When there are how many Provinces left (if that is the way the game will most likely end), should you switch from buying Gold to Duchy (when you don't have 8 money)? Does this amount change for 3, 4 player? Is there a good rule of thumb based upon the number of players/potential buys before your next turn?
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For 2 player, the generally accepted tipping point is when there are 5 Provinces left, buy Duchies (and Estates when there are 2 Provinces left). This has been shown as optimal according to simulator testing for BM-based strategies (e.g., BM only or BM + any given card, e.g., Smithy). For race games (e.g., Gardens or IGG), the tipping point is much earlier, although it depends on the set in question. The answer will also change if you or your opponent is playing a mega-turn engine deck.
For multiplayer, the key is to remember that 3 player games have 4 Provinces/player, just like 2 player, but 4 player games only have 3 Provinces/player. So, the Duchy-buying should occur earlier in a 4-player game.