I'm trying to design a zero sum bonus structure for a board whereby the gains of each player is subtracted from all the opponents equally such that the total bonus is zero sum.  Since the fraction of subtracted bonus changes as the number of opponents decrease in order to maintain balance, however, I need to keep track of how many players remain and this needs to be with regard to each player in their own colour such that continents can be created to redeposit bonus in order to maintain equilibrium at the beginning of each player's turn.  The board has a starting space for each player that goes neutral after they are eliminated, and, because the maximum number of players is 8 I could make an 8x8 matrix that starts off with each player owning an entire row.  Is it possible, however, to somehow get one territory in each players row to "auto neutral" as opponents are eliminated such that the number of remaining territories "lit" in each row remains faithful to how many players are still in the game?  Or, can any of you think of another way of "keeping count" of how many opponents remain in a way that can be used to facilitate the deployment of bonuses?

Thanks a lot!

Can you give us a simple example with hard numbers (maybe with 3 or 4 players) just so we're not misunderstanding things?

Lets say that we have 6 players so then on player 1's turn he gets a bonus of 1000 added to a capital specific to him while the other 5 players all have 200 deducted from their specific capitals such that 1000-200*5 = 0.  If a player gets eliminated then it would then give player 1 the same 1000 bonus on his turn, but would now subtract 250 from each of the others, such that 1000-250*4 = 0.

To manage this, I need to be able to create continents that recognize how many players are remaining in the game, which is what I'm working on theoretically in my above query.  So, since each player gets a starting space that would go neutral if they are eliminated, or, if that seat didn't start the game, then I need to be able to reduce the lit spaces in the matrix once certain spaces are seen to be neutral.

Lets say the game starts with 6 players so two of the eight start off as neutral...  1 2 3 x 5 6 x 8

Now lets say I have an off screen matrix to keep count of how many players are in the game:

Starts like                                            After first round                            After 2 is elim

1 1 1 1 1 1 1 1                                     1 1 1 x 1 1 x 1                               1 x 1 x 1 1 x 1

2 2 2 2 2 2 2 2                                     2 2 2 x 2 2 x 2                               x x x x x x x x

3 3 3 3 3 3 3 3                                     3 3 3 x 3 3 x 3                               3 x 3 x 3 3 x 3

x x x x x x x x                                       x x x x x x x x                                 x x x x x x x x

5 5 5 5 5 5 5 5         ------------->         5 5 5 x 5 5 x 5        ------------->     5 x 5 x 5 5 x 5

6 6 6 6 6 6 6 6                                     6 6 6 x 6 6 x 6                               6 x 6 x 6 6 x 6

x x x x x x x x                                       x x x x x x x x                                 x x x x x x x x

8 8 8 8 8 8 8 8                                     8 8 8 x 8 8 x 8                               8 x 8 x 8 8 x 8

If I can keep such a record off screen then on player 1's turn I can add player 1's bonus to his stack and then adequately split the penalty against all opponents equally by using the 1 1 1 x 1 1 x 1 part of the matrix which allows player 1 to negate bonus according to how many players are remaining and then to do so against each of their stacks such that the net sum is zero.  Of course, because bonuses don't know what 1 1 1 x 1 1 x 1 means I would have to do it quite systematically and start with the assumption that it's 1v1 and subtract the entire amount from each player, then, if it is actually a 1v1v1 I would have to add 500 back to each player by looking for certain territories that are still "lit" and not neutral.  Then it would have to check if it's still a 1v1v1v1, and if so, then when it looked for the 1v1v1 state it would have overcompensated with it's +500's, so now it would have to subtract to correct it such that each player's bonus should be equivalent to -333, and so on, and so forth, up to checking for 8 players.  Once the "lit" spaces are not enough, however, it will stop adding or subtracting bonus and it will already be appropriate for the number seen.  So, I can do the math so long as I can get a matrix working to keep track of the player number for each player in the game in territories homogeneous to their own such that bonus deploying continents can be formed.

Sorry, I am confused now.  What is the desired result (not the process) in a game with 5 people where 2 are eliminated with a 60 troop bonus to split?  That each player gets 20 placed on their capital?  ..or in-hand? ..every turn? only on their turn?

That, in a game with 5 people that if player 1 is getting a bonus of 1000 put onto his capital that the same is divided and deducted from his opponents capitals, so, the other 4 players lose 250 from each of their capitals.  If two players are eliminated and only 3 players remain, then, when player 1 collects from that same bonus of 1000 onto his capital that the other 2 players now remaining, lose 500 from each of their capitals.  In this way even as players are eliminated, the net sum always remains roughly zeroed.

I have one method figured out theoretically so long as I can create the matrix as described above to keep track of player counts in territories homogeneous to each players colour.  I'm just not sure how the matrix can be "updated" with each elimination?  Any simpler methods would be greatly appreciated, of course! ;-)

So..

Starts like                                            After first round                            After 2 is elim

1 1 1 1 1 1 1 1                                     1 1 1 x 1 1 x 1                               1 x 1 x 1 1 x 1

2 2 2 2 2 2 2 2                                     2 2 2 x 2 2 x 2                               x x x x x x x x

 

" x x x x x x x " at the end looks like at the end of round 2 the "counter" sees everyone eliminated???

..or does it mean that if everyone has 2 on their capital, it's different than if everyone has 1 on their capital?

 

x means it has become neutral, maybe I should have used n.  So, since player 2 was eliminated, all their counting territories became neutral, x, in that example and the second marker territory for player 1 should also somehow go neutral, as well as the second marker for every other active player, so the continents for calculating player deductions can take that elimination into consideration.

