Notre Dame: Conclusions

Two and a half years late, but I've finally gotten around to digging up the conclusion I wrote for my Notre Dame strategy series. Here it is!



Putting it all together...

Ok, so we know we need to kill 28 rats, pick up 10 cubes, make 8 gold... Oh yeah, and pick up as many VPs as we can. We only get 27 actions total and yet we want to pick up 46 resources. Assuming each of rats, cubes, and gold are equivalently 'hard' to do, a good strategy has to be finding a way to take actions which generate large numbers of at least one of those resources. The more we can get in one action the more actions we free up for actually winning the game! So, lets go over all the actions you can take and look at what each can provide. There are 24 different actions you can take, 9 cards and 15 bribes.

The Cards

Guesthouse - 1 resource only (lets not kid ourselves, if you play 4 guesthouses you can't win)
Car - 1 resource and between 1 and 3 VPs (or no resources and 4 VPs)
Bank - geometric resource progression (~2 resources, see below)
Cube-house - geometric resource progression (~2 resources, see below)
VP-house - geometric VP progression (though mostly just to proc parks!)
Hospital - Between 2 and 9 resources depending on when you play it
Park - 1 resource and potential VPs (~7 VPs, see below)
Balki - any of the above
Notre Dame - lose 2-4 resources for VPs (~4 VPs, see below)

Basic Townsfolk

Moneylender - 2 resources and 1 VP
Monk - 2 resources and 1 VP
Doctor - 2-8 resources
Wench - 1 resource and 3 VPs
Jester - Best action of above
Minstrel - 3-6 resources or 3-6 VPs or 18+ resources or 21+ VPs (see below)

Phase A Townsfolk

Night Watchman - 3-6 VPs
Bishop - 1 resource + best unused card
City Guard - 2-7 VPs

Phase B Townsfolk

Rat King - 0-9 VPs
Lawyer - 0+ VPs (Most often 0 or 3)
Guild Master - 2-12 VPs

Phase C Townsfolk

Queen - 4+ VPs
Carpenter - 3-7 VPs
Mayor - 3-15 VPs


So, what does it all mean? By and large, very few actions actually generate multiple resources. The only ones that really do all kill rats, so while you need to take a couple of them you can't focus on just those as your big resource actions. Minstrel is the clear winner in terms of both resources or VPs, but he's tricky to use. He can bring in the most gold, but doing so strands a lot of cubes in the bank. In order to use him fully you need to have 3 cubes in one square already. Moving 2 into the bank is pretty mediocre, it's like a very bad money lender and still requires a plan to get them out again. (A second jester or maybe just leave them in for +3VPs on phase C guyo.) Minstreling two into the hospital or park actually seems really good early game now that I look at it. The only downside to moving two out early is you won't have three stockpiled to move out from that square for a better jester later.

One thing really worth pointing out is winning scores are often in the 70-80 range. Ignoring park related actions the best you're looking at realistically is scoring 9 from a single action, and there are preciously few chances to score even 9. What this means is over the course of the game if you're going to win you're going to be scoring small numbers of VPs frequently. Scoring points frequently is what really makes the park shine, so I'm pretty sure a winning strategy has to involve the park.

Remember how we wanted 46 resources out of 27 actions? Most of the big point plays don't generate any resources at all, so you need your resource plays to make as many resources as possible while trying to maximize the jester. As such it seems like a very strong plan is to try to get 3 cubes into the bank or the cube house early. Get in, get your 6 of a resource, and then throw them into the park or the hospital. (Park if you won't get plagued by doing it, hospital if you will otherwise get plagued.) If possible, repeat again for the other one. Use your early bribes to generate the cubes and cash you need to get this plan going. (Bribing the night watchman for 6VPs on turn 1 seems good, but I'd rather take moneylender, wench, or monk over it.) Playing into the park is worth a resource and is the highest VP card play you can make. I've been passing these early to set up a tripleton and I'm no longer sure that's correct.

