1163
« on: May 27, 2012, 12:26:26 pm »
Suppose we're playing Borinion, a much more boring game then Dominion. Two players, P1 and P2, take consecutive turns. P1 gets to start, and due to the unfair nature of this game it ends after 9 turns. So P1 always gets to make one extra turn. Both players start at 100 points, and every turn they choose...
option A: 60% chance at +3 points, 40% at -3 points
option B: 50% chance at +5 points, 50% at -5 points
option C: 40% chance at +10 points, 60% at -10 points
If you play this game in isolation, it's easy: always option A is best. In fact, it's the only option with a positive mathematical expectation. Simulation over one million games shows that if both players follow this simple minded strategy, P1 will win approximately 555000 vs 445000 (55.5 win% for P1).
However, this game is not about scoring as many points as you can. It's about scoring more points than your opponent. And thus, plans that might look bad at first glance end up being better after all.
Suppose we leave the game plan of P1 what it was ('always go A'), but experiment a bit with P2. If we change it to 'option A when ahead, option B when behind' the win% for P1 drops to 51%. 'option A when ahead, option C when behind' works even better; now P1 only wins 46% of the games. We can improve P2 further by delaying the risky things, and enforcing option A on his first turn (42.5% for P1) or his first two turns (42.1% for P1).
I'm starting to get convinced the optimal strategy is actually quite complex. I think it uses all 3 options, and also includes the 'turns to go' and 'actual point difference' (not just 'am I behind or ahead'). But I won't go into that - I didn't name it Borinion for nothing.
So what does this game teach us about Dominion? Most of all that the optimal strategy always involves your opponent. Even on kingdoms without any attacks, it matters a lot what he's doing and how well he's doing. If you both start out the same, but he has some shuffle luck and you don’t, it's time for crazy things. I he stumbles where you thrive, try to buy safe cards.
It also suggests it’s good to have options. If you create an option B, C or D for yourself to use later on, that choice itself is already good. Engines give you much more options than BigMoney. So in playing engines right, it's not just about 'how can I effectively build this engine in solo play'. It also requires a good feeling/understanding for taking risks. Simulators we use today don't understand it at all, and that may very well be the reason variants of BigMoney strategies do so well in simulation and so poorly in reality.
Opening two terminals isn't all that bad just because they might collide. P1 has no real reason to take this risk, but P2 is already behind at the start. It of course depends on the questions 'how good is it if they don't collide' and 'how bad is it if they do'.
One of my favorites is double Steward, because if they collide I can still get rid of 2 cards. I wasn't going to do much more on a turn with steward without collision anyway. Don't get me wrong - I'm not happy with the collision at all - but it's not a game losing disaster either. And depending on the kingdom, being able to get rid of 4 cards in the first round may very well be winning. As a rule of thumb, opening with two terminals is too soon to take risks though.
It’s not easy to define risky or safe things in general. A safe choice that happens often midgame is adding a little more +actions to your deck than the bare minimum. Another safe choice is to stop playing your engine where you could draw some more cards, just to prevent a reshuffle. Maybe you can put a good card on top for next turn?
Risky things could include adding more cards that require other cards (Baron, Remodel, Forge) or buying slightly too many terminals in general. Village + smithy is more risky than laboratory + laboratory. Swindler has the risk build-in all by himself. So do treasure map and tournament, but they’re not really an addition to a deck - they require building your entire deck around them.
In the endgame it can get quite complex because of the ending conditions of a Dominion game. The most common risky thing is buying the next-to-last province. There is a rule for not doing it, but even if it made you lose, that doesn't automatically say it was a bad thing to buy it. If your deck is not so good, and you're losing the long run for sure, try to sneak out a victory now.
To summarize: constantly figure out whether you’re ahead or behind. If you’re ahead consolidate, if you’re behind make a plan to get back. As player 2, you’re behind when you start - do something with it.
I won't say I love it, but I certainly don't ignore it either. It doesn't feel like the lamest $3 card to me at all. 