by ender516 on Wed Sep 14, 2011 9:25 pm
Oh, dear. It's hard to believe no one picked up on that earlier. Zones with 3 regions are routinely broken up by neutrals or starting positions. I guess someone should have run this through the calculator.
EDIT: Okay, I have run this through MrBenn's calculator. If three starting positions of 3 regions each are created, spread over the those zones (Andalusia, Northern Towns, and Coal Valley), then the chance of dropping a bonus on one of those is eliminated. However, it does mean that in the 1v1 case, the two players each start with 24 regions. 70 minus 1 (for Arsenal) minus the nine regions in starting positions makes 60 basic regions in the pot, but with each player getting one starting position containing 3 regions, the 3 regions in the unused starting position also go into the pot, for a total of 63 to be divided three ways (red, green and neutral). So red gets 3 plus 63/3 (3 + 21 = 24), green gets 3 plus 63/3 (3 + 21 = 24), and neutral gets 1 (Arsenal) plus 63/3 (1 + 21 = 22). 24 + 24 + 22 = 70, so all present and accounted for.
Having players start with 24 regions is bad. The first player gets eight troops to deploy, and if he takes one from the second player, that player only gets seven troops on his turn.
This can be corrected by making one region in each starting position an underlying neutral, so that in a 1v1, when the third starting position is not given to either player, only two regions go into the pot for distribution, with the underlying neutral going directly to the neutral player. With 62 in the pot, red gets 3 plus 62/3 (3 + 20 = 23), green gets 3 plus 62/3 (3 + 20 = 23), and neutral gets 1 (Arsenal) plus 1 (underlying neutral) plus 62/3 (20) plus the remainder of the pot (62 modulo 3 = 2) (1 + 1 + 20 + 2 = 24). 23 + 23 + 24 = 70.
In a 1v1v1 game, everyone gets one starting position consisting of three regions, and 60/3 or 20 from the pot. Arsenal remains the sole neutral. With four or more players, the starting positions are ignored, and the board always start with at least Arsenal and the (fixed) underlying neutrals as neutrals. The remaining 66 regions are split as evenly as possible, with the leftovers also becoming neutrals. So in a 4 player game, each player starts with 16 regions, and two more random neutrals join the fixed four. In a 5 player game, each starts with 13, and one random neutral emerges. In a 6 player game, each starts with 11 regions, and no extra neutral is needed. In a 7 player game, each starts with 9, and three extra neutrals appear. Finally in an 8 player game, each starts with 8 and two extra neutrals appear.
This seems like a clean solution. Going forward with this, a decision is required regarding which regions will be the underlying neutrals and how the starting positions will be grouped (one region from each of the small zones should go into each position: are some more favourable than others? what is a fair mix?)