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remote-site-searching

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remote-site-searching [2025/01/16 16:50]
isitaris [Formula] 		remote-site-searching [2025/01/16 17:15] (current)
isitaris
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 ====Scenario ==== ====Scenario ====
-Searching with a X2 mage (no crosspaths) using a remote search spell for a given number of turns, then searching manually by walking and using the search order on a new province every other turn for another given number of turns.+Searching with a X2+ mage (no crosspaths) using a remote search spell for a given number of turns, then searching manually by walking and using the search order on a new province every other turn for another given number of turns. 
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 +I have not tried modelling mages with more than one path.
  
 ====Variables definition==== ====Variables definition====
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 The expected number of gems received since starting the remote searching is: The expected number of gems received since starting the remote searching is:
  
--C·r -------------------------------------- cost of the r remotes\\+- C·r ------------------------------------- cost of the r remotes\\
 + r·(r+1)/2·G  -------------------------- gems found by the remoted target provinces during the r turns of remote searching\\ + r·(r+1)/2·G  -------------------------- gems found by the remoted target provinces during the r turns of remote searching\\
-+ (N-r)·(N-r+1)/2·g·2 ----------------- gems found by the remoted target provinces during the 2·(N-r) turns of walking search\\ ++ (N-r)·(N-r+1)/2·g·2 ---------------- gems found by the remoted target provinces during the 2·(N-r) turns of walking search\\ 
-+ 2·(N-r)·r·G ------------------------- gems found by the N-r provinces searched manually during the 2·(N-r) turns of walking search\\++ 2·(N-r)·r·G -------------------------- gems found by the N-r provinces searched manually during the 2·(N-r) turns of walking search\\
 + (T-(r+2·(N-r))·(r·G+(N-r)·g) ----- gems found by all the provinces during the T-(x+2·(N-x) turns left after everything has been searched\\ + (T-(r+2·(N-r))·(r·G+(N-r)·g) ----- gems found by all the provinces during the T-(x+2·(N-x) turns left after everything has been searched\\
  
 to be compared with N·(N+1)/2·g·2 when casting 0 remotes . to be compared with N·(N+1)/2·g·2 when casting 0 remotes .
  
-Here is the difference for 15 provinces and T=2x15 turns of horizon (that's a lot) as a function of the number r of remotes used: https://www.desmos.com/calculator/hlhzskmuvr+====Result with an example==== 
 +Here is the difference for 15 provinces and T=2x15 turns of horizon (that's a lot) as a function of the number r of remotes used: https://www.desmos.com/calculator/hlhzskmuvr. The values entered for G, g and C are those for the F path with a F2 mage and with LA gem frequency in Dominion 5, but they can be edited to fit your own scenario.
  
 The optimum way of searching those 15 provinces with a single mage if you look at your gem income in 30 turns (ie when the mage has finished walking in the no remote scenario) seems to be 5-8 casts of remotes (less than a gem of difference). (assuming no error in the modeling)  The optimum way of searching those 15 provinces with a single mage if you look at your gem income in 30 turns (ie when the mage has finished walking in the no remote scenario) seems to be 5-8 casts of remotes (less than a gem of difference). (assuming no error in the modeling) 
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 +Contact: Isitaris on most dominion's discord servers
remote-site-searching.1737046217.txt.gz · Last modified: 2025/01/16 16:50 by isitaris

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