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--- remote-site-searching [2025/01/16 16:48]
isitaris
+++ remote-site-searching [2025/01/16 17:15] (current)
isitaris
@@ Line 3: / Line 3: @@
 ====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.
+I have not tried modelling mages with more than one path.
 ====Variables definition====
-C: cost of the remote
+C: cost of the remote\\
-r: number of provinces searched with a remote
+r: number of provinces searched with a remote\\
-N: number of provinces to cover with the mage
+N: number of provinces to cover with the mage\\
-T: number of turns considered total (T gotta be larger than 2N here)
+T: number of turns considered total (T gotta be larger than 2N here)\\
-G the expected gem income from the remote spell, g the gem income from the mage search (per turn value)
+G: the expected gem income from the remote spell, g the gem income from the mage search (per turn value)\\
 ====Formula====
 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 .
-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)
+Contact: Isitaris on most dominion's discord servers

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