Deep underground, for reasons of profit

Last week I played a game of Castles of Mad King Ludwig with some friends including Naked Man.  I went hard into basement rooms and came out the victor by a substantial margin, largely on the back of 2 key things.  First, I had ridiculous cards.  I got the first stairway and ended up building all 6 basement rooms using 4 stairs in total.  This set me up perfectly for the basement card for 12, stairs card for 8, completed rooms for 7, and 450 rooms for 6.

The second thing that won me the game was me getting the basement room that likes basement rooms, and then rescoring it when I closed it as my sixth basement room.  That part was kind of funny, actually, as nobody else saw that as a possibility.  Many players, most even, seem to get stuck on the idea that when you score a basement completion you simply take another turn.  That is often good, but it isn't anywhere near automatic.  Taking another turn often involves getting 7 points for 2 bucks or so, and that is often worse than 5 pure points, 10 bucks, or rescoring the basement room itself.  Heck, even a Hail Mary for a bonus card or a blue room dig can be the best play at times.

The surprise came on the final turn of the game when I was master builder and everybody else bought the most expensive stuff from me, leaving me with a collection of mediocre tiles worth about 5 points each.  Nobody expected me to buy a hallway and rescore my basement that loves basements... but doing so got me 14 points in total so it was automatic.  Didn't matter to me what was left on the board, nothing was going to be as strong as that, especially for only 3 bucks!

Naked Man spent much of the early game insulting my basement investment, talking about how lots of basement rooms is bad.  After all, all but one of them give bonuses to upstairs rooms, so you really want two basement rooms that match your upstairs really nicely, in an ideal world.  Getting a ton of basements generally means each one is only worth 4 points or so, and that is quite weak.  I agree with this principle in general.  I like having a stairs available so nobody can pin me on basements, but I don't generally want to get more than two basement tiles.

However, when you have the basement card, and intend on rescoring the basement that loves basements... that +6 points / tile really changes the math a LOT.

Also I was extremely pleased to crush Naked Man with basements after he spent so much time telling me how terrible they were.  I was sitting to his left, no less, and he still couldn't stop me.  Or at the very least he did not choose to stop me - he could have taken the critical tile from me, but it would have cost him 8 bucks and would have only been worth 3 points to him.  Still, doing so would have dropped my final score by something like 19 points overall, which is a pretty crushing blow.  It would have given him the victory, I think.

The lesson here is firstly that yes, most of the time lots of basements isn't great.  Secondly, if you close basements, do not just automatically take another turn.  Regularly this is worse than other options.  Thirdly, if you happen to talk to Naked Man, ask him how he managed to lose to someone employing a massive basement board, given how bad basements are.  I am sure his reply will be entertaining.

Crushing lefty's dreams

Below is a picture of my final board at the final table of the world boardgaming championships Castles of Mad King Ludwig tournament.

I am not that happy with this board.  My bonus cards got me 14 points which is about right for 3 cards but I had to work hard to get those points, taking tiles I otherwise wasn't that happy about.  I also didn't time the ending of the game all that well and had to put my 300 elbow blue room on just to finish up my purple room instead of planting something better there.  With one more turn in the game my position is drastically better as I can get an additional 4 points for the blue room and probably another 4 points for whatever red / green room I used to finish off the purple.  Still, I got second overall in the tournament, so I can't complain too hard about it.

The most interesting point in the entire game to my mind was on turn 1.  I was fourth chair (Fourth chair is awful in CoMKL, and next year I hope we are on a bidding system for seating) and Drummo was in first chair.  The flop contained the basement that likes basements, a 300 blue room, and a bunch of random stuff.  The blue room is relevant because both of the blue room favours were out, so blues were extremely high value.

Drummo arranged the tiles with the basement in 1, four reasonable rooms in the 2, 4, 6, 8 slots, and the blue room at 10.  First player bought a stairs, second player bought the room at 4, I bought the circular green room at 2, and Drummo was faced with a decision.  His purchases at 6 and 8 were bad, so realistically he was either buying a stairs for 3 or paying 10 for the blue room.  This decision was critical because player two was the only one in stairs, and the corridor square footage and completed rooms favours were out, heavily favouring basement play.  If Drummo buys the blue room, player two gets the basement that likes basements for free on his master builder turn, and also gets to stockpile a ton of cash.  This puts him in a dominating position.  If Drummo buys stairs then Drummo has position in terms of buying basement rooms ahead of the others stairs and has more cash on hand to run through the next 3 turns.

Drummo bought the big blue room for 10.  Player two happily put the basement at 1 buck on his master builder, got it, and proceeded to win the game in part by dominating the completed rooms and corridor square footage favours.  Drummo came last.

I am pretty sure that this was the key play that set up that victory.  Now, player two played a tight game throughout, and I don't want to take away from that.  But getting that basement room for free and making sure he had a big bankroll right from the outset was crucial to his dominance.  Drummo also had cash problems throughout the game, and I think these were exacerbated by him blowing too much of his stack on turn one.  The blue room he got ended up being worth 11 points, but buying 11 endgame points for 10 bucks on the first turn seems too aggressive to me.  Plus there is the argument that you need to be defensive and prevent any one player from getting too great a deal.  This is something I focus on hard in CoMKL, more so than other players I think.

We were talking afterwards about the play and defensive play in general.  Someone said that if I really wanted somebody to take the defensive stairs I should have done it myself.  This is reasonable as a general rule, but I don't know that it applied here.  I was fourth chair, so other players expecting me to be the one to give up value for defence seems unreasonable.  Plus Drummo was in the ideal spot to defensive stairs, him being directly before the other stairs.  Moreover, he lacked other good value options.  He wasn't giving up a great buy to defend, just foregoing what I see as a sketchy purchase for 40% of his stack.

