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.