Hello folks,
I am beginning to have some doubt about the actual randomness of train generation from portals. I noticed some portal-generated trains appear much often than others that are very rarely seen, so I took some notes while testing a session.
The session uses 4 portals (actually, trackmarks configured as portals using the "Un-portal" rule) to generate random freight trains. Portal 1 has a 6-consist list, Portal 2 has a 7-consist list, Portals 3 & 4 have a 4-consist list.
NOTE: A friend of mine has noticed the same behaviour - even though he has not recorded it - when using the "Un-portal 2" rule. We do not know it this issue also applies to other portal types (e.g. the standard Auran built-in portals), but we think - maybe wrongly - the random selection process used is the same.
These are the data I collected after 40 tests:
[TABLE="class: grid, width: 512, align: center"]
[TR]
[TD="align: center"]Portal #1[/TD]
[TD="align: center"]Generated[/TD]
[TD="align: center"]Actual %[/TD]
[TD="align: center"]Expected %[/TD]
[TD="align: center"]Actual/Expected[/TD]
[/TR]
[TR]
[TD="align: center"]Train #1[/TD]
[TD="align: center"]15[/TD]
[TD="align: center"]37,5%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]225%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #2[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]7,5%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]45%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #3[/TD]
[TD="align: center"]5[/TD]
[TD="align: center"]12,5%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]75%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #4[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]10,0%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]60%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #5[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]10,0%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]60%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #6[/TD]
[TD="align: center"]9[/TD]
[TD="align: center"]22,5%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]135%[/TD]
[/TR]
[TR]
[TD="align: center"] [/TD]
[TD="align: center"]40[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Portal #2[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Train #1[/TD]
[TD="align: center"]11[/TD]
[TD="align: center"]28%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]193%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #2[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]8%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]53%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #3[/TD]
[TD="align: center"]5[/TD]
[TD="align: center"]13%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]88%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #4[/TD]
[TD="align: center"]2[/TD]
[TD="align: center"]5%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]35%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #5[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]15%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]105%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #6[/TD]
[TD="align: center"]5[/TD]
[TD="align: center"]13%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]88%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #7[/TD]
[TD="align: center"]8[/TD]
[TD="align: center"]20%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]140%[/TD]
[/TR]
[TR]
[TD="align: center"] [/TD]
[TD="align: center"]40[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Portal #3[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Train #1[/TD]
[TD="align: center"]18[/TD]
[TD="align: center"]45%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]180%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #2[/TD]
[TD="align: center"]5[/TD]
[TD="align: center"]13%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]50%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #3[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]15%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]60%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #4[/TD]
[TD="align: center"]11[/TD]
[TD="align: center"]28%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]110%[/TD]
[/TR]
[TR]
[TD="align: center"] [/TD]
[TD="align: center"]40[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Portal #4[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Train #1[/TD]
[TD="align: center"]19[/TD]
[TD="align: center"]48%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]190%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #2[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]10%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]40%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #3[/TD]
[TD="align: center"]7[/TD]
[TD="align: center"]18%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]70%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #4[/TD]
[TD="align: center"]10[/TD]
[TD="align: center"]25%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]100%[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]40[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[/TABLE]
As you can see, in all portals Train #1 is generated much often than expected: 180% to 225%; the same could also be true - to a lesser extent - for the last train (100% to 140%).
Is this effect inevitable - and associated with the way computers generate random variables - or there are ways to obtain uniformly distributed random results?
Thanks in advance.
I am beginning to have some doubt about the actual randomness of train generation from portals. I noticed some portal-generated trains appear much often than others that are very rarely seen, so I took some notes while testing a session.
The session uses 4 portals (actually, trackmarks configured as portals using the "Un-portal" rule) to generate random freight trains. Portal 1 has a 6-consist list, Portal 2 has a 7-consist list, Portals 3 & 4 have a 4-consist list.
NOTE: A friend of mine has noticed the same behaviour - even though he has not recorded it - when using the "Un-portal 2" rule. We do not know it this issue also applies to other portal types (e.g. the standard Auran built-in portals), but we think - maybe wrongly - the random selection process used is the same.
These are the data I collected after 40 tests:
[TABLE="class: grid, width: 512, align: center"]
[TR]
[TD="align: center"]Portal #1[/TD]
[TD="align: center"]Generated[/TD]
[TD="align: center"]Actual %[/TD]
[TD="align: center"]Expected %[/TD]
[TD="align: center"]Actual/Expected[/TD]
[/TR]
[TR]
[TD="align: center"]Train #1[/TD]
[TD="align: center"]15[/TD]
[TD="align: center"]37,5%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]225%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #2[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]7,5%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]45%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #3[/TD]
[TD="align: center"]5[/TD]
[TD="align: center"]12,5%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]75%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #4[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]10,0%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]60%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #5[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]10,0%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]60%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #6[/TD]
[TD="align: center"]9[/TD]
[TD="align: center"]22,5%[/TD]
[TD="align: center"]16,7%[/TD]
[TD="align: center"]135%[/TD]
[/TR]
[TR]
[TD="align: center"] [/TD]
[TD="align: center"]40[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Portal #2[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Train #1[/TD]
[TD="align: center"]11[/TD]
[TD="align: center"]28%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]193%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #2[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]8%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]53%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #3[/TD]
[TD="align: center"]5[/TD]
[TD="align: center"]13%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]88%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #4[/TD]
[TD="align: center"]2[/TD]
[TD="align: center"]5%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]35%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #5[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]15%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]105%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #6[/TD]
[TD="align: center"]5[/TD]
[TD="align: center"]13%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]88%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #7[/TD]
[TD="align: center"]8[/TD]
[TD="align: center"]20%[/TD]
[TD="align: center"]14,3%[/TD]
[TD="align: center"]140%[/TD]
[/TR]
[TR]
[TD="align: center"] [/TD]
[TD="align: center"]40[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Portal #3[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Train #1[/TD]
[TD="align: center"]18[/TD]
[TD="align: center"]45%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]180%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #2[/TD]
[TD="align: center"]5[/TD]
[TD="align: center"]13%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]50%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #3[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]15%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]60%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #4[/TD]
[TD="align: center"]11[/TD]
[TD="align: center"]28%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]110%[/TD]
[/TR]
[TR]
[TD="align: center"] [/TD]
[TD="align: center"]40[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Portal #4[/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[TD="align: center"] [/TD]
[/TR]
[TR]
[TD="align: center"]Train #1[/TD]
[TD="align: center"]19[/TD]
[TD="align: center"]48%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]190%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #2[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]10%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]40%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #3[/TD]
[TD="align: center"]7[/TD]
[TD="align: center"]18%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]70%[/TD]
[/TR]
[TR]
[TD="align: center"]Train #4[/TD]
[TD="align: center"]10[/TD]
[TD="align: center"]25%[/TD]
[TD="align: center"]25,0%[/TD]
[TD="align: center"]100%[/TD]
[/TR]
[TR]
[TD="align: center"][/TD]
[TD="align: center"]40[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[/TABLE]
As you can see, in all portals Train #1 is generated much often than expected: 180% to 225%; the same could also be true - to a lesser extent - for the last train (100% to 140%).
Is this effect inevitable - and associated with the way computers generate random variables - or there are ways to obtain uniformly distributed random results?
Thanks in advance.