In general you can't just refuse to defend and always expect the last person in last to do the defending.  People won't put up with that sort of leverage being applied if they are good.  On the other hand you probably should expect defensive play if the player in question has no other good options.

At any rate this game really reinforced the value of position in CoMKL.  Playing after me is not ideal because I am going to play defensively.  I will guess your cards held (made 3 guesses during the final match and was correct on all 3) and work hard to prevent you getting the tiles you want.  But some players lean far more towards offence rather than defence and playing after them will get you deals now and again.

In the end the game itself was a great experience.  I am friends with all three other players at the table and having a final table with three strong gamers in a game I love where everyone has a good time is a far more positive experience than merely winning.  It doesn't hurt that Drummo and I were trashtalking the entire time and I crushed his hopes and dreams along the way.  He claimed that since I didn't win the game I can't really crow about my victory... but I submit that I beat him and the player to his left won, which thoroughly cements my claim of superiority at CoMKL.  If lefty wins, you should have done something about that!

Maybe next year I will finally get my 1st place trophy at that game.  Eventually a final table has to work out for me!

Push that lever

This past weekend I played a lot of 1v1 board games.  I won them all, and I won them all in the same way - pinning my opponent into a spot where I had leverage against him that forced him into terrible choices.  Both in Agricola and Castles of Mad King Ludwig you can put your opponent in nasty situations when they are short on the key resource of the game - food, or money, depending on which game you mean.

Squeezing an opponent on food is something that I learned a lot about at Farmageddon.  The players there are good enough that they can easily keep track of exactly how I am feeding myself and if I got too aggressive with my food plans they would happily punish me for it.  I got a much better sense of exactly how close you can get to the edge in playing there, and I used that sense to deliver some crushing blows over the past few days.

In all the games I won long before the final turns arrived.  In each case I spent early actions collecting food so that when crunch time came my opponent had to scramble to get food and I could rake in all the piles of resources.  Several times I grabbed piles of food I didn't need just to pin my opponent into having to take actions for 1 or 2 food and that let me rush out to enormous early leads.

Observers in the games seemed to feel I was being mean.  After all, why take stuff you don't need, just to make your opponent suffer?

Well, for one, winning isn't about having the highest possible score yourself.  It is about having the highest possible differential between your score and your opponent's.  Secondly, pinning someone into taking terrible plays gives you all kinds of great stuff.  In one game I won 29-58 because I kept my opponent off of wood for pretty much the entire game.  Every time 6 wood came up I managed to put him into a spot where he was starving and he couldn't take it, so I ended the game with 4 wooden rooms, 15 fences, and 4 fenced stables while he had no fences or stables at all.  My huge score was on the back of keeping my opponent unable to take the great stuff that came up, so my aggressive play ended up not being about spite, but rather about setting up big turns.

Sometimes you don't realize how much you have learned until you really get an opportunity to use it like this.  I have improved a lot at Agricola in particular, and playing against someone who is solid at the game and ruining him made me see how much better I have gotten over time.  That is harder to notice when you are playing against experts.

Of course afterwards we cracked out Crokinole, a Canadian dexterity game, and he blew me out five games in a row.  I guess that means I should stick to the games I know!

Half a game

Over the past little while I have been playing a lot of Castles of Burgundy and Castles of Mad King Ludwig with just 2 players.  I really like both games, though certainly Mad King is the better of the 2 castles games, but I am struggling to love the 2 player versions because the level of randomness is ratcheted up in ways I disapprove of.

This weekend I played 2p Mad King against Naked Man and came out victorious.  He had beaten me the past 8 times we played so this was good for my ego, though honestly when many of those victories came down to just a couple of points either way one should hesitate to draw significant conclusions from a streak.  When we play 4p we both consistently clobber the other players so I don't have to sit up at night worrying about being total rubbish.

The weird thing about both Castles games is that the tiles that appear in the 2p version are roughly half the ones that appear in the 4p version.  In the 4p game you can predict things.  You can assume that there will be basements in the game in Mad King, and you can expect the "Points for shipped good types" tile in Burgundy.  You can plan!

But when half the tiles are removed from the game randomly you have no idea what sort of stuff is coming up.  You can decide to go for sheep in Burgundy and then never see another sheep tile.  You can finish a blue room in Mad King and dig into a pile looking for more blue rooms and find none at all.  I had this come up in my last game because I was staring at 4 200 size tiles knowing that there might be 2 blue rooms in there, which would be great, or there might be none.  The mean and mode of the distribution is 1, but you just don't know what it is until you invest resources to find out.

This doesn't make them bad games, but it seriously changes the flavour of the game.  Memorizing all the tiles and planning around them is great and I enjoy it but you can't rely on your knowledge when you don't know what stuff is available at all, which forces you into either safe plays or big gambles.

The 2p version of Mad King also has greater randomness in the bonus card draws.  When all the tiles are in play you have a lot more control and you know with greater accuracy what stuff will come out so all bonus cards have potential.  But in 2p some cards that you select correctly will end up being rubbish with little you can do about it.

This effect doesn't make these games bad.  It just changes them in ways that feel like they break the feel of the game.  It isn't just a new set of strategies, it is a new game entirely in terms of the way randomness and preparation affect results.  It is odd particularly because most games that scale down to 2p seem to up the skill factor a lot, and while these two games do that, they also ratchet it back down again by randomly tossing out half the game without anyone knowing *which* half.

