That's Combinatorics

I had some people over after the Serenity movie on Saturday to play board games. I learned two new games and played a third I’d only played once before (Louis XIV, Endeavor, Ra:Dice Game). All three were games I enjoyed and would like to play again. Louis XIV had an interesting ending that sparked a bit of debate due to a hidden scoring mechanic in the game that I thought was a little interesting. I ended up writing a script to simulate the ending which I ran about half a million times to crunch some numbers about how the game ‘should’ end from the game state we got to.

Without going into the specifics of the game itself, know that there’s only three way to score points in the game. The first is accomplishing a task and is worth 5 points. The second is to collect tokens each worth 1 point. (These tokens have pictures on them but you get them blindly so you have no control over the pictures.) The third is to have the most of a given picture of token. Each picture that you have the most of is worth 1 bonus point. The first two sources are easy to calculate, the question becomes how many of the bonus points do you expect to get?

Now, the token pile is split into 6 pictures, and there are 10 of each picture. We played a three player game and ended up with a 9-11-13 split. The debate broke down into how reasonable is it for a given player in that position to score up enough bonus points to win. I was the 9 and had completed an extra task over the course of the game, so I had an extra 5 points. Pounder had the 11 and Duncan had the 13. Since each token is worth 1 and I had 5 extra points I was in the lead going into the bonus phase. I was up by 1 point on Duncan and 3 on Pounder. The bonus points ended up being split 2-2-2 (ties go to no one) so I won, but ‘should’ I have won? How reasonable would it have been for Pounder to come back from down 3 to pass me? (This came about from a debate about who to ‘screw’ if you have the choice.) Assuming no tiebreakers, the approximate odds from my simulation for each result are:

Nick Wins 24.06%
Pounder Wins 0.02%
Duncan Wins 39.50%
Nick-Duncan Tie 35.88%
Nick-Pounder Tie 0.03%
Pounder-Duncan Tie 0.02%
Nick-Pounder-Duncan Tie 0.50%

Turns out being down 3 with the 11 of a 9-11-13 split is a very bad spot to be. Pounder has practically no chance of outright winning and not much better of pulling off a tie. Even if he wins all tiebreakers (in the specifics of the game he won tiebreakers, then I beat Duncan) he doesn’t even win 1 game in 100. I outright win 24% of the time which is pretty reasonable, so despite it being a little favourable to have gotten a 2-2-2 split it’s not like I stole the win. When you consider I had the tiebreaker on Duncan my win chance shoots up to almost 60% which is pretty reasonable. And indicates a very close game took place. If Pounder had some way to give Duncan or I a point during the game it would have had a pretty big impact on the outcome of the game. (All those ties turn into straight wins for Duncan and some number of my wins turn into ties.)

A question then is how many points is a chit worth? It’s worth 1 plus the amount of bonus you earn divided by the number of them it took to get there. In the specific game my chits were worth more because it only took 9 of them to get the same number of bonus points Duncan got with 13. But how much are they worth in general? This is a question I should be able to answer with combinatorics but it’s been a good 10 years since I took an enumeration course and I just can’t work it out right now. (Aidan said he was going to try!) I should probably get a book and refresh myself on it. (And on stats, so I could work out confidence intervals for my simulations instead of just assuming they’re good enough…) But for the specific breakdown of 9-11-13 I can say that the 9 expects to get .86 bonus points, the 11 expects to get 1.4 bonus points and the 13 expects to get 2.1 bonus points. (With 1.6 wasted to ties.) On a per tile basis, my chits were worth 1.09, Pounder’s were worth 1.13, and Duncan’s were worth 1.16. The more you get the more they’re worth, but they still aren’t worth very much extra.

The final question then becomes: “Is this a good mechanic”? (The initial debate on Saturday started with this very question.) My viewpoint hasn’t changed given the numbers but I’m curious if anyone else has an opinion on the matter before I go into details.

Can't Stop The Serenity

Yesterday I went to a charity event for Equality Now, an organization devoted to women's rights worldwide. It turns out the organization was founded by a student of Joss Whedon's mother and he's a supporter of Equality Now and gender equality in general.

They showed the movie Serenity and then had an auction of various sci-fi/fantasy/Whedon related stuffs. I'd seen the Firefly series once but had never seen the movie, so when Duncan told me about the event I decided to go. (I enjoyed the movie but wasn't exactly blown away.) I ended up buying something in the auction that I thought was pretty cool, and the money went to a good cause. I'd have been happy to just bump up the price for someone else but I ended up with something I can hang on my very barren walls so it's all good!