Notre Dame is bad. It costs you two resources (you lose the gold and a cube) and it only returns 4 VPs in the worst case. Being the only one into ND might be worth it, but I'm pretty sure I'm going to try to skip it from now on. Later game NDs get better because it's one action to proc the park twice.


Geometric Resource Progression - What does this game mechanic actually do? Assuming you don't Jester into a production building you earn 1, then 2, then 3, then 4, then 5 resources. Note, 15 cubes is more than you could possibly want. 15 gold is enough to play a full ND every phase on its own with no other gold pickups. So, the 5th guy will rarely if ever be played in either building. While you get a ton for him, it's a mostly wasted ton. Anyway, how much is an action worth on average? It depends how often you go. If you go once, it's worth 1 resource. 2 is worth 1.5. 3 is worth 2. 4 is worth 2.5. 5 is worth 3. So you're likely getting 2 resources per action from the bank and cube-house, maybe 2.5 per.

Park - How much is it actually worth? As an upper bound, assume each guy in the park is worth .5 VPs per VP generating action. Notre Dame counts as two VP generating actions for this analysis. Each phase you can take at most 3 bribes worth VPs (and likely will) likely one ND, and maybe 1-2 cars/VP houses. So a park guy to start phase 1 is likely worth 10.5 VPs. To start phase 2 is likely worth 7 VPs, and to start phase 3 is likely worth 3.5 VPs. Likely is actually a misnomer here since it's not precise at all and quite possibly an overestimate since sometimes you won't bribe for VPs and sometimes you play parks mid-phase, but you could also end up earning more points out of it because you could just play all cars and VP-houses. Also, the first guy in the park is worthless, he doesn't make .5 VPs in reality but if you get two guys in the park they make the full 1. Overall, the park action is probably worth around 7 VPs in the early-mid game and 4 in the mid-late game. It's not worth much at the very end.

Notre Dame - How much is it actually worth? At worst, everyone plays their ND card and you end up with 2 bonus points to go with the 1 for going to ND in the first place. As well you get 2 park procs, which can be very clutch. At best you get a solo-ND for anywhere from 6-12 bonus points. Most likely you'll get 4 plus the park procs, which we're really assigning to the park and not to ND.

Minstrel - What does it do? What it does really depends on where you put the cubes. If you put them in the bank or cube-house then you're likely to only actually go there once or twice. As such, you're getting 3 or 6 resources from the action. If you put them in the hospital you kill 3 rats a turn for the rest of the game, so if there are 7 turns left (best case scenario) it's worth 21 resources. (I say that's best case because you need to have 3 cubes in one spot before you can make optimal use of it, and that'll take a couple turns.) If you put them in the park you score 1.5 points per VP action for the rest of the game on average, so using the park calculations above you're getting 21ish VPs out of doing it at the end of phase A. Moving them to the car or the guesthouse is a huge mistake. Moving them to the VP house is worth 3 VPs every time you move to the VP house which sounds good, but consider moving them to the park instead. Unless more than half of your remaining VP actions are VP houses, you're better off in the park in the abstract sense. Now, since the park works only on even numbers it's not quite as clearcut, you might only need more than a third of your actions to be VP houses to profit. Most likely, though, that still won't be the case. Especially since I'm going to hate draft your VP houses on you if you need them to win! End result... The hospital and the park both benefit from leaving cubes in and not so much from activating them, and they have monsterous payouts if you move 3 cubes into either of them, especially early. A final thing to consider with the Minstrel is how it impacts the final scoring cards, discussed next.

If everything has worked out swimmingly for you then you'll have all the resources you need by the final round and you'll be able to buy all 3 of the big point cards. So if you have 3 cubes in the bank and transfer them all to the park you lose 3 points from the Mayor. Assuming the park was your biggest spot before that you get the 3 points right back with the Queen. If you didn't have 3 in the park before then you don't lose anything making the trade. You also lose 1 point from the Carpenter by emptying the bank. Overall you likely lose 1 or 2 points by making this play but do get them right back by proccing the park for at least 1 more on all 3 of these bribes.