Endless corridors

This year on my annual trek to Thunder Bay I got in a couple games of Castles of Mad King Ludwig and they had one odd thing in common with one another - in both games the bonus point favour pucks had the bonus for number of corridors and also square footage of corridors.  When you have both of these in play it warps the game quite substantially as everyone rushes to build hallways instead of ignoring them as is usual.  Also the 350 corridor rooms which are normally the worst cards in the deck end up being quite powerful and often sat in the 15,000 spot because people were terrified of others getting all that corridor space.

My feeling is that when the corridor favours are both out the game really favours experienced players.  Most of the favours aren't that difficult to sort out - if purple rooms are the bonus, then you think of each purple room as being worth +2 points.  Not exactly complicated, and at the end of the game you can math out their exact values to you fairly easily.  Corridor rooms cause a lot more consternation though because you have to figure out how to sequence your plays to get lots of them at just the right time.

In the second game my second last turn was simply playing the second last Stairs.  Not what you want to do with your second last turn most of the time!  However, my last turn was playing a basement room to finish those stairs, getting a bonus stairs up out of the basement room, using that basement room completion to take another turn, building a yellow room on the end of the stairs going up, using my free bonus hallway (emptying the hallways) to finish the yellow room, getting another turn, and using that final turn to by the 350 corridor to snatch both most corridors and most square footage of corridors.  Five tiles laid in a single turn was enough to absolutely blow out the game in my favour.

Setting that up and realizing that you will get to do it is not something a starting player is going to do, even if they are good at games in general.  It takes time to get used to how best to use extra turns and extra Hallways/Stairs and if you have that all sorted you can do some nutty things.  Beginners at the table found themselves cut out of Stairs and Hallways unexpectedly and that can be really key if you have been building your game around getting a specific amount of those things on the board.

This has made me like Castles even more than before.  The changing favours really keep you thinking and make new playthroughs different.  You can't just develop a simple metric for how good each room is so you have to recalculate everything each time through.  While eventually you would get used to the favours that come out something is always going to be a bit different in the game to keep it fresh and new.

Note to self:  In a game with all the Corridor favours out, Hall of Mirrors is *really* good, even if you get it halfway through.

Hang out next to the kitchen

I played Castles of Mad King Ludwig last night and was asked a tricky question at the end of it.  I was in seat 4 and won the game by about 15 points or so, and the player in seat 2 asked what I thought of her arrangements of the tiles during her master builder turns.  2 had the issue that she ran low on cash in the middle of the game and felt like she just hadn't been able to make enough money.

It is tricky sometimes to figure out whether arrangements were correct when you didn't know at the time what everyone's cards were.  I might look askance at a placement but if a tile has 5 bonus points on it from secret cards it really changes how you think about it, and how the placement goes.  That said, I thought her placements were fine and she certainly wasn't giving up money like crazy.

So why was it that 2, who should have had more money than me because I was 4th chair, struggled with cash?  Also why was it that I ended the game rich?

A big part of the answer is yellow rooms.  Yellow rooms give you extra turns and you usually want to use those extra turns when you have the best selection, so most of the time you use them when you are the first player to choose tiles.  Also when you use yellow rooms you end up paying a ton of money out all at once, so you really want to do that right before your own master builder turn so that going low on cash won't break you.

When I thought about this I looked at the board and lo and behold the player after me in position 1 had three completed yellow rooms and I recalled distinctly that I got paid off on the turn when he activated two of them.  Not only did he buy three things, but the other players also bought stuff and I sold all but one of the tiles in front of me.  That happened on turn 4 and it took me from nearly broke to rolling in cash.

Part of this was deliberate of course because I priced those yellow rooms to move.  I wanted to get paid so I let people have some sweet buys to build up my bankroll.  But part of it was just luck because those tiles might well have come out differently.

I think the key is that you want the player after you to buy yellow rooms.  When they do that you can set it up so that they have multiple good buys and make sure that the options get scarce, which means that other players after them will often end up paying more for things than they would otherwise.  Cash itself may not be that great but I noticed during the game that I had plenty of chances to pay about X money for X points and that means that if I can sell an additional tile at 8 bucks it is absolutely amazing for me and could easily raise my final score by 8, assuming I am cash limited at any point.

Getting yellow rooms into the hands of the player after you is a hard thing to take advantage of.  Aside from giving away yellow rooms for really cheap on your own master builder phase it isn't exactly an easy thing to do and is highly luck dependent.  I think though that it strongly emphasizes the strength of giving people good deals on your turn when they have yellow rooms out no matter which seat they are in.  You don't want to give away the farm obviously but if you make sure that they are at least strongly tempted to use both turns you rate to get paid.  You can't afford to let them get a deal on a tile for 1 coin but any intermediate amount is pretty solid.  The trick is that they are going to spend those turns buying stuff.  Once they have the yellow room that much is a given.  What you can control though is whether or not those extra turns and the associated income come to you, or to somebody else.

That concept is a key thing to grasp in many games and I see a lot of players fail at it.  They often see someone setting up something big and do everything they can to stop it but fail to consider whether or not that interference will actually work for the whole game.  If someone sets up a big score and you know that they are going to cash in on it at some point you shouldn't desperately try to delay it; rather you should figure out how to cash in as much as possible personally when they finally do make their thing work.  Making sure people with yellow rooms use them on your master builder turn to get yourself paid is a great example of this.

