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Value of Anti-Linked


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I was trying to come up with the value for a Limitation that is the opposite of Linked. That is, I can't use Power A when I am using Power B [EDIT: and vice-versa, in case the symmetry does not appear obvious]. Which Power should take a Limitation (or should both), and what should the value of that Limitation be?

 

Basically, I am looking for a simple Limitation-based implementation of a 2 slot Multipower (with ultimate slots rather than flexible ones). So let's figure out the effective cost based on placing the Limitation on the larger Power, the smaller Power, and both Powers. Let's call the larger Power 'A' and give it an Active Point value 'x'. The smaller Power we'll call 'B' and give an Active Point value 'y'.

 

If we first assume the Powers are approximately equal in value, the cost of a Multipower containing only Powers 'A' and 'B' as ultimate slots would be:

cost = x + x/10 + y/10 ~= x + y/10 + y/10 = x + 2/10 y = x + y/(1 + 4)

cost = x + x/10 + y/10 ~= 1/2 (x + y) + x/10 + y/10 = 6/10 x + 6/10 y = x/(1 + 2/3) + y/(1 + 2/3) ~= x/(1 + 3/4) + y/(1 + 3/4)

so this is equivalent to the cost of Power 'A' plus the cost of Power 'B' with a -4 Limitation on it, or the cost of both Powers with -3/4 Limitations on each. Now let us make Power 'A' roughly twice the size of Power 'B' (x ~= 2y):

cost = x + x/10 + y/10 ~= x + 2y/10 + y/10 = x + 3/10 y = x + y/(1 + 7/3) ~= x + y/(1 + 2)

cost = x + x/10 + y/10 ~= y + x/2 + x/10 + x/20 = y + 13/20 x = y + x/(1 + 7/13) ~= y + x/(1 + 1/2)

cost = x + x/10 + y/10 ~= 2/3 (x + y) + x/10 + y/10 = 23/30 x + 23/30 y = x/(1 + 7/23) + y/(1 + 7/23) ~= x/(1 + 1/4) + y/(1 + 1/4)

This is the equivalent of placing a -2 Limitation on the smaller Power, or a -1/2 Limitation on the larger Power, or a -1/4 Limitation on each.

 

I have so far neglected what might happen if there are other Limitations on the Powers, but I am tempted to simply make, "Anti-Linked," a -1/2 Limitation on both Powers. What do you think?

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Re: Value of Anti-Linked

 

 

I have so far neglected what might happen if there are other Limitations on the Powers, but I am tempted to simply make, "Anti-Linked," a -1/2 Limitation on both Powers. What do you think?

I think you have too much time on your hands :whistle:

I'd tend to agree with the -1/2 limitation, more or less as a Conditional Limit.

It seems theres no reason this couldn't also be one sided as well, where one power won't work if a particular other one is active, but the other power still has full utility.

Other names besides Anti Linked might include Power Conflict, Exclusive (Mutually Exclusive if taken on multiple powers?) or some variation on the same.

Hmmm....

Think it'd be worth a larger limit if there were more mutually exclusive powers in the set? Not that there would be any reason to build like this instead of a MP unles it was for a no frameworks game.

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Re: Value of Anti-Linked

 

I think you have too much time on your hands :whistle:

Probably. I'm not very good at prioritizing tasks. :)

 

I'd tend to agree with the -1/2 limitation, more or less as a Conditional Limit.

It seems theres no reason this couldn't also be one sided as well, where one power won't work if a particular other one is active, but the other power still has full utility.

I suppose so. I just didn't want to start thinking about the differences between activation and maintaining Constant Powers. I was being lazy. Heh.

 

Other names besides Anti Linked might include Power Conflict, Exclusive (Mutually Exclusive if taken on multiple powers?) or some variation on the same.

Oh yes. Quite. I wan't dead-set on the name. I just thought people would understand what I am talking about best if I put it in terms of Linked.

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Re: Value of Anti-Linked

 

Think it'd be worth a larger limit if there were more mutually exclusive powers in the set? Not that there would be any reason to build like this instead of a MP unles it was for a no frameworks game.

