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Possible combinations of starting picks: 1/15/2013 22:03:29

Warguan
Level 27
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Can anyone please tell me what the potential combinations of picks are at the start in 1v1 with 3 picks each. I think that information would be handy but I just can't get my head round it to work it out.

If my opponent doesn't pick any of my first three obviously I get my first three...thats actually where i get stuck trying to work it out although somewhere in the back of my head that not all combinations are possible.
Possible combinations of starting picks: 1/15/2013 22:26:47

Richard Sharpe
Level 59
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Combination in what respect? How many different ways can you get awarded territories from your six selections based on how your opponent picks?
Possible combinations of starting picks: 1/15/2013 22:29:22

Master ARC
Level 57
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Can't find it, but there was another thread with a couple pages of debate on this very subject.
Possible combinations of starting picks: 1/15/2013 22:41:57

[REGL] Pooh
Level 60
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Well, picks, as I understand them, are assigned to you as what is the highest pick available.

So, assuming you have the following table:

Territory / Player A Rank / Player B Rank
A / 1 / 3
B / 2 / 4
C / 3 / 1
D / 4 / 5
E / 5 / 2
F / 6 / 6

So, Assuming A get's first Pick, he gets his first 1 available: So A.

Then B gets his highest two avail: C, E,

Then A gets his two highest: (already has A), so he gets B and D because C was already taken.

Then B gets his last pick, F.

So, at the end of the day, Player A gets: A, B, C (or his 1, 2, 4 picks) and B gets C, E, F, or his 1, 2 and 6 picks.

But if Player B gets his to pick first, then the selections goes:
Player B: C, E, D (1, 2, 5)
Player A: A, B, F (1, 2, 6)

This just assumes each player picks the same exact territories.
Possible combinations of starting picks: 1/15/2013 23:40:44

Warguan
Level 27
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I tried looking through the archives but couldnt find anything. Thanks for that John but what I meant may be better explained like this...???

123
124
125
126
134
135
136
145
146
156
234
235
236
245
246
256
345
346
356
456

Clearly not all of the above combinations are possible (for example 456). Was just wondering if someone could point out which ones. Even better if they could explain how they worked it out.
Possible combinations of starting picks: 1/15/2013 23:51:15

ChrisCMU
Level 60
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All possible since you don't know their order:
123
124
125
126
134
135
136
145
146
156
234
235
236
245
246
256

Not possible as you'd get 1 or 2:
345
346
356
456

Most of the top ones are possible if they pick 1st (not overlapping with your picks), then you get two picks and they get two picks. Allows for things like 1,2,6.

So, 16 possible outcomes from your picks. Does that seem right?
Possible combinations of starting picks: 1/16/2013 01:02:09

Richard Sharpe
Level 59
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Can't get 245, 246 or 256. Only way you get stuck with your 2 is if opponent gets first pick. Should that happen, you automatically get the next two picks which would be 2-3.

I also don't believe you can get 146 or 156. If you get first pick then you are guaranteed 4-5 at worst. If you get second pick then you are guaranteed 2 of the top 3.
Possible combinations of starting picks: 1/16/2013 01:20:16

JSA
Level 59
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123
124
125
126
134
135
136
145
234
235
236

Those are the only 11 possible combinations. Richard is right in the post above this one that those 5 he mentioned, are impossible. I bet if I looked at all my games, I could find an example of each one of these combinations, although some are much more common of course. No others are possible.
Possible combinations of starting picks: 1/16/2013 05:51:41

Lord Fred100
Level 35
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I had to do it , lol.
Possible combinations of starting picks: 1/16/2013 13:28:10

awesomely bitchtastic beta 2.o
Level 58
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Yep, jsa listed all th combinations I can think of. Try to get 125 or 126, when you do, you most probably will win.
Possible combinations of starting picks: 1/16/2013 13:42:25

Grumpy Cat
Level 13
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Warlight:

Possible combinations of starting picks: 1/16/2013 17:16:44

Lord Fred100
Level 35
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^Lmao
Possible combinations of starting picks: 1/16/2013 20:06:55

Warguan
Level 27
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There are 11 possibles. Got it. Everyone should know that. Very handy.

So who can do the same for a 4 pick each scenario?! No prize for the winner.

1234
1235
1236
1237
1238
....