The end times

Knowing the duration of a game is critical.  So often strategy games come down to various players building plans that will peak at different points in the game and the winner ends up being the person who manages to get the game to end just when their strategy peaks.  Puerto Rico is a great example, where the builders want the game to end as fast as possible because their strategy peaks right when their second big building finishes, while the shippers peak right when the last shipping point leaves the pile.  If the builders manage to finish the game quickly they will win because their strategy peaks much sooner.  Generally that means that in a game with three people shipping and one building the builder loses because all three shippers refuse to take actions that end the game and the shippers will help each other lengthen the game to generate more points from the Harbour and Wharf.  Similarly a single shipper will lose to three builders, with the winner almost always being the person who builds the Guild Hall.

During my birthday party on Saturday this was on display quite clearly.  I didn't get my timing perfectly right but on my last turn I completed my second Basement room and also finished off my big purple room to rescore it for 9 points.  I had thought the game would go one more turn and if it had I would have done better but I can't complain because I did manage to complete all of my major plans, albeit a bit awkwardly.  I won the game by a big margin, which wasn't a surprise because I was teaching all three of the other players the game.

Some of the other players asked what they had done wrong and why they lost, and as usual the obvious errors were mostly the placement of the best tiles on the 15k space.  In an auction game you don't want to let people get good stuff cheaply, but you can't keep the good stuff out of their hands indefinitely so you really want to sell it to them at a high price rather than having them buy something else for cheap.  The best tiles shouldn't be put out of reach - the optimal placement for them is *just barely* within reach.  That is when you get paid, and being rich gives you options, including the option to pay a ton for a tile if you really want to.

However, I don't think their tile placements were the reason I won by a lot.  The main factor was that I knew when the game was going to end.  I bought one big purple room and focused my game around bulking it up and completing my other stuff opportunistically.  The other players bought multiple big purple rooms and aimed to complete everything and they all ended up with a bunch of rooms incomplete.

There is nothing wrong with incomplete rooms in theory but you have to pick which ones you will leave out.  Buying a cheap 4 point room for 1 or 2 coins and sticking it on to close a door is a great play even if you make no attempt at all to finish it.  Paying 6 coins for a 2 point room that has a huge completion bonus and then never completing it is a disaster.  It isn't always true that buying a second big purple room to build around is a bad choice but you have to be really careful that you don't bite off more than you can chew.

One of the key tricks is knowing when to take the money and run.  I bought the big purple room that gives a 4 point bonus for each attached yellow room.  I quickly slammed another tile onto it that wasn't yellow because hoping to get a full 4 yellow rooms attached to it is just too optimistic.  You need to know when to start closing doors and accepting that you won't get the maximum points possible.  You can spend the game desperately trying to score 34 points from that room, but the likely result is that the game ends and you get 9 instead.  Being willing to accept a lower payout that is much more likely to come home is how you make 18 points like I did, and that is the more likely path to victory.

Knowing when to start finishing up is a skill that takes time to hone.  If you give up too quickly you won't score many points because you attach the wrong stuff, but if you wait too long you don't finish your room.  You want to end the game with every major completion bonus done, but only just barely.  Too soon, and you miss opportunities to max out.  Too late, and you get nothing.

It should not be taken that the people I played against were bad.  They played well, for first time players.  Castles is a game that is extremely sensitive to the timing of game end and I think that skill is actually one of the hardest ones to master when playing a new game.  You need a full understanding of the way the game flows before you can really make any decent decisions in that regard anyway, so until you have played a number of times figuring out how to design your plan to peak right at game end isn't really plausible.

For anyone looking for a best guess on how fast to finish up your rooms, I would suggest assuming that you need twice the number of plays as you have doors available.  If your big room has three open doors and there are about five turns left, start closing them off with anything you can.  If you have eight turns left, chill and wait it out.  With brick rooms you can generally assume about the same since there are more tiles that work and you don't get nearly as much from finishing it so you really don't want to slam crappy things on there.  Leaving a brick room incomplete isn't so bad because you got most of your points when you dropped it, so you can afford to be picky.

Expectations of success

Last week was World Boardgaming Championships week.  I had thought I might write gaming posts from the event itself, but the wifi was shoddy enough and the games were distracting enough that I never did get around to it.  This week I am to remedy that to some extent.

The short version is that I racked up eight semi final qualifications, played in six of those semi finals, advanced to the finals twice, and have a third place plaque for Castles of Mad King Ludwig to go with my second place plaque from last year.  I also got a fourth place in Santa Fe Rails, though for that I didn't get any hardware to clutter up my home.  Maybe that is a good thing?

Overall it was similar in terms of success to last year.  Both years saw two finals tables, though last year had better results at those tables.  In both years my team game was Puerto Rico, and in both years I failed my team by scrubbing out in the semi finals.

Also in other silly news I skipped the semi finals of Lords of Waterdeep both years to participate in a Puerto Rico heat.  I also missed the semi finals of Monsters Menace America for a heat, but that game is kind of silly and fluffy so I didn't mind so much.

Overall the experience at the convention was a good one, but I had a few moments that really weren't great.  The first was in a semi final for Santa Fe Rails where it was me, my teammate, the GM of Santa Fe Rails, and a dude I didn't know.  The game was about to end and the GM had a decision to make.  He could either give four points to me and to the random dude, or give fourteen points to my teammate.  Now normally this is an easy choice and you give four points to two people, especially when one of those two is clearly last place.

But instead of doing that the GM explained that he was sure that my teammate was winning, so he wanted to hurt me as much as possible to secure second place for himself.  He handed my teammate fourteen points and the game ended.

