Competitive Chapel variants
We continue to evaluating the Chapel, but now concentrate results rather than how to analysis.
Single Chapel
Previously we saw that using a single Chapel does not yield great results when not buying Duchies and Estates. But what if you allow both the Chapel and the competing Big Money strategy to do so? Finding the optimal strategy is not easy, and I’m open to suggestions to make it better. My current best is Single Chapel 1, and is very much a combination of Single Chapel canonical 1 and Bmu. Optimal [d/e] values for the Chapel strategy seems to be [3/2] but [3/1] gives almost identical results. Single Chapel strategies favor buying Duchies and Estates later than Big Money. Which makes sense to me.
But how good is it?
Single Chapel 1 wins 5319 (55%)
Big Money Ultimate wins 4306 (45%)
Ties: 375
Hmmm, not impressive. But on the bright side I finally found a graph that makes it easier to understand what is going on: the average change in VP (delta VP), weighted with the percentage of games that is running. Say that Bmu -on average- gains 3 VP in turn 18, but only half the games are still playing in turn 18 then the graph will display a value of 1.5.
The result is a sort of relevant average VP gain in a given turn. The area under the graph is a measure for the total score of the strategy over all games. From this graph it is possible to compare how well strategies are contributing to certain stages in the game, as well as do a general overall comparison.
The simple conclusion is that the single Chapel strategy just does not cut it, barely beating Big Money. The graph shows the Chapel strategy outperforms Bmu from turn 13 onwards. But the negative scoring in the first turns seems to roughly match the better performance in the later turns. So even with Duchies and Estates in play, the trashing of the Estates still hurts the Chapel strategy a lot.
Chapelab
Ok, moving on to a more competitive strategy: Chapelab. In this strategy you combine the trashing power of Chapel with the non-terminal drawing power of Laboratory. The idea is that you create a deck that can draw all cards each turn, guaranteing a Province draw each turn. Matt Sargent posted an elegant set of rules for a Chapelab strategy in his article on Board Game Geek. It only buys 2 Golds and at most 4 Labs and scores 61% against the Bmu. We can do even better if we take the basic buy rules from single Chapel 1, and the trash rules from Matt’s strategy to form a hybrid strategy.
The results:
Chapelab 1 wins: 6356 (66%)
Big Money Ultimate wins: 3224 (34%)
Ties: 420
The graph shows that with the addition of Labs the Chapel starts to seriously out buy the Bmu in turn 9, which is 4 turns earlier than without the Labs. From turn 10 the influx of Provinces hurts the buying power, but in turn 14 the buying power of the Chapelab increases again. I guess that is due to the extra Golds being bought when Provinces were to expensive.
Thoughts so far
Given the reputation of Chapel, I’m not impressed with the performance of real Chapel strategies. It’s actually nothing new if you have read Matt’s simulation results, but I don’t share his conclusions that the Chapel is a good card until I actually see it shine. From his data I would guess that Chapel performs better as a counter to opposing curses, which was what it was intended for in the first place. I will have to investigate. But not before looking into a very specific Chapel based strategy.
Up next is Turbo Remodel.
[Edit: I decided that card names should be capitalized.]
I’d be interested in seeing how the Chapel strategies do with less of an emphasis on Silver. What if you removed the rule that stops the trashing of Copper if it would prevent a Silver buy? For instance: when I draw Silver + Copper + Chapel + Copper + Copper in my hand early, I always Chapel all three Coppers.
Likewise, I also avoid buying Silvers (in favor of other cards) after about the second or third reshuffle, but I guess that’s harder to model.
Thx for the feedback, I might simulate that. My general tinkering showed that it is better to buy silvers when you have the hand you describe. But stopping buying silvers after a certain turn, I did not try that.
Nice work – it’s been interesting gaining some insight into the strengths and weakness of these simple models – it seems like a great place to start.
When reading your strategy files I did wonder if allowing the duchy / estate buying decisions to be determined by factors such as difference between each players score, number of cards to draw until reshuffle and which player went first may allow for small optimisations. (I’m sure number of provinces left is still the most important variable though).
For the purpose of your analysis though I guess it’s largely irrelevant – as a) all the examples where I’d want to switch from the given buying decisions are probably quite rare occurrences – and b) any advantages that could be gained like this by one side could also be gained by the other, so for the purposes of evaluating the core of the paradigms I guess a simpler model is sufficient.
Keep up the good work!
You say Chapel doesn’t seem all that strong even when combining it with a Laboratory, but in real games with a silly combo on the board, the chapel will allow the quickest enabling of that combo. A little example:
http://dominion.isotropic.org/gamelog/201101/31/game-20110131-024450-9625600a.html.gz
No other card than Chapel will allow such a degenerate game state so quickly.
Thx for challenging me. And I think you are right that no other card allows you to cull your deck as fast as chapel does. If the board contains a very good -or silly, as you call it- combo, then I guess that removing the unwanted cards really speeds up the combo.
The problem I have with Chapel is that people expand that scenario and conclude that it is a really good card. So I turn it around, and demonstrate that in the other extreme: having only a single other action card to play, chapel is not that good. I actually believed that Chapelab would be viable strategy before I simulated it. If you compare the results of Chapelab (66%) to just buying Labs (61%) then the benefit of chapel is marginal. I find that interesting.
The real problem is the definition of a “real game”. I don’t consider the example a real game because it contains too many great cards from Prosperity. But if you can point me to a single card that the chapel boosts significantly, then I am very interested.