Deathless Wasteland

Often when I'm playing games I'll be listening to music. Pandora got shut down a few years ago now, so I was forced to find an alternative for my internet radio fix. I've settled on Jango which does a pretty reasonable job of doing the 'similar music' thing Pandora did, though not nearly as well.

One great thing Jango does do, though, is allow budding artists to pay to have their music played over the air. There are lots of different ways to target listeners based on what they already listen to or where they live or how old they are and whatnot. For the listener it pops up a box when one of these 'new artist' songs comes on and lets you choose if you like it or not. If you don't the song immediately ends and it lets you pick an artist to come next. (Normally it's random.)

At any rate, there's one song that came on like this that I think is awesome, despite being classified as 'country'. They've put a free mp3 download up on their website (for a limited time) and I think anyone who might read this should check it out. It's about zombies!

Deathless Wasteland (Behind Zombie Eyes) by Lynn Lister

Expansion Ore

I have a bit of a predicament coming up with the impending release of Cataclysm. You see, my main character is a blacksmith/jewelcrafter. These are two professions that both require massive amounts of ore to level. You get ore by being a miner or by buying it from one. Now, I believe the price of the expansion ore is going to be astronomically high when the expansion is first released for a few reasons.

- There’s likely to be an achievement for being the first one to max out a given profession. As such, hard core achievement people are going to want to get there first. I don’t see any way to mine enough ore yourself, so even a miner/blacksmith is going to need to buy ore to max blacksmithing first.
- Mining is a useless profession stat-wise for any hardcore raider that isn’t a tank. Jewelcrafting is the best. Blacksmithing is second best. (At least for some classes, and they’re both very good for everyone.) As such, a lot of the hardcore raiding player base can’t produce ore but will consume ore.
- Jewelcrafting makes an absolute fortune when everyone is gearing up and few people are providing gems. Therefore hardcore money makers are going to see getting a lot of ore early to level jewelcrafting to be a good investment.
- My friend Sky is a hardcore raider who cares about achievements and loves to make money. I know he intends to buy gobs and gobs of overpriced ore. He has way more money than I do, therefore outbidding him isn’t feasible.

So, what can I do? I saw three options and Blake provided me with a 4th. (Go false trichotomies!)

- Wait for the price to go down. I don’t necessarily need to cap my professions right away (especially if I’m not trying for the realm first achievements) and I’m sure the price of ore will fall at some point.
- Drop blacksmithing now and level mining. That way I can accumulate ore at a reasonable pace to level jewelcrafting. I won’t get there first, but I will still get to a point where I can make money off cutting gems and then I can sell the rest of my ore off while it’s very expensive. Note that I am a tank so mining actually has a raiding relevant benefit for me.
- Level my hunter to 80. She’s a miner, so I can use her to mine ore to level both blacksmithing and mining. I still won’t get there first, but I will get there before the price of ore goes down I would think.
- (Blake’s plan) Level my druid to 80. Drop one of her professions so I can level mining. Do the same as above, but with a character that has instant flight form. I don’t like the idea of dropping a profession on my old main for sentimental reasons but there’s no real reason why I couldn’t. (He actually suggested dropping both professions to get mining and herbalism and go crazy on the gathering. Not a terrible plan; if I go partway I might as well go the whole way.)

There are still a few months before the expansion hits at least, so I have plenty of time to decide, but since most of the options involve levelling characters or mining or both I need to get a head start on it. Does anyone see something I may be missing? My gut feeling right now is to go with Blake’s plan. I do like playing a druid…

WBC Scheduling

I’ve attended the World Boardgaming Championships (hereafter referred to as WBC) each of the last three years. Each of the three years I went into the week with different levels of planning in terms of what I wanted to play and when. The main reason for the differences year to year is the different tools I had available going into the event.

The first year I pretty much just wanted to see what was going on and do things that seemed fun. Optimizing the week wasn’t really on my mind, and as such I didn’t look on their website for scheduling aids. I used the schedule they gave me at the event and picked things coming up that looked fun. (Or that were Risk...) As such, I remember leaving the event and somewhat lamenting the various things I didn’t find time to do. For example, I wanted to play a crayon rails game but didn’t find time to as there was always something else I wanted to do that overlapped it in some way. Not that I actually wish I’d done anything differently, it was a blast, but there had to be a way to optimize my time better.

The next year there was a scheduling spreadsheet for download on their website. Every round of every event was listed and had coloured cells blocking out the times a game was played. There didn’t seem to be a lot of fancy things you could do, but it made it easier to visualize the overlap of events. I didn’t play around with it very much, pretty much just on the car ride down. (Hey, gotta find something to annoy Pounder with for 8 hours, right?) It helped identify in advance certain things (like how Vegas Showdown and Queen’s Gambit massively overlapped) but it wasn’t everything I’d want.