I felt almost ill.  I felt like I had played well, and was pretty sure my teammate was really close behind me, so it really sucked to have someone throw points away from me in such a fashion.  It would not have been fun to lose like that.

But instead it turned out that I was way ahead, more than anybody thought.  I won the game anyway, with points to spare.  But because my teammate got those fourteen points he pulled ahead of the GM and got second.

Ouch for the GM.  Onward to the finals for me!

Then later on in the week I was in my Puerto Rico semi final, and again I was playing against the GM of Santa Fe.  He was fourth chair and quickly sold a corn, bought a coffee roaster, and sold coffee.  His game was looking amazing.  However, I decided that it was my mission to prevent any more coffee sales and I jammed the trading house as hard as I could.  This was helped by lefty and righty both having tobacco to sell so nobody was able to safely craft.  I managed to wrangle selling sugar, and it was the third last turn of the game before someone finally sold a tobacco to clear the trading house.  When the game ended there were two Offices that had never been used, a Small Market that had never been used, and a Small and a Large Market that got used once.  Totally nuts.

I realized on about turn six or seven that all three opponents were going hard for Guild Hall.  Everybody was buying up production buildings as fast as they could.  I decided that the only chance I had was to get it myself, so I saved up cash and snagged it right before two other people could step in and buy it.  All three opponents were unhappy as all of them would have gotten far more points from it than me.  I ended up getting six from the Guild Hall so it was still the best choice for me but two of the others would have gotten the full ten.

The GM from Santa Fe Rails then announced that he was deliberately throwing the game to my right hand opponent because he had been jammed so hard this game.  He ended the game instead of trying to score more points himself, and was left in last place.  I came second and failed to advance to the finals, though I did crush lefty and the GM across from me by huge margins.

So this one guy went to great lengths to throw the game away from me in two semi finals this year.  Once it worked and made me lose (though I might well have lost anyway, to be fair) and the other time it just screwed him over and did nothing to stop me.

Not the ideal way for games to go.

Thing is, I don't regret losing Puerto Rico that way.  I think I played a brilliant game.  I stopped my opponents from running their game plans, I had perfect tempo when I grabbed the Guild Hall, and I wrangled a strong endgame position from a terrible early game situation.  I played great, and crushed both downstream opponents mercilessly.  The guy upstream of me really isn't my problem - I can't do much to stop him, that is the job of the player to his right!

But despite doing things right I lost, partly due to spite, partly due to the other two people not jamming my righty enough.

So while I wish I had managed to win to help support my teammates, I don't find any blame for myself here.  I did the right things and I lost anyway.  That happens.  However, next year I am definitely not making Puerto Rico my team game.  It is so frustrating to have a game where you do it all right and lose anyway, and Puerto Rico really jams up my schedule.  Maybe I will make my team game Castles of Mad King Ludwig next year.  I am apparently consistently good at that, and I love playing it.

Lessons learned.

The stair gambit

When talking about Castles of Mad King Ludwig recently I opined that the Utility Card that gives bonus points for Stairs wasn't so great.  It has substantial potential if you can effectively corner the market on Stairs, but otherwise it isn't exciting.  A game of Castles recently saw me go turbo Stairs to test this theory, and it worked out superbly well giving me a 136 point finish with a wide margin of victory, largely on the back of getting 5 Stairs.

We had Kings Favours for both square footage and number of corridor rooms so the game was ripe for a hardcore Stairs opening.  I started off with the Utility cards that benefit Utility rooms and 200 rooms, and after building 4 sets of stairs I scooped up the Stairs Utility Card!  I would have built more Hallways than I did but one opponent went nuts and scooped up 3 Hallways in a single turn leaving my last Stairs looking lonely and sad.

My board doesn't look that super at first glance but my Utility cards are strong coming in at 10, 8, 6, 6, and 3 points.  I also have 14 points from Stairs and Hallways, and the 200 stack emptied so the fact that I was collecting those was fantastic for me too.  The last two King's Favours were doorways (where I scored 1) and purple rooms (where I scored 0).  However, I cleaned up the two Favours for Corridors and Corridor square footage so I got a solid 17 points from Favours.

One thing that I was wondering was how good Basement rooms are in general.  Clearly if you already have Stairs you might as well build Basement rooms if they look tasty, but are they really worth it?  Do you give up much by simply not having any Stairs at all?  The interconnectedness of the points of various rooms makes this calculation quite challenging, but I am going to have a stab at it on this board.  It won't be easy to generalize it to all games, obviously, so take this as a data point, not a thesis.

I will assign points from cards to the Utility Rooms that generate the cards, not the rooms.  The points from my starting cards will be assigned to the rooms.  I will ignore the 350 Corridor I bought because it was obviously purchased only for King's Favours and isn't representative.

Utility Rooms:  12, 9, 5
Green Room:  5 + 10 coins
Blue Room:  4 + (empty 200 stack = 8 - 3.33 = 4.66)  = 8.66
Yellow Rooms:  4, 4 + (2?) bonus turn(s)
Basement Rooms:  11, 7, 6, 5, 1 + 5 points + bonus turn

My upper rooms generated 6 points + 1.25 coins + .25 bonus turns.
My basement rooms generated 7 points + .2 bonus turns.

The difference between the two set is quite small.  The basement rooms come out on top if you count the kitchen as not completing, but if you treat it as though it completed they are very much on par.