In conclusion, what do I advise? Well, you need to balance acquiring enough of every resource with the need to focus on specific resources in order to get enough of them in the early game. I like to get one of my gold or cubes by playing cards and the other with bribes or by driving my car. Then you can minstrel them out and into the park where they'll have the biggest impact on your VP acquisition. Notre Dame is a trap early game and just costs too much to use. Late game it's not very efficient but it's one of the few ways to proc the park so it's good if you've overloaded the park. It's also good if you've got a ton of money because you can cash in for many bonus points on the play.

Markov Chains 2

Yesterday I investigated using Markov Chains to work out how long the average person would take to get the A Mask for All Occasions achievement in World of Warcraft. However, in order to get the problem into a simple Markov Chain format I had to assume the player was only getting masks by Trick or Treating which is not the only way of getting them. On top of the 16% chance you have of getting a mask by trick or treating you also have a 14% chance of getting one by defending a town from the Headless Horseman and (as of Wednesday) what seems to be a 100% chance of getting one from the Headless Horseman daily dungeon.

To save the casual reader from Wall of Math, details are after the jump.

Markov Chains

Hallowe'en is approaching which means the Hallow's End event is up in World of Warcraft. One of the achievements for this event is to collect 20 different masks (one for each race/gender combination in the game) and the odds of actually getting it done are pretty absurd as Sthenno posted about here. I have no reason to believe his numbers are anything but correct but I've heard people talk about Markov chains in the past, think they could be used to generate the odds, and want to learn about them so I'm going to crunch the numbers myself for fun.

Unfortunately I don't have any mathematics software so I'm stuck with Excel, my brain, and brute force for now. Maybe I'll try to find a trial version of Maple or Matlab or something when I get home. So I'm going to have to start small, which is good, since it should hopefully make things easier to understand. This is going to be a pretty big wall of crunching the numbers text, so I've added in a jump break here. Jump on if you don't value your sanity!

Bridge Match 1 - Board 58

Board 58 – Dealer East – All Vul

My hand: ♠ A Q J 7 3 ♥ 4 2 ♦ A K J 4 ♣ J 9

I open 1 spade in second seat. West doubles and East bids 2 hearts which gets passed out. I lead the A of diamonds.

WEST ♠ K 4 ♥ A J T ♦ 7 6 2 ♣ A K 6 5 4
	SOUTH ♠ A Q J 7 3 ♥ 4 2 ♦ A K J 4 ♣ J 9

West	North	East	South
		Pass	1♠
Double	Pass	2♥	All Pass

A-2-3-8. If partner can't encourage I don't want to play another diamond. It looks like declarer might want to ruff a spade on board so I play a trump. 4-T-Q-6. Partner fires a diamond back. 5-T-J-6. I cash the K of diamonds. K-7-9-Q. And now another heart through. 2-J-K-5. Partner draws the last of dummy's trump. 8-3-7 of spades-A.

Now declarer starts cashing clubs. 4-8-Q-9. 3-J-K-2. A-7-5 of spades-3 of spades. 5-T-7 of hearts-J of spades.

Declarer tries to steal the K of spades but I hop with the A. I think I'm giving up but I cash the 13th diamond just in case. It holds. Then partner ruffs the K of spades. Down 3.

	NORTH ♠ 9 8 ♥ K Q 9 8 ♦ 9 5 3 ♣ T 8 7 2
WEST ♠ K 4 ♥ A J T ♦ 7 6 2 ♣ A K 6 5 4		EAST ♠ T 6 5 2 ♥ 7 6 5 3 ♦ Q T 8 ♣ Q 3
	SOUTH ♠ A Q J 7 3 ♥ 4 2 ♦ A K J 4 ♣ J 9

Professor Jack disagrees with my pass. He'd get in there with 2 spades. Without a 6th spade and with partner passing over West's double I'm not so sure that's a good idea.


On the replay my seat does get in there with 2 spades which gets passed out. The defense seems to do everything it can to give tricks to declarer and they make up 1, but I'm not actually sure they could have taken anything more.

