WanderingHead
Posts: 2134
Joined: 9/22/2004 From: GMT-8 Status: offline
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OK, bearing in mind that I am in a kind of brainstorming mode, just throwing out ideas. One issue I see is that if you are behind in one tech, you have some probability of stealing it. If you are behind in N techs, you have the same probability for EACH tech, so now you will actually steal N times as many tech points (on average) just because you are further behind in so many. For the same investment. Perhaps the incremental probability of stealing techs should be reduced the more techs you are actually behind in. For example, change item #10 (#9 shown just for reference)9. If Random (Attacking Spies *2) > Random (Defending Security) then technology can be pillaged.
10. If Random (Attacking Spies) > Random ((Defending Security) * (1 + (number of eligible techs behind)/2)) then
gain 1 research point in technology you are behind in. If we set N=(number of eligible techs behind) and look at the probability of stealing a tech, for attack<defend (this restraint just for simplicity of analysis, and with this formula it is valid for large N anyway) we haveprobability(#10 satisfied) = att/def/(2+N)
= att/def/3 (N=1)
= att/def/4 (N=2)
= att/def/5 (N=3)
= att/def/6 (N=4)
~= att/def/N (N large) Which means that the average number of stolen techs passing #10 (assuming #9 already passed for the time being), given that the above is applied to all N techs, is ave #techs passing #10 = N * probability(#10 satisfied)
= 1/3 * att/def (N=1)
= 2/4 * att/def (N=2)
= 3/5 * att/def (N=3)
= 4/6 * att/def (N=4)
= 5/7 * att/def (N=5)
~= att/def (N large) So you always get a little more when you are behind in more techs, but not linearly. In other words, if you are behind in 1 tech you can have a reasonable chance to steal it, but if you were behind in 10 techs you'd only have a reasonable chance of stealing about 3 or 4 instead of stealing all 10. I know the math may look too much for the non-mathematically inclined, but I think it just plain makes sense, frankly. You shouldn't be able to steal so much more for the same cost just because you are behind by more. This would also discourage throwing a point of research here and there just to be able to steal the techs, because you'd now rather focus on the techs you care more about. So you'd only throw a point into something that you were really prioritizing.
< Message edited by WanderingHead -- 10/5/2007 8:58:54 AM >
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