Looking at this board it appears as though my basement and upstairs were similar in scoring on a per room basis.  In that case it appears as though Stairs were a fine investment even aside from the massive stack of bonus points they got me as I did well on basement rooms and having the flexibility to buy them was excellent.  I am not yet convinced that being the third person into Stairs is strong in a game unless the Favours or Utility cards benefit Stairs, but I am eager to see what data other people have in this regard.

Just pass

When I started playing Castles of Mad King Ludwig I thought that passing a turn was a pretty crappy thing to do.  Normally on each turn you spend some cash to buy a room to add to your castle, but if you want you can skip buying to collect 5 coins.  My thought in my first few games was that this was a rubbish choice, one only made by people who mismanaged their money and ended up broke.  I am still convinced that mostly it is taken by people who screw up their money management, but I think it deserved a closer look to figure out if it is a good thing or not.

The key to managing your cash is to realize that if you get really low on funds your opponents can use it to really jam you up.  They can put powerful rooms just barely above the amount you can pay and scoop them up for far less than they should.  They can use basement rooms to put you in a position where you can't buy anything at all and are forced to pass and take 5 coins.  You always want the option to buy things up to 8 cost because then if somebody makes a terrible mistake you can capitalize and nobody can really punish you for being low on cash.  You might want to buy the room at cost 10 or 15 but it is not often going to be such a deal that you get blown out by missing it.

However, if you keep too much money on hand you find out that it is nearly worthless at the end of the game and you might miss out on great upgrades in the interim where you could have bled off excess cash to get more points.

The key is figuring out a ratio of cash to points so you can know when to buy the awesome room at 8 instead of the pretty good room at 2.  How many points more do you need to get for that 6 bucks to be a good choice, given that you have a decent bankroll and aren't worried about going broke?

Some things to think about.  44 room cards are in the deck, generally you go over by 2, and generally 2.5 blue rooms finish, so that leaves about 51 room cards in play.  Mostly 3 of them are left at the end, so that leaves us with 12 rooms per player on average.  Assuming an average score of 110 for good players I think we should model an average purchase giving 9 points.  On each turn where you buy a room you spend 4 coins (I can't defend this mathematically or anything, but a did some figuring and it seems about right for the groups I have played with) and you also give up the option to take 5 coins by passing.  That means that a pretty normal turn where you purchase a room costs you 9 coins and gains you 9 points.

Keep in mind those 9 points are often coming from King's Favour pucks, empty stack bonuses, utility cards, and room completions so the points on the room itself will clearly be far less than 9.

This 1:1 ratio isn't the be all and end all, but it gives us a useful point of comparison.  If you can spend 6 additional coins and get 9 points, it is probably a good exchange.  Next time you are third chair you can skip what is likely a mediocre purchase, take your 5 coins, and you are probably ahead of the game.  If you manage to get more points than the coins you spend you will almost certainly be able to get that money back and be ahead on points in a later turn when your choices happen to be poor.  That is a good rule of thumb!

It also means that if you are staring at a board where you can spend 6 coins to get 3 points it is likely a poor proposition.  Of course if game end is imminent you take the points, but when money still matters you probably don't want to take deals like that because keeping your opponents poor and you rich is important leverage.

One thing all of this analysis ignores is the effect on your opponents.  When you spend money one of your opponents gains money (except when you are master builder, of course) and that matters.  Buying an expensive room because it happens to match your utility cards is good, but if it ships a cheaper room down the line to your opponent that could be a poor choice.  Those are complicated to fit into the basic formulas though, so I have ignored them for now.  I suspect that neither of these things changes the conclusion overmuch.

The real takeaway I have from this is that I really need to consider the cost of skipping 5 coins when buying something.  Buying a garbage room for 1 coin is deceptive as I am actually losing 6 coins to take it.  Usually you will be able to get 1:1 on something on the board but when you don't have a ton of cash you should really think about whether or not to take the money instead.  Paying 4 coins instead of 2 isn't double the price, it is 9 instead of 7.  The absolute differences are the important thing, not the ratio of costs.

I also really need to mind that rooms have a lot of random points attached to them.  Between utility cards, Favour bonuses and empty pile bonuses people accrue roughly 40 points in a game.  That only leaves 70 points for room completions and the actual points on rooms themselves, so when I look at a room and see it is worth 5 points I should really tack on an extra point to account for all the bonuses it might give that I don't know about yet.

So for those looking for a simple set of instructions to figure out how to spend money:  Make sure you don't go so broke that people can take advantage of your poverty, but otherwise just look for deals where you can gain more than 1 point for each additional coin you spend.  1:1 extra purchases are meh, and lower than that is bad unless money doesn't matter anymore.

Starting utility

At the start of a game of Castles of Mad King Ludwig every player gets 3 utility cards and must choose 2 of them to keep.  These cards give bonus points at the end of the game based on the castle you have built.  There is a pretty fair range in the quality of the cards, and some are clearly more powerful than others.  There are two questions to answer.  First, which cards are better in general, and how does the existence of the King's Favour change the value of the cards?

Among the utility cards that give you bonus points based on room size there is serious equality:  All of them either give 3 points per room with 6 copies of each room in the game, or they give 2 points per room with 9 copies of the room in the game.  In either case you have 18 points available in the game.  Taking a bunch of copies of a single size does make it easier to get a bunch of points if you empty out that stack, so these are a little better than the 18 points would indicate.

However, the cards that award points based on room colours are much more imbalanced.  When you multiply the card point value by the number of those rooms in the game you get the following amounts:

Purple:  28
Yellow:  27
Blue:  24
Brown:  24
Green:  22
Grey:  20
Orange:  18

This means that colour based utility cards are generally about the same quality as size based cards when you account for the 2 points per depleted stack benefit for stacking size, but the purple and yellow cards seem like clearly the top of the heap.  