Nick: 300
Jack: 140
IMPs: +4 (+10 total)

Bridge Match 1 - Board 57

Board 57 – Dealer North – EW Vul

My hand: ♠ A Q 6 4 ♥ K T 4 3 2 ♦ T 3 ♣ 7 2

Partner opens 1 club and East doubles. I bid 1 heart. West overcalls 2 diamonds which gets passed to me. I don't think my hand is quite good enough to head to 2 spades so my options are 2 hearts or double. I don't know what partner will take double as but I think it should show about this hand. Maybe 4-5-1-3 instead, actually. I double anyway. West pulls to 2 hearts which again gets passed to me. This time double should be for penalty I think, which I want to go for. It gets passed out.

Partner leads the A of hearts!

	NORTH ♥ A
		EAST ♠ J 8 7 5 ♥ Q J 8 ♦ A Q J 5 ♣ T 6
	SOUTH ♠ A Q 6 4 ♥ K T 4 3 2 ♦ T 3 ♣ 7 2

West	North	East	South
	1♣	Double	1♥
2♦	Pass	Pass	Double1
2♥	Pass	Pass	Double2
Pass	Pass	Pass
1Penalty
2Penalty

So declarer has at best 9765 of hearts. That seems like an awfully sketchy suit to me and means we get to take 4 trump tricks. I have the A of spades so any more tricks partner can take are money in the bank. At any rate, A-8-4-5.

Partner shifts to the 3 of clubs. 3-6-7-9. Declarer plays on diamonds. 2-4-J-T. Q-3-6-8. A-2 of hearts-7-9.

I'm in and return a club for partner. 2-A-4-T. Declarer throws out another club. 5-8-J of hearts-4 of spades.

Declarer draws trump. Q-K-6-J of clubs. I'm in. Declarer has two hearts left, and 1 diamond. if he has Kx of spades then I can set him by throwing him in with a heart after drawing a round of trump. If he has 2 small spades left then we can set him two by cashing 3 spades. Actually, if I start with a low spade anyway and declarer has Kx then I still set him. Or with A and low, which is safe since partner has at least 3 spades...

Maybe I should look at it from declarer's perspective. He has 5 tricks in and 1 more for sure in trump. If he has the K of spades he gets it unless I endplay him out of it, but that gives him his diamond which he can only get if he draws my trump. He can't do that unless I let him. Maybe he has two high clubs? Then he makes no matter what I do.

So, I think A of spades is the way to go. A-2-3-5. 6-7 of hearts-9-7. Now that he ruffed in my hand is up. Down 2, doubled.

	NORTH ♠ K T 9 3 ♥ A ♦ 9 8 4 ♣ K J 8 4 3
WEST ♠ 2 ♥ 9 7 6 5 ♦ K 7 6 2 ♣ A Q 9 5		EAST ♠ J 8 7 5 ♥ Q J 8 ♦ A Q J 5 ♣ T 6
	SOUTH ♠ A Q 6 4 ♥ K T 4 3 2 ♦ T 3 ♣ 7 2

Professor Jack disagrees with my first double since apparently it's for penalty. He also disagrees with my second double since it's also for penalty. (That one I knew!)


The auction on the replay is substantially different. Instead of doubling 2 diamonds for penalty my seat bids 2 hearts, which West then doubles for penalty. Wouldn't that have been something, both tables down in 2 hearts doubled from different directions? It doesn't happen since North pulls to 2 spades. East gets in with 3 diamonds and South jumps to 4 spades. The defense takes two diamonds, two clubs, and a spade for down 2. I'm back to positive IMPs!

