795091488653253649628649410789376 ~= 1.0

For 1000 machines, Average Organs from spending all machines

330407532301911592002872943666390079460858389685307696235591348692688246953563999476899513603164464819147118609410072873791409399309979676390346902754050255700736087947480340902513858992722129915158067496054022125445476208254471684978886412751442208008396954913448456451387654592148260052196293963508064448695715170758699493425828257141535393054628262870186955330897089997673076772504054490728597779409252876907260634556731276929839164826137380779583931731826448386377563191357036 / 1322070819480806636890455259752144365965422032752148167664920368226828597346704899540778313850608061963909777696872582355950954582100618911865342725257953674027620225198320803878014774228964841274390400117588618041128947815623094438061566173054086674490506178125480344405547054397038895817465368254916136220830268563778582290228416398307887896918556404084898937609373242171846359938695516765018940588109060426089671438864102814350385648747165832010614366132173102768902855220001 ~= 249.91666666666666

07/23/2013 04:15 AMPosted by NixstaThe simple answer is there is no answer. It all comes down to the simple coin toss, 50/50 chance at getting heads or tails but 10 coin flips in a row could all be tails meaning a 50/50 chance ends in 100% 1 sided result. So basically it comes down to luck, no mathematical work will result in a correct answer no matter how smart you think you are : )

The simple answer is that there is an answer; and you, my friend, definitely aren't very smart, no matter what you think...

Jul 23, 2013
-1

The real answer is 200% because he is multiboxing 4 characters.

And the final answer is that this has already been solved and is over with. LOL

Sheesh.

Sheesh.

1/3*1/2+1/2*1/2+1/2=1/6+1/4+1/2=11/12

I knew from the get go that the odds were better than 50%, because there are more variables thrown into the equation than just 3 portals, 1 game. I wasn't sure of the

*exact*figure, but I knew it was better than 50%. I was swayed a little bit by the number of people insisting on 50%, but I am glad that the problem was resolved and my initial hunch was proven correct (hence the reason for the question).

In any case, thanks to everyone who participated. I owe Getch a prize and if he doesn't add me by the end of today I will give the gold to the first person who confirmed Getch's answer. My ignorance of algebraic statistics was the cause for my asking the work to be shown, but after carefully looking at the solution, it's clear that .58 is the correct answer.