There are also cards for round rooms and square rooms, and they both have a value of 15 which makes them quite weak because they are harder to focus on to generate big numbers.  You could potentially combine them with size cards to get a lot of points for each purchase but generally I think they are not good.

The cards that give you points for completed rooms and open entrances seem to cluster really tightly around 4 points per game.  You can get higher, but I don't think I have ever seen them go above 6 points.  They are extremely reliable, require no investment to pay off, and are a fine fallback.

The three utility cards that give points for various corridor cards are really different from each other.  The one that boosts hallways is garbage.  It is extremely difficult to get more than 3 points out of it, and mostly you will get 1.  The one that gives 1 point for every corridor is okay, almost never exciting, and strictly better than the hallway one for some reason...?  The third one that gives 2 points per stairs is tricky.  In the late game it is trash.  On most normal boards it is trash.  But it is possible but quite involved to build tons of stairs and basement rooms completing each other and do really well.  If you empty the stairs stack you rack up 4 points for each of them which is decent.  However, it is a big investment for a not spectacular return so the card overall isn't great.

One card gives you points for every 5 coins you have left at game end.  It isn't great and getting a big score off of it requires you to waste a huge amount of currency.  Mediocre at baseline.

The last two cards give you 8 points for having all 10 room sizes or 7 points for having all 8 room types.  I don't think either of them is great, but I like the 7 point one for all room types much better.  There are at least 9 of every room type and only 6 of each room size for some sizes, so the room type is a much easier condition, plus I find it is actually useful to have all of the room types in your castle whereas having all room sizes has no obvious utility.  Both of those cards suffer from the fact that you can't reliably plan around them in the early game because you don't know what you will lack in the endgame.  They often revolve around desperately hoping you get to buy a room you don't much want on the last turn and often the people aiming for them fail.  I really don't like the idea of a bonus card that you spend resources trying to fulfill and end up scoring 0 points for.  Perhaps the best argument against these all or nothing cards is that they combine terribly with the other cards.  If you want a bunch of blues, for example, it is going to be extremely difficult to also get the variety needed to fulfill one of these cards.

In summary, I think the strategy for keeping starting utility cards can be summarized by a priority list.

Yellow or Purple Colour   2 cards
Other Colour / Size    16 cards
Completed Rooms / Open Entrances   2 cards
Cash/Round Rooms/Square Rooms/Corridors/All Colours/Stairs   6 cards
All Sizes/Hallways   2 cards

Now I want to consider how we combine this with the King's Favour pucks.  Say the King's Favour has the green room puck.  Everyone now has an added incentive to build green rooms.  If you also have the green room utility card, should you keep it?  Generally I see people keeping cards that match the Favours because they think that since they are going to want green cards anyway, might as well score even more for them!

This is not the right approach.  The thing about rooms affected by the Favour is that everyone wants them and there is a real incentive to get at least one of them.  Having a single Favoured room gives you 1 point at worst and often more than that.  Moreover it puts you in contention to jump into first place and score up 8 points if other people get stuck at single Favoured room and you can scoop up a second one.  Even if you just tie with one other player at two Favoured rooms each you grab 6 points, so threatening to do that is powerful.  It is common for one player to corner a lot of a particular colour or size of room under normal circumstances, but doing so when it is the Favoured one is rare and extremely costly.

The key is to remember that nearly every room will be bought at some point.  It isn't as though the ones that aren't worth a ton of points are ones you will just ignore.  You will end up with low value rooms and it will be a lot easier to collect a bunch of them if other people aren't aiming for them particularly, especially if they don't feel that they need at least one.

Ideally you want to take utility cards that give bonuses to the rooms that *aren't* part of the Favours.  You want to be able to cash in on stuff that other people will hand over for cheap, and you don't want to be hunting for room types that everyone wants one of.

So if you see green rooms in the Favours and you have a green room card and a orange room card, keep the orange.  You have a much greater chance of being able to grab a ton of orange and get an outstanding result.

This is especially true because in a four player game you will win more if you take risks.  A player who gets 5 guaranteed points will not win as often as a player who takes a series of coin flips for 10 or 0 points.  You have to have a big score to beat all three players so fighting for the same thing as everyone else and getting predictable, moderate scores is not the ticket.  Aim for something different and try to catch em all.

How much does this matter?  14 of the pucks are coloured ones, and there are 10 other pucks.  (I count the corridor pucks among the 'other' because they work so differently from the coloured pucks.)  When a coloured puck is out that matches a starting card of yours, I would downgrade the card by one tier.  Much of the time this won't matter because even if a blue card is worse when blue pucks are out it is still vastly superior to garbage like the 'collect all' cards or the hallways card.  You will probably still have some other trash you can safely dump but if you happen to have 3 similar cards drop the one that matches the Favour.

Strangely I think the corridor Favours work the opposite way.  Even if they are in play people aren't going to be spending their turns spamming hallways or stairs, it just isn't efficient.  If you happen to have the stairs card or the corridors card when a corridors Favour is out, I think it becomes a really reasonable keep and I would upgrade them both by a tier.  You can pretty easily scoop the Favour and a bunch of points for your cards and that could be quite the coup.

The cash Favour works in favour of the cash card, like I said earlier.  It incentivizes people to complete greens and keep their money around on their Master Builder turn instead of launching it off to the bank.  There will be more money around as people fight for the cash Favour, which helps you get more points off of the cash card even if you don't win the Favour.