Well, let's try it. First assume there are 'n' Powers of roughly equal value (call this value 'x'). The relavent Multipower would cost:

cost ~= x + n x/10

= nx (1/n + 1/10)

= nx [(n + 10)/10n]

= nx/[10n/(n + 10)]

= nx/[1 + (9n - 10)/(n + 10)]

So the Multipower would cost the same as 'n' Powers with 'x' Active Points each and each with a Limitation of -(9n - 10)/(n + 10). Here is a chart:

 

n	Limitation
2	-0.75
3	-1.25
4	-1.75
5	-2.25
6	-2.75
7	-3.00
8	-3.50
9	-3.75
10	-4.00

As 'n' gets much larger than 10, the Limitation will go to -9 (but no further). This makes sense, as splitting the cost of the Pool between all the many slots of a large Multipower will make it tiny compared to the cost of the slots themselves (which is AP/10, or a Limitation of -9).

 

If there are 'n' Powers of rougly 'x' Active Points and 'm' Powers of roughly half that many points (assume that the smaller Powers are just over half the value of the bigger Powers, so you can still only use one at a time), the cost of the Multipower would be:

cost ~= x + n x/10 + m x/20

= (n + m/2)x/(n + m/2) + (n + m/2)x/10

= (n + m/2)x [2/(2n + m) + 1/10]

= (n + m/2)x [(2n + m + 20)/(20n + 10m)]

= (n + m/2)x/[1 + (18n + 9m - 20)/(2n + m + 20)]

Here is the corresponding chart:

 

n	m ->	1	2	3	4	5	6	7	8	9	10
1		-0.25	-0.75	-1.00	-1.25	-1.50	-1.75	-2.00	-2.25	-2.50	-2.75
2		-1.00	-1.25	-1.50	-1.75	-2.00	-2.25	-2.50	-2.75	-3.00	-3.00
3		-1.50	-1.75	-2.00	-2.25	-2.50	-2.75	-3.00	-3.00	-3.25	-3.50
4		-2.00	-2.25	-2.50	-2.75	-3.00	-3.00	-3.25	-3.50	-3.50	-3.75
5		-2.50	-2.75	-3.00	-3.00	-3.25	-3.50	-3.50	-3.75	-3.75	-4.00
6		-3.00	-3.00	-3.25	-3.50	-3.50	-3.75	-3.75	-4.00	-4.00	-4.25
7		-3.25	-3.50	-3.50	-3.75	-3.75	-4.00	-4.00	-4.25	-4.25	-4.50
8		-3.50	-3.75	-3.75	-4.00	-4.00	-4.25	-4.25	-4.50	-4.50	-4.75
9		-3.75	-4.00	-4.00	-4.25	-4.25	-4.50	-4.50	-4.75	-4.75	-4.75
10		-4.00	-4.25	-4.25	-4.50	-4.50	-4.75	-4.75	-4.75	-5.00	-5.00

As 'n' and 'm' both get large, the size of the Limitation will again go to -9.

 

I would probably go with the most restrictive case of one larger Power, make it -1/2 for two Powers, and add an additional -1/4 per extra Power in the set.

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Re: Value of Anti-Linked

 

Um' date=' why not just put both Powers into the same Multipower? Problem solved.[/quote']

What if the Powers are part of a well-put-together Elemental Control? What if the Powers are part of a larger Multipower that has a Reserve that is big enough for both of them to be active at once? What if the Powers are part of a, "single spell," that you want to put into a VPP?

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Re: Value of Anti-Linked

 

What if the Powers are part of a well-put-together Elemental Control? What if the Powers are part of a larger Multipower that has a Reserve that is big enough for both of them to be active at once? What if the Powers are part of a' date=' "single spell," that you want to put into a VPP?[/quote']

 

Personally I think that you're over-thinking this. In all those situations I would say use the lockout disadvantage. You're original idea is a good one, and one that is already in place in the Hero system. (In the rules the limitation is a much more limited version.)

 

Another way of saying it is: Limited power (Cannot be used with power X) -1/2

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