Last year the previous spreadsheet was gone and in its place was one that just listed every round and some small details about the rounds. The extra work to build out a picture of how long things were going to take was gone. Basically it was a big collated list of the printed schedule they hand out. You could derive all the information about conflicts and such from it if you worked at it, but you really had to work for any detailed information. I didn’t notice the difference until the car ride down (I downloaded it to my laptop beforehand assuming it was the same as the year before.) I definitely feel like I had less of a plan last year than I did two years ago. (It didn’t help that my laptop battery died on the way down and my power cord was conveniently in my apartment in Toronto.)

At any rate, I went to their website a month or so ago and browsed the scheduling tools they had available. Pretty much the same as last year, and no sign of the detailed spreadsheet from two years ago. This made me a little sad, but then I remember that my job is basically building funky spreadsheets and I could probably make a pretty good scheduling tool if I set my mind to it. And in a twist I actually have put some effort into it! The spreadsheet is starting to get pretty fleshed out, and I’m going to post some screenshots here. Feedback would be very appreciated, and I can send an alpha copy of the sheet to interested parties.
I’ve set it up so that there are two ways to add a round to your plan. You can pick and choose individual rounds you want to play in or you can select a specific set of rounds you’re interested in for a whole game and it will select all the rounds that compose that event. Here’s a screenshot showing the Games tab, where you can make global choices.

Column G is where you make choices. The dropdown menu there lets you pick between All, All No Demo, Finals No Demo, Playoff No Demo, and Demo Only. All chooses every round associated with that game name. All No Demo does the same but ignores the demo. (I don’t really need to go learn how to play Vegas Showdown, for example!) Finals No Demo takes all currently available heats and all of the playoffs. Playoff No Demo takes all currently available heats and the first round of the playoffs. Demo Only takes just the demo.

After a choice has been made the sheet autoupdates the information in columns F and H. Column F tells you the maximal selection you could make for that game given your current choices. Note in the example I cannot add Liar’s Dice to my plan as it’s availability is “Conflict”. I could plan to play a game of Queen’s Gambit, but I cannot play even the first round of the playoffs. Column H tells you why you can’t sign up for all the rounds of the event. I can see that the only thing holding me back from playing Liar’s Dice is the Vegas Showdown final. So, if I don’t end up making it that far, I can go play Liar’s Dice.

If you don’t like what the sheet has done for you and want to edit the selections you can switch to the Rounds tab, shown below. You can also use this tab just for gathering more information.

Look at the Saint Petersburg rows in the above screenshot. The demo is currently Available as it has no conflicts but I haven’t chosen that I want to play it. The first round is coloured red and marked as a Conflict. Column N then tells you what it conflicts with. I chose to plan for Can’t Stop round 1, so I can’t play Saint Petersburg round 1. If I wanted to release Saint Petersburg round 3 for some reason (maybe I’m cocky, I’m pretty sure I can win just round 2 and advance) I could just go clear cell K589. It would then autoupdate everything else. Great! Note you can sort or filter this sheet by the availability column to see what stuff remains as possible choices to fill in gaps in your week.

Speaking of gaps, what does my week look like? Switch over to the Time Slots tab and take a look at the summary, shown below.

I can use this to see where I can fit more stuff in. (Looks like Wednesday afternoon is free!) You can also use this tab to look for food breaks. Friday at 4pm looks like a great time to grab a bite! Or I could play Ace of Aces heat 4… I don’t really need to eat, do I, Pounder?

When it comes right down to it I’ll probably end up throwing the schedule out the window once the week starts and something random comes up, but the C&O minor in me wants to find a way to optimize my week and I think this sheet is off to a good start to getting there!

How Do You Play? How Do You Win?

I find myself teaching board games to my friends quite often. This happens partly because I’m an anal retentive perfectionist and therefore want to read the rules and partly because once I find a game I like I want to show it to everyone I know. For most of the people I play with there’s really only two things you need to worry about, as told so eloquently by James Coburn in his tv ad about slot machines. How do you play? How do you win? I’ll show you how!

For the most part how you win is pretty straightforward. Most if not all of the games we play lately are “euro” style games where you accumulate points over the course of the game. Eventually the game ends and whoever has the most points is the winner. Games like this tend to have scoring summaries to hand out which tell you exactly what actions can earn you points and how many. You probably need to iterate over the summary and explain what each item means, but it’s pretty straightforward. You win by doing the stuff listed here!

