Okay, I've played around with the simulator a little and was somewhat surprised.
The optimal value for D (buy a Duchy if P <= D) seems to be 7 with the BMU strategies.
It seemed somewhat high to me, since 7 Provinces seems still a long way to go.
On the other hand, 5 Provinces are already gone which is 1.67 per player and this is less than in a 2p game.
Am I right in thinking 3p games are more "scrambly" than 2p? In 2p games, you can somewhat control the pace of the game and react to to your opponent's style. 3p's (and probably especially 4p's) are more "free for all" style games in which you have to focus more on yourself and grabbing as big a share of the points you can get. I think it's a lot harder to control the game and use the normal 2p rules of thumb like the PPR. You may withhold from buying the penultimate Province, have your neighbor buy it and the third player as well, making yourself lose to both.
In the tournament format I mentioned in which you get points for 1st, 2nd and 3rd place (a percentage of the points gained in each game is also noted for tiebreakers, e.g. 40 of the total 98 points shared between 3 players gets you 40,81%), I think it's more essential to just focus on getting the green instead of going all out or bust for the win. Surely, you want to win and getting a lot of green will help you towards this goal.
I am hoping to see some input from Theory and RRenaud, since they played at GenCon or WBC, see this topic:
http://forum.dominionstrategy.com/index.php?topic=439.25 and probably have some experience with 3p.
Some more Simulator findings:
- A single Workshop/Gardens crushes 2 BMU's (and BMU Militia for that matter) hard: 99%
- 2 Players going for Workshop/Gardens will share their wins with the 3rd BMU player winning virtually 0%, although this may be tweaked to make the 3rd player more privy to what is going on and try to react somehow.
So if I see 2 players open Workshop/Workshop before me, I guess I just have to join the fun and hope my shuffle luck is better than theirs.
If I try adding some juice like buying Duchies, the results only get worse. Of course, being 3rd can really hurt, since there are only 10 Workshops and 6 will be gone the first round, meaning we will need some luck getting at least one more!