Nick: 500
Jack: -100
IMPs: +12 (+6 total)

Bridge Match 1 - Board 56

Board 56 – Dealer West – No Vul

My hand: ♠ T ♥ K J 9 6 2 ♦ A T ♣ A J 6 5 2

Partner opens 1NT in second seat and East passes. I bid 2 diamonds as a transfer to hearts. Partner super accepts by jumping to 3 hearts. I cuebid 4 clubs and partner cuebids 4 spades. I bid 4NT to make sure partner has the A of trump. He bids 5 spades showing 2 keycards with the Q of trump. We have all the aces and trump locked up solid. I bid 5NT to check for kings. Partner bids 6 diamonds showing only 1 king. I know of 13 of his points, so he has between 2 and 4 points in Q's and J's. If those points are in clubs we can probably make 7, but I don't want to risk it. We're still short two kings, after all. I bid 6 hearts and everyone passes. East leads the 7 of diamonds.

	NORTH ♠ A J 3 ♥ A Q 8 3 ♦ K Q J 4 ♣ 7 3
		EAST ♦ 7
	SOUTH ♠ T ♥ K J 9 6 2 ♦ A T ♣ A J 6 5 2

West	North	East	South
Pass	1NT	Pass	2♦1
Pass	3♥2	Pass	4♣3
Pass	4♠4	Pass	4NT5
Pass	5♠6	Pass	5NT7
Pass	6♦8	Pass	6♥
Pass	Pass	Pass
1Transfer
2Super-accept (5 hearts or 4 hearts and max)
3Control in clubs for hearts
4Control in spades for hearts
5Blackwood for hearts
62 aces and queen of trump
7King ask
71 king

Well, I have 5 hearts, 1 spade, 4 diamonds, and a club right off the top. I need to find a 12th trick somewhere which could easily be 2 spade ruffs on board or a club ruff in hand. There's no way to get a 13th trick so I should just take the safest path to 12 which has to be win this on board, draw trump and concede a club. The first diamond doesn't get ruffed and hearts split 3-1 so there's really nothing to the play. Making 6.

	NORTH ♠ A J 3 ♥ A Q 8 3 ♦ K Q J 4 ♣ 7 3
WEST ♠ Q 9 8 4 2 ♥ T ♦ 9 6 3 2 ♣ K Q T		EAST ♠ K 7 6 5 ♥ 7 5 4 ♦ 8 7 5 ♣ 9 8 4
	SOUTH ♠ T ♥ K J 9 6 2 ♦ A T ♣ A J 6 5 2

Professor Jack disagrees with my 5NT bid. He says it's the wrong time to try for slam and would just bid 6 hearts. I guess it wasn't really possible that I could build a hand for partner that would go to 7 so I was just revealing information to the opponents by asking.


On the replay the auction is almost identical. They're playing normal Blackwood instead of keycard so North shows just 2 aces. South bids 6 hearts instead of asking for kings.

They got the same lead and took the same line of play. Also making 6.

Nick: 980
Jack: 980
IMPs: 0 (-6 total)

Bridge Match 1 - Board 55

Board 55 – Dealer South – All Vul

My hand: ♠ J 7 5 ♥ 7 3 ♦ 9 7 3 ♣ T 9 8 6 4

West opens 1NT in second chair, partner passes, and East bids 2 hearts, transfer. West bids 2 spades, they bid a bunch of stuff and end up stopping in 4 spades. Partner leads the K of diamonds.

	NORTH ♦ K
		EAST ♠ K Q 8 3 2 ♥ Q T 9 6 5 ♦ 8 5 ♣ A
	SOUTH ♠ J 7 5 ♥ 7 3 ♦ 9 7 3 ♣ T 9 8 6 4

West	North	East	South
			Pass
1NT	Pass	2♥1	Pass
2♠	Pass	3♥	Pass
3♠	Pass	4♣2	Pass
4♦3	Pass	4♠	All Pass
1Transfer
2Control in clubs
3Control in diamonds

K-5-3-A. Declarer cashes dummy's stiff A of clubs and then plays a heart to his A in hand. He cashes the K of clubs in his hand pitching dummy's remaining diamond.

He then draws 1 round of trump and plays a heart to his K in hand. Another round of trump and partner is in with the A. A heart through lets me ruff with the J of spades. I have to lead a minor for dummy to ruff, which is then up. Making 5.