How do you play flows nicely from there. There’s normally a turn order summary (often on the same card!) and then you just need to link the potential actions you can take to the scoring items. Easy peasy! First time players who learn the rules this way aren’t terribly likely to win but they should have a reasonable shot at playing the game properly, of having fun, and of learning how to win for future games. The alternative where a lot of strategy is spelled out in the rules explanation makes set-up take a ton of extra time and most people would rather just get to playing. (Try to teach Agricola to someone who wants to win on their first game and needs to learn everything before the first turn!)

Scoring by victory points in this way also lends itself nicely to figuring out how you ‘could’ play when you can’t win. You have a number you can make bigger! It’s ok if you’re not going to win, you still have a relevant in-game goal. Score more points! (How to deal with player ‘elimination’ in general is a topic of lively debate and not really the topic at hand. Suffice it say when you’re learning a game just scoring points will be hard to argue against.)

This works great for euros, but how do you deal with games with odd winning conditions. The game that brought this to light for me is Republic of Rome, a game from 1990 that simulates the Roman senate. The game has many different end conditions and different winners depending on game state when the game ends. In particular there are 3 potential outcomes:

- Rome falls to some catastrophe and everyone is loyal to Rome. Everyone loses.
- Rome falls to certain catastrophes and someone is a rebel. The rebel wins.
- Someone loyal to Rome accumulates enough influence to win.

Consider a specific player’s point of view. How do they win? Take it one step further… Once they know they can’t win (as new players rarely can in any game) how can they play without screwing the game? Taking actions to score victory points in a euro is unlikely to be massively disruptive, what about here?

In a euro you’ve got a grading system that’s easy to understand. More points is better! But in Republic of Rome the potential outcomes from a single person’s point of view are:

- Be loyal to Rome and get enough influence to win. You win!
- Be a rebel and have Rome fall in some way. You win!
- Everyone loses.
- Have Rome fail when someone else is a rebel. They win, you lose!
- Have someone else be loyal to Rome and get enough influence to win. They win, you lose!

The question then is how do you order those 5 things to determine what our player’s goals are. How do you win? Once you can’t win, what do you do? Is it better to have someone who isn’t you win or to have everyone lose? Does the answer to that question change after the ‘learning’ games are done and you’re playing ‘for reals’?

I’ve only played the game twice (and we got the rules muddled all over the place due to the reprinted version having terribly printed rules) but I still don’t know what the right thing to do is. I asked Andrew about this and his response was rather predictable. “If I can’t win, no one should win!” Which, I must admit, is the stance I took. Unsurprisingly this resulted in Rome collapsing and everyone losing in both games. I know for sure I could have stopped the second one from happening (I could have donated enough money to Rome to field a big enough army to survive for game end, but I was guaranteed to not win if I did) and I’m pretty sure the first game was lost because Matt came to the same conclusion. (In his case he blackmailed the leader, which had two possible outcomes. One - he became the leader. Two - we lose…)

My gut feeling is that I’m always going to take the 1% chance to win in a game like this and if I can’t win, well, no one should. Does that mean I can’t play games like this? Do we need to come to some sort of agreement that having everyone lose is somehow worse than having someone win? I could be convinced that having Rome survive with a winner is better than having Rome burn with a rebel who wins. Is it really that much more of a stretch to believe that it’s also better than everyone loses? Alternatively, maybe the game is better if it’s harder for Rome to burn. (We didn’t play with any optional rules, maybe those would help too.)

Maybe it all comes down to how you feel about kingmaking. If you hate the idea of kingmaking then you’d need to get into a position to brute force a victory which seems hard to do (especially in a 6 player game). On the other hand, if I have no problem picking a winner it would be fairly easy to team up with someone else to make them win.

False Dichotomies

I read a backgammon strategy book a while ago where the author made the case that decent backgammon players make mistakes not because they can't properly choose the best move between their options but because they fail to even consider the best move at all. The problem being that they find two moves that look good, work out which one is the better between the two, and go with it. The problem, obviously, is that there's way more than 2 different moves in almost every backgammon position and you're giving up little edges every time you don't consider all the good moves.

This flaw exists in more than just backgammon. It's human nature to fall for this logical fallacy, and I believe I've fallen for it in terms of how I gear my Death Knight for tanking. Some background:

There's currently a stat in World of Warcraft called expertise. This stat reduces the chance a mob has of dodging or parrying your attacks. Having my autoattacks get dodged or parried costs me damage and threat. Having my specials get dodges or parried costs me time and possible damage, threat, and healing. I don't like any of those things, so it seems like I want expertise.

Unfortunately right now there is exactly one tanking piece at top level for me with expertise on it. On top of that I get to use a 2-handed weapon, which can also have a lot of expertise on it. That item is pants, and there is another great set of pants with a lot of armor on it.

