====== Analysis of remote searching strategy ====== ====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. I have not tried modelling mages with more than one path. ====Variables definition==== C: cost of the remote\\ r: number of provinces searched with a remote\\ N: number of provinces to cover with the mage\\ 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)\\ ====Formula==== The expected number of gems received since starting the remote searching is: - 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\\ + (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\\ + (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 . ====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