I have got you started lol.
Possible combinations of starting picks: 1/17/2013 00:38:45

kazcal
Level 10
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Handy indeed. If all of the picks overlap, one player will get 145 and the other 236.
Possible combinations of starting picks: 1/17/2013 04:43:16

JSA
Level 59
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1234
1235
1236
1237
1238
1245
1246
1247
1248
1256
1257
1258
1267
1345
1346
1347
1348
1356
1357
1358
1367
1456
1457
1458
1467
2345
2346
2347
2356
2357
2367

I don't play 4 pick games much at all so I'm not 100% sure these are right. So if anyone can add others, please explain how it is possible and add it to this list. Sam e for taking any away. I think this is almost copmletely accurate though and it might be.
Possible combinations of starting picks: 1/17/2013 13:48:17

Diabolicus
Level 58
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1467 does not seem possible:

Either you get 1st pick, then it is:
you: 1
Player B: 2 + 3
you: 4 + 5
Player B: 6 + x
you: 7

-> 1457

Or you get 2nd pick, then it is:
Player B: 2 or 3
you: 1 + (3 or 2)
Player B: 4 + 5
you: 6 + 7

-> 1367 or 1267
Possible combinations of starting picks: 1/17/2013 16:02:34

ChrisCMU
Level 60
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What about 2v2 (assuming you have same picks)?
Possible combinations of starting picks: 1/17/2013 16:51:47

Diabolicus
Level 58
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2v2, 2 picks each player, assuming you have coordinated your picks and do not overlap with your teammate (though this might be desireable in some occasions):

Players in order A, B, b, a - a, b, B, A (spot the elk!)

with A + a = Team 1 and B + b = Team 2

(IIRC it is not possible anymore for one team to get the first 2 picks, so an order of A, a, B, b should be impossible?)

Player A (=1st pick) might end up with:
1 2 (0 overlapping picks)
1 3 (1 op with B or b)
1 4 (2 op with B and/or b)
1 5 (3 op with B and b)
1 6 (4 op with B and b)

Player B (=2nd pick):
1 2 (0 op)
1 3 (1 op with a)
1 4 (2 op with a)
2 3 (1 op with A)
2 4 (2 op with A and a)
2 5 (3 op with A and a)

Player b (=3rd pick)
1 2 (0 op)
1 3 (1 op with a)
1 4 (2 op with a)
2 3 (1 op with A)
2 4 (2 op with A and a)
2 5 (3 op with A and a)

Player a =(4th pick)
1 2 (0 op)
2 3 (1 op with B or b)
3 4 (2 op with B and b)

-> possible outcome:
1 2
1 3
1 4
1 5
1 6
2 3
2 4
2 5
3 4

someone else do it for teammates with overlapping picks :-)
Possible combinations of starting picks: 1/18/2013 12:43:14

Wenyun
Level 59
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2v2 with both teams doing mirror picks gives the same results as a 4 pick 1v1. One player will get the first and last picks, while the other player will get the two in the middle.
Possible combinations of starting picks: 1/18/2013 14:17:13

EARTH.NIGGA..MOTHER.FUCKER.FUCK.you.all.guys.I>AM>
Level 2
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Whats the best 3 starting points in SMALL MEDIUM AND BIG EARTH _ bold
Possible combinations of starting picks: 1/18/2013 14:26:41

Richard Sharpe
Level 59
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There are no objective best starting spots. Too much depends on map settings, opponent and preferred strategy.
Possible combinations of starting picks: 1/18/2013 14:26:54

Pink
Level 60
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it depends.
Possible combinations of starting picks: 1/20/2013 21:19:27

Knugen
Level 7
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1vs1, then I think to start in teeritories belonging to the small bonuses is best example small earth to start in Austrila and have one in SA to the border of Africa (or vice versa), and one in NA at the border to Europe (or vice versa). Taking control over Australia would be much eaiser then taking control over Asia (and also much faster). With standard settings (no cards) this would give you 5+2armies each turn, then you will be able to take SA (5+2+2 armies/turn(s)). If you still have armies in in Greenland or Iceland your opponent can then only control Africa (assuming you have armies in Siam). This means that you will receive 9 armies and your opponent max 8. Then you should take control over Africa and at the same time NA (if the opponent is only receives 5 armies).

However, looking at a big map with many territories such as the US map with 3.1K territories it depends on your strategy and where your opponent start.
Possible combinations of starting picks: 1/23/2013 03:56:52

dunga • apex
Level 57
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to realize all possible 4 spots you pick, you pick all combinations from the 3 spots and analize the possible locations of last picks.

For example, if you pick your 123 as your 3 initial picks, is very easy to understand that you can get all other 5 picks as the last one.
1234
1235
1236
1237
1238
being all possible. From there on you can do the proper table. Tired to do it, but is not hard at all.

And Kerostar statement is completely accurate and usefull, and putting that knowledge in picking can do wonders.
Possible combinations of starting picks: 1/23/2013 05:11:04

nich
Level 59
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For 1v1 with 4 starting spots the possibilities are:
1234
1235
1236
1237
1238
1245
1246
1247
1248
1256
1257
1258
1267
1345
1346
1347
1348
1356
1357
1358
1367
1368
1456
1457
1458
2345
2346
2347
2356
2357
2367

JSAs list was extremely close.
Possible combinations of starting picks: 1/23/2013 08:53:18

Diabolicus
Level 58
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Some combinations require you to get either 1st or 2nd pick, others are always possible, regardless of 1st/2nd pick. These latter ones are twice as likely.