In that matrix example, 1,2,3...etc reflect player territories owned whereby all 1's are territories owned by player 1, 2's territories owned by player 2, etc.  When a player is eliminated, all their territories go neutral and hence how that 'x x x x x x x x' forms for player two after elimination.

Can you think of a way for auto neutral to neutralize player 1's second 1:

1 1 1 x 1 1 x 1     ------->   1 x 1 x 1 1 x 1

After player 2 is eliminated there is a territory on the board which is definitely seen to go neutral.  Is it possible for that territory, when neutral only, to neutralize the other corresponding territories in the matrix.  Or is it possible for another territory to look at the now neutral territory and say, if this is neutral, then I'll make this one in the matrix neutral too?  Or, can any other way be devised to accomplish the same?

I think maybe I need some kind of "anti factory" whereby it triggers when the continent becomes neutral but does nothing while it is still owned by any player.

This is cool and I am sure it is doable.  You will need to have "abandonment on" and "revert to neutral" at either immediately or at end of turn. 

Here is what I am thinking -

Each territory (except those in the upper left to lower right diagonal) in your matrix needs a -1 factory to itself.  Each territory also needs a +1 factory to each one in the corresponding column (except itself)  

Start the matrix like this (We'll do 4 players to keep it simple.)

1 2 2 2

1 1 2 2

1 1 1 2

1 1 1 1

After P1 Turn 1

1 1 1 1

2 1 2 2

2 1 1 2

2 1 1 1

after p2 Turn 1

1 2 1 1 

1 1 1 1 

2 2 1 2

2 2 1 1

after p3 Turn 1

1 2 2 1 

1 1 2 1 

1 1 1 1

2 2 2 1

after p4 Turn 1

(suppose P4 eliminates P2 here)

1 2 2 2 

1 1 2 2 

1 1 1 2

1 1 1 1

after p1 Turn 2

(what happens to P2's depends on your type of factory but it doesn't matter.  I'm saying you have +1 universal.)

1 1 1 1 

2 1 2 2 

2 1 1 2

2 1 1 1

we skip P2

after p3 turn 2

1 1 2 1 

2 1 3 2 

1 0 1 1

2 1 2 1

after p4 turn 2

1 1 2 2 

2 1 3 3 

1 0 1 2

1 0 1 1

after p1 turn 2

1 0 1 1 

3 1 3 3 

2 0 1 2

2 0 1 1

and so on ...

So if I did this right the 2's would swap corners until someone was eliminated, then after that player gets skipped 0's start showing up in his column.

 

 

 

There's that pesky "Abandon ON" problem.  It just ruins game-play on most boards.  Being able to set individual "Territory Minimums" would be a great feature, and not to hi-jack the thread, but I have suggested a workaround that uses what might be an easier feature to implement..

http://www.wargear.net/forum/showthread/3728/Factory_suggestion

@Amidon..

With your example, won't the first -1 in the first column go to 0?

1 2 2 2

1 1 2 2

1 1 1 2

1 1 1 1

So after P1 Turn 1

0 2 2 2  ???

 

..or are we looking at player 2's matrix? I really want to understand this..  Does everyone have their own matrix -  .or is it shared? ..or does each of the four lines belong to each player respectively?

 

OK just re-read - still confused, but getting closer. the upper left lower right diagonal never changes - not sure how that happens though.  Also, I see that each player has a row, Do the array territories need to be capped at 2 units?  ..or will they never make it to 3?

Abandon on.  I'll have to think through the rest of the board on how that'll effect things, but that's definitely one way to go.

Each row is each player respectively M57.  Each column is how bonuses can calculate who is still in the game at the beginning of each players turn.

So long as a player is still in the game then it'll be +1, -1, +1, -1 and stay at 2 or 1.  Once a player is eliminated then the now neutral territories can grow bigger in the eliminated players row, but, would be irrelevant, so, I don't think a cap is needed.  Since the eliminated player would no longer be adding +1 to protect their markers in the others' rows it would effectively allow those markers to suicide such that bonus could recalibrate and calculate properly, so, it works as far as I can tell.

There would probably be a lag for the bonuses to recalibrate to the number of players which would give a little more growth then reduction for the one round it would take to recalibrate, I think, but, I think that it wouldn't effect game play too badly for the board I'm conceptualizing.

Assuming your working this out for monopoly berickf - you'd be sacrificing the tax and jail mechanic (as it is now) if you turned abandon on. 

ratsy wrote:

Assuming your working this out for monopoly berickf - you'd be sacrificing the tax and jail mechanic (as it is now) if you turned abandon on. 

I was thinking about that too.  Was wondering if I could just tell it to add a troop to all the "abandoned" movement spaces at the beginning of each turn to retain those autocaptures, but, I think they go neutral immediately, don't they?  Is it possible to set min 1 for some spaces so they act normally and don't apply to abandon?  I have not tried using abandon before and am not really sure what rules apply or what workarounds might exist.

Territory Minimums would be awesome, but they pose a real problem for the fundamental structure of the game, so no, it is not possible to set those.  

It wouldn't cause any problems if it just allowed min 1 to be applied in abandon games though.  Then it would just allow the designer to pick and choose where abandon was operating and where normal operating procedures were in effect.

But how do you win? You can't eliminate a player if there is a territory minimum?

Non abandon has a built in territory minimum of 1, so, it would just mean that you'd have to have 4+ to roll 3 dice from a min 1 territory and leave one behind as you moved on from it.  All you'd have to do to eliminate a player is kill and occupy.

This could be a great solution. Minimum 1 is the "standard" game, so you would think the infrastructure there is strong.

Tom, could this work?   Min 1 selectable by territory "as the only option" with Abandon ON?