The other Favours are broad, so I don't think they have a significant effect on card valuation.

That is quite the wall of text, so I will give a quick summary:  Keep the starting utility cards that give bonuses for room colours (except corridor ones) or sizes.  If you have to choose between those, keep the ones that are different from the Favours.  If you have to choose between lesser cards, keep the ones that match the Favours instead.

*Edit:  I changed the advice regarding the Stairs card because I didn't know the rule that you can't attach Stairs to Stairs, which makes a heavy Stairs strategy a lot harder to do.  It is still possible, but it is much weaker.

Increasing utility

I played a couple of games of Castles of Mad King Ludwig over the past couple days and have been smashing my brain against the approximate value of the utility cards in the game.  For those that haven't played, Castles is a game where you build a castle out of a bunch of differently shaped and sized rooms that you fit together into something wild and crazy.  The rooms have a variety of properties like colour, shape, door number and location, and scoring bonuses or penalties.  Utility cards are cards each player gets in secret and they award points for various things.  You might get 3 bonus points for each size 400 room, for example, or 7 bonus points if you have a room of every colour.

Initially I thought the utility cards were worth about 3 points each.  This is important because you have opportunities to acquire more utility cards throughout the game and it is really useful to have a ballpark for what you can get out of them.  It is theoretically possible to get as much as 28 points out of a single card, but generally the high is around 12 with a minimum of 0.  In my game at Naked Man's place I got 28 points from my four cards and he questioned my estimate of 3 points per card, so I thought I would take a look at what utility cards are usually worth.

I took a castle that I finished a game with on Saturday that was pretty middle of the road and figured out what each utility card would have been worth if I had been awarded it at game end.  The high was 12, five of the cards were worth 0, and the average was 3.04 points per card.  Pretty good so far!

But there is more to it than that.

When you get new utility cards you get dealt two of them and you choose one to keep.  When you take the distribution of cards I got from Saturday's game and choose the best of two of them you get an average of 4.49 points per card instead.  So getting a fresh card on the last turn of the game is likely worth close to that value.  There are two cards that give a lot of points if you have fulfilled a difficult condition and if you happen to have a castle that has already done both of those things your expected value rockets up to 5.54 instead, and you know this before you make a play to get a card.  If you don't want to bother counting up your castle it is likely right to count a new utility card for 5 points, which is rather a large number.  It means that unless any other option has some really powerful benefit utility purchases on the last turn are likely to be top notch.  For certain if you feel like you are in a bad position in the game you should go for utility cards at game end to try to luck your way out.  If you bust and get no points you are still losing, but if you get lucky and hit a 10 or 12 point card it might eke out a victory.

However, that is only the easy part of the calculation.  The hard part is figuring out what a utility card is worth partway through the game.  At the start of the game you get three utility cards and you keep two of them.  These help guide your building by changing your evaluation of the tiles.  My initial impression was that early utility cards would be extra powerful because you can then tailor your builds towards them as the game progresses.  Knowing that I get bonus points for size 400 rooms means I can load up on them, right?

Not exactly.

The problem is that even though I know that I get bonuses for such rooms I often can't capitalize anyway.  Sometimes those rooms just don't come out or the person ahead of you is grabbing them all for unrelated reasons.  Even if you do get them you are usually giving something else up for them.  If I take a 4 point tile because I have a utility card that grants 3 bonus points on it I only really make the full 3 points if I pass up another 4 point tile.  Often I end up passing up a 6 point tile to get 4+3, which is still a benefit, but not nearly as large as the point values from the utility cards make it appear at endgame.  You usually lose something to alter your gameplan to maximize your utility cards.

The other reason that early utility cards aren't great is that your choice isn't terribly useful.  You might get offered a orange bonus card and a green bonus card, but since you haven't seen which tiles come out during the game your choice is often really just a guess.

But when you get a choice at the end of the game it is *much* better.  You can know which will give you more points for sure so you don't end up with a worthless card very often.  Utility cards at game start have higher potential but higher tradeoff and a far greater chance to totally whiff.

It is pretty easy to come up with a useful range for early utility cards even if it would take an enormous amount of data to get a really firm average.  Even if you don't bother to look at the card at all you have a floor of 3 points per card, as noted above.  That means that you definitely do better than that since you can alter your plan slightly to maximize your value there, at least some of the time.  I can't imagine you could exceed 5 points per card though as you would have to double its expected value while giving up only .5 points / card and from experience I can say that doing so isn't practical.  My experience and instinct tells me that the value is somewhere between 4 and 5.

I imagine that the optimal time to get a utility card is in the middle of the game.  By that point you can see whether or not you have a basement set up, which tiles you are already hunting for to finish off your big point rooms, and you know what right hand opponent is angling for so you can avoid that.  You also can see some of the tiles that will come out in the next turn so you can make some good guesses about what will be available to you later.

Combine that information with the flexibility to spend the last five turns of the game picking the tiles that work with your utility card and I feel like the midgame is the ideal place to farm up utility cards.

In any case talking about the ideal point in the game to take the utility card is kind of silly because if they fluctuate in value between 4 and 5 throughout the entire game there isn't much real sense in shifting your internal valuation as time passes.  Simply put, I think the utility cards in your initial hand where you have no information are worth about 4 points, but since you are simply handed those at the start you just take the best of what you have.  Once the game is going and you have a grasp of what is happening I think you should assume that utility cards are worth 5 points, but never forget that their high variability favours buying them when you are losing.

Tomorrow I will write about which utility cards are most valuable and discuss strategies based on which King's Favour pucks come out at the start of the game.