	NORTH ♠ A T ♥ J 8 4 ♦ K Q J T 6 ♣ Q 7 3
WEST ♠ 9 6 4 ♥ A K 2 ♦ A 4 2 ♣ K J 5 2		EAST ♠ K Q 8 3 2 ♥ Q T 9 6 5 ♦ 8 5 ♣ A
	SOUTH ♠ J 7 5 ♥ 7 3 ♦ 9 7 3 ♣ T 9 8 6 4

Professor Jack disagrees with my play to the heart suit. Turns out I signaled odd so there was no reason for partner to give me my ruff. Of course he had no other possible play so I guess it didn't hurt but it's the principle of the matter!


The auction is the same on the replay. So is the play. Making 5.

Nick: -650
Jack: -650
IMPs: 0 (-6 total)

Happy Birthday NES!

25 years ago today the Nintendo Entertainment System was launched in the US. As anyone who has an original generation NES knows the system didn't age well. By this I mean 25 years later the consoles don't exactly work optimally anymore. Plug a game in and you're apt to see the power light blink on and off. On and off. On and off. I knew all the old wives tales on how to fix it. Blow in the game! Blow in the machine! Hold he reset button down and power it on and off! Hit the NES! Don't push the game all the way in! Force the spring thing down lower than it should go! Hold it a little higher than it should go!

Very rarely did any of that stuff work. Today I did a little poking around to try to figure out why the blinking happened and the actual reason really surprised me. You see, it all comes down to DRM, and none of that earlier stuff dealt with that underlying problem at all.

What those other things tried to deal with was two other flaws in the design of the NES. The first is they made the internal connectors out of low quality metals so they easily corroded with dirt and wear. The second is that the whole spring loaded system slowly but surely bent the low quality connectors with each use until eventually they stopped connecting as well as they used to. (Both of these problems were fixed with the second generation NES which loaded the game in from the top like the SNES did. Also, you can argue the spring loaded system was needed due to wanting the NES to look like a VCR instead of an Atari what with the console crash and all.) These two reasons would make the console not work at all, though. Lose connection with the game and the system should become unstable and possibly crash. Why would it turn on and off, on and off?

It turns out that Nintendo was worried about bootleggers making their own NES games, so they built a system into the console and into every cartridge to verify that the cartridge was a legitimate Nintendo authorized game. (Nintendo Seal of Quality, as Andrew would say.) So what they did is they put identical chips into the NES and into every cartridge (apparently the chip was $9 per for third party vendors) that would communicate with each other when the power was turned on. If this chip had voltage on its 4th pin and the cartridge didn't properly echo the right response to the chip then it would power off the console. Hence, if you put a bootleg cartridge into the console it would blink on and off, on and off.

But why does my NES blink? Due to a combination of the shoddy connectors and this chip if the connectors lost connection for even an instant the chip in the console would decide you were on a bootleg game and turn the power off. So even if the game itself didn't crash (maybe only the one pin for the DRM chip gave out for that instant) you were screwed.

I pulled out the NES I have here (once owned by Byung) and decided to try it out for the NES' birthday. To no one's surprise, blinky-blinky. It was time to operate! I took some pictures but sadly they didn't turn out well, but I managed to fully disassemble the console and find the DRM chip. I took an exacto-knife to the 4th pin and eventually managed to cut it apart, negating the DRM. I also took out the connector and gave it a quick wipe with windex and a q-tip in the hopes that might do something. I put it all back together and gave it another shot... No blinky-blinky! No game either, though. I definitely managed to turn off the DRM chip but the connector itself must be shot (or I blew something up playing with the motherboard, but the power light did come on). The plan now, if I want to resurrect the machine, is to buy a new connector. I just may do that, especially since I know now how easy it is to open the machine up.

But I wanted to play a game for the NES' birthday, so I downloaded Nesticle and a TMNT rom. Possibly my favourite NES game of all time, and I was surprised that I remembered the end to Shredder's speech on the TV after you save the dam from stupid bombs.