The following guest article is written by Jeroen Aga (Geronimoo on Isotropic).
Last time I left you with the conclusion that combining Mountebank with Warehouse is superior to the combination with Caravan (but only by a very slim margin). Judging from the comments my readers are either very smart, very educated or very both, neither of which I am, so I’ll try to avoid drawing any conclusions and let you guys figure it out yourselves from my observations with the simulator. Here’s the second (and final?) part of my analysis of theory’s first annotated game:
Emulating real player’s strategies
I re-read theory’s game annotation and programmed the strategies I found into two (ro)bots. Here are the little fellows (aren’t they adorable?):
The theory bot emulates theory’s behavior in the annotated game and vice versa for the Yaron bot. I tried to get their behavior as close as possible to that of the real players.
Here are the bot’s buy rules. I didn’t include the other Kingdom cards like Secret Chamber and Harem to keep things simple. Their impact on this game seemed minor anyway. I’ve also omitted the play rules because they are almost trivial:
Buy Rules (theory-bot): -buy a Province (if you’ve bought at least a Gold) -buy a Duchy (if there are only 5 Provinces left) -buy an Estate (if there are only 2 Provinces left) -buy a City (if there are only 7 Cities left) -buy a Mountebank (buy maximum 2) -buy a Gold -buy a Warehouse (if you’ve bought at least a Province) -buy a Caravan (if you’ve bought at least Warehouse and Silver) -buy a Warehouse (if you’ve bought at least a Silver) -buy a Silver -buy nothing
Remember these buy rules will be read by the simulator top-to-bottom and he will do the first thing he’s capable of and then stop reading; extra buys will make him repeat this process. Unless you’re thinking in zeroes and ones this is hard to read, so here’s what these buy rules come down to:
- the theory-bot will open with Silver/Warehouse (Mountebank/nothing on $5/$2)
- It will get Mountebank as soon as possible (over Gold).
- After the first Warehouse it will buy Caravans over them
- No more than one Silver will be bought
- when he sees the Yaron-bot going for the Cities he jumps on them as well (like in the real game after Yaron has 3 of them).
- Warehouses will be bought over Caravans as soon as the end game starts (when VP’s are being bought).
Buy Rules (yaron-bot): -buy a Province (if you’ve bought at least a Gold) -buy a Duchy (if there are only 5 Provinces left) -buy an Estate (if there are only 2 Provinces left) -buy a Mountebank (buy maximum 1) -buy a City -buy a Gold -buy a Warehouse (if you’ve bought at least a Province) -buy a Caravan -buy a Warehouse (if you’ve bought at least a Silver) -buy a Silver -buy nothing
- the yaron-bot will open with Silver/Caravan (and Mountebank/nothing on $5/$2)
- It will get one Mountebank as soon as possible (over Gold).
- He then jumps on the Cities (over Golds)
- Caravans will be bought over Warehouses
- No more than one Silver will be bought
- Warehouses will be bought over Caravans as soon as the end game starts
The difference comes down to the yaron-bot opening with Caravan/Silver instead of Warehouse/Silver and immediately jumping on the cities while the theory-bot starts buying Cities later. I think this emulates the actual game quite nicely.
Here’s the resulting clash (10,000 simulations):
The yaron-bot gets crushed! It seems to be stuck buying out the City pile while the theory-bot is already buying Provinces. Level 0 Cities are identical to Villages and don’t improve your buying power until they level up which explains the long flat line on yaron-bot’s graph. When the Cities get into first gear (one empty pile) the yaron-bot finally starts to outbuy the theory-bot, but it only profits from super-charged Cities for two turns before the game ends (mostly on piles).
Improving the bot’s strategies
Let’s play around with our bots a little. This is what happens when we let the theory-bot completely ignore the Cities:
As this graph shows and some posters speculated, theory shouldn’t have been afraid of yaron’s so-called City advantage and could have completely ignored the City pile. By ignoring cities, his winning percentage increases from 70% to 89%.
When I helped out the poor yaron-bot by letting it buy Golds over Cities its win rate improved to 35% against theory’s Cityless strategy. So, still a big dog!
Answering our initial question
Finishing up, let’s make both strategies identical with one small difference: theory-bot uses his Warehouse/Silver opening and yaron-bot goes for Caravan/Silver. The rest of the buy rules are identical (so no more Cities since they are probably not part of a winning strategy):
As expected the Warehouse/Silver opening has a tiny edge over the Caravan/Silver opening in the complete strategy where players are buying a mix of Caravans, Warehouses and Mountebanks. This complete strategy has about a 20% edge over the Warehouse-only and Caravan-only Mountebank strategies from part I.
I’ll be “ready” for you to crush me on isotropic!