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Math Problem: 11/3/2014 03:01:47

[REGL] Pooh
Level 60
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How many variations are there for a strategic 1v1 map? for picks?

Accounting for:
-Random Warlords,
-Set Wastelands,
-Sometimes a wasteland overrides the starting spot.

For Picks, account for:
each person picks 6 picks,
first pick is random.
Math Problem: 11/3/2014 06:12:09

Dutch Desire
Level 59
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variations Random Warlords with no Wastelands set:
4^4=256
5^9=1953125
6^4=1296
7^6=117649 *
76236552000000000

variations 7 Wastelands on 131 terretories:
131*130*129*128*127*126*125= 562469019840000

total variations on ladder 1v1 map:
562469019840000*76236552000000000= 42880698679421191680000000000000

Edited 11/3/2014 06:12:31
Math Problem: 11/3/2014 07:04:26

Genghis
Level 54
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428 ( 11-illion ) 806 ( 10-illion ) 986 ( 9-illion ) 794 ( 8-illion ) 211 ( 7-illion ) 916 Hextillion, 800 pentillion. Damn.
Math Problem: 11/3/2014 14:16:01

Math Wolf
Level 63
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Except that there is a small overlap (double or triple count the same scenario) when 2 or more wastelands are located in the same bonus. Using a rule of thumb to estimate this (a very difficult problem to quantify), this happens in about 60% of the cases, so Orange's estimate should be reduced by about 30%.

The picking is difficult as well as it is conditional on the number of starts (which could 23, 22 or lower down to 16 minimum). Given the number of starts, you may have theoretically different situations that result in the same practical situation: (for example 1-3 pick completely different between 2 players, so no information, but 4-6 picks many different options still possible)
If you ignore this, you are talking about 1.05653 * 10^(16) combined picks for 23 possible starts. Combined with Orange's estimate, we are talking about an order of 10^(37), which is somewhat comparable to the number of atoms in all living organisms on earth.
Math Problem: 11/3/2014 14:26:48

Genghis
Level 54
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What does that number and my first high school semester have in common? ! Lots of zeroes. ..
Math Problem: 11/3/2014 16:22:34

Dutch Desire
Level 59
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Did forget that yes.
But how did you get by a reduced of about 30%?

It seems a bit high, i was thinking it is around 11%:
When 2 wastelands are located in the same bonus, then that bonus will have 1 possibility less.
so a 5 territory bonus will be seen like a 4 territory bonus. what will lower the number by 20%.
But that there are multiple wastlands in one bonus happens only in about 60%, so 20*0,6=12%. but its not always a 5 territory bonus what makes it a bit below 11%, and there is also the possibility that there are more than 2 wastelands in one bonus and multiple bonuses with more than one wasteland what highers the % a litle bit.
Math Problem: 11/3/2014 19:14:37

Math Wolf
Level 63
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@ Orange: yes, my mistake, I didn't correct for the fact that out of those 60% counted double (so reduction of 30%) there are only few cases where the wasteland actually "covers" the start.

So yeah, approximately 1/5th of those removed seems more correct. :-) (magnitude remains more or less correct, I think)
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