1v1, 3 spots:
123 1st/2nd
124 1st/2nd
125 1st/2nd
126 2nd
134 1st/2nd
135 1st
136 2nd
145 1st
234 2nd
235 2nd
236 2nd

1v1, 4 spots:
1234 1st/2nd
1235 1st/2nd
1236 1st/2nd
1237 1st/2nd
1238 1st
1245 1st/2nd
1246 1st/2nd
1247 1st/2nd
1248 1st
1256 1st/2nd
1257 1st/2nd
1258 1st
1267 1st/2nd
1345 1st/2nd
1346 1st/2nd
1347 1st/2nd
1348 1st
1356 1st/2nd
1357 1st/2nd
1358 1st
1367 2nd
1368 2nd
1456 1st/2nd
1457 1st/2nd
1458 1st
2345 2nd
2346 2nd
2347 2nd
2356 2nd
2357 2nd
2367 2nd

Statistical probabilities are rather pointless though, since the outcome is influenced much stronger by other factors (total number of starting spots in distribution, wastelands/bonus size/expansion options -> starting spots not being equal, strategy (single, double, triple pick, large/small bonus etc.), personal preference).
Lucky for you, I like numbers and am really, really bored right now, so here are the probabilities for 1v1, 2 picks.
1st column = pick / combination of picks
1st row = number of territories in distribution / number of territories you want to consider elegible (= non wastelanded bonus, no 3/4-turns-to-complete for example)
Percentages = probability of getting exactly that pick / combination of picks.

6	8	10	12	14	16	18	20	22
1	80,9%	84,3%	86,9%	88,7%	90,2%	91,3%	92,2%	92,9%	93,5%
2	63,0%	69,0%	73,9%	77,6%	80,4%	82,6%	84,4%	85,8%	87,1%
3	55,3%	64,8%	71,3%	75,8%	79,1%	81,7%	83,6%	85,2%	86,6%
4	59,0%	59,9%	54,5%	48,8%	43,8%	39,5%	35,9%	32,9%	30,3%
5	38,5%	20,9%	13,0%	8,8%	6,4%	4,8%	3,8%	3,0%	2,5%
6	3,4%	1,1%	0,5%	0,3%	0,2%	0,1%	0,1%	0,0%	0,0%

6	8	10	12	14	16	18	20	22
12	43,9%	53,3%	60,7%	66,3%	70,6%	73,9%	76,6%	78,8%	80,6%
13	36,2%	49,1%	58,1%	64,6%	69,3%	73,0%	75,8%	78,2%	80,1%
23	25,9%	38,0%	47,8%	55,1%	60,8%	65,2%	68,8%	71,7%	74,1%
14	48,7%	48,7%	44,1%	39,4%	35,3%	31,8%	28,9%	26,5%	24,4%
24	30,8%	33,4%	31,1%	28,2%	25,5%	23,1%	21,1%	19,4%	17,9%
34	30,8%	33,4%	31,1%	28,2%	25,5%	23,1%	21,1%	19,4%	17,9%
15	30,8%	16,7%	10,4%	7,1%	5,1%	3,9%	3,0%	2,4%	2,0%
25	23,1%	12,5%	7,8%	5,3%	3,8%	2,9%	2,3%	1,8%	1,5%
35	15,4%	8,4%	5,2%	3,5%	2,5%	1,9%	1,5%	1,2%	1,0%
45	7,7%	4,2%	2,6%	1,8%	1,3%	1,0%	0,8%	0,6%	0,5%
16	2,3%	0,7%	0,3%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%
26	2,3%	0,7%	0,3%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%
36	2,3%	0,7%	0,3%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%

6	8	10	12	14	16	18	20	22
123	6,8%	22,3%	34,6%	43,9%	51,0%	56,5%	61,0%	64,6%	67,6%
124	20,5%	22,3%	20,8%	18,8%	17,0%	15,4%	14,1%	12,9%	11,9%
125	15,4%	8,4%	5,2%	3,5%	2,5%	1,9%	1,5%	1,2%	1,0%
126	1,1%	0,4%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%	0,0%
134	20,5%	22,3%	20,8%	18,8%	17,0%	15,4%	14,1%	12,9%	11,9%
135	7,7%	4,2%	2,6%	1,8%	1,3%	1,0%	0,8%	0,6%	0,5%
136	1,1%	0,4%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%	0,0%
145	7,7%	4,2%	2,6%	1,8%	1,3%	1,0%	0,8%	0,6%	0,5%
234	10,3%	11,1%	10,4%	9,4%	8,5%	7,7%	7,0%	6,5%	6,0%
235	7,7%	4,2%	2,6%	1,8%	1,3%	1,0%	0,8%	0,6%	0,5%
236	1,1%	0,4%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%	0,0%

I don't really claim these numbers to be 100% correct, so please prove me wrong. Which might be difficult though, because I am too lazy to explain my calculations to you ;-)
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