When I first looked into this situation a couple months ago it looked like I had two options. Either I could wear the pants with expertise and give up on the armor pants or I could wear the armor pants and give up on the expertise. I won't say I had threat problems persay but I was definitely skirting the line so I decided to stick with my expertise pants.

The problem, of course, is that those aren't my only two options at all. Another option (the reason I'm making this post) is I could just gem expertise instead of stamina in a couple sockets to make up the difference. I need to look into exactly what I'd be giving up to do it, but it is certainly something I should have looked at in the first place. A fourth option which I hadn't even thought of until right now is switching in an expertise trinket, or enchants. In all of these cases I need to decide between threat and survivability but I should look at what I'm giving up in each case instead of just ignoring their existance.

Which takes us back to the false dichotomy. I didn't say to myself "Hey, socketing expertise isn't a good choice for reasons X and Y." No, I just didn't think of it at all. I got sucked into choosing between A and B and forgot to even look for C.

Right now the only fight that matters to me is a fight where I am dying a lot and where my threat is largely irrelevant. My gut feeling now is to just switch pants and screw expertise entirely but I want to see what the costs are this time around to make that decision!

So, my options are:

A) Status Quo: Wear Sanctified Scourgelord Legguards. 2310 ac, 123 str, 273 sta, 118 def, 92 dodge, 82 expertise
B) Just Pillars of Might: 3500 ac, 162 str, 279 sta, 10 def, 79 dodge, 77 parry

Switching to B from A gains 1190 ac, 39 str, 6 sta, 77 parry at the cost of -108 def, -13 dodge, -82 expertise.

I remain uncrittable without the defense, so I’m fine there.

C) I currently have 6 red sockets filled with purple gems at the moment. As such, it’s pretty easy to make up 60 of the expertise by switching those from dodge/sta gems to expertise/sta gems. Beyond that, I can give up 30 stamina to get the remaining 20 expertise I’m losing.
D) Enchant gloves: Expertise gives me 15 expertise at the cost of 10 parry and 2% threat. The expertise won’t make up that threat difference, so this is terrible.
E) Enchant bracers: Expertise gives 15 expertise at the cost of 40 stamina. This is a worse ratio than changing my gems, so this is also terrible.
F) Put on Victor’s Call. It is 83 expertise and costs me 228 stamina.

Now, my slightly outdated stat valuation for ac puts 18 bonus ac as worth the same as 1 stamina. So picking up 1190 extra ac is worth 66 stamina, so giving up 30 stamina to get there is good. Giving up 228 stamina to get there is not. Option F is therefore terrible.

I also don’t need to get all the way to the first expertise cap. It’s certainly good to get there (worth trading dodge for, for example) but may not be worth giving up stamina for. Especially given my current role on Lich King hard I think giving up dodge is fine but giving up stamina is not. So, assuming I switch purple gems all around my overall change by switching legs is:
1190 ac, 39 str, 6 sta, 77 parry at the cost of -108 def, -73 dodge, -22 expertise.

The parry and dodge about cancel each other out so I’m giving up 108 defense for 1190 ac and 39 strength. This is actually pretty close, since the 108 defense has very real value in terms of avoidance. In fact, my old values slot 108 defense as being worth 1166 ac. So making the swap is a marginal gain there, but it`s not the end of the world if I stick with my current setup.

I think I’m going to make the switch. It’s not a big gain but it is a gain. I also don`t have the T10.5 pants yet, just the T10 ones, so it is a big upgrade until I would get a 5th token.

Failure!

One thing I noticed going through the old posts is just how often I made a New Year's resolution to post more and just how rarely I stuck to it. The first time: 5 days. The second time: 4 days. The third time: I started 3 months late and made it 3 days.

I think part of the reason there is a set a specific goal; to post every day. As soon as I missed a single day I had failed. Why continue after that, really? And thus, it fell off the rails completely thanks to failure.

This time around, I have no such resolution. A 2010 resolution is growing on my face and has not, as yet, been deemed a failure. As such, if I miss a single day I won't have failed and maybe my mind won't just give up completely. One can hope!

Now, to turn to the colour scheme...

Welcome Back, Kotter!

Hi Everybody! {Hi Doctor Nick!}

In the past month I've been reading some blogs. One from my friend Sky who I talk to several times a week, another from someone I went to high school with but have had no subsequent contact and one from a random dude who grows moustaches. I really got lost in their worlds while I was reading them. Now Sky's makes sense; he writes about a lot of things we do together (WoW and board games mostly) and since a bunch of people I know comment on his blog it's a lot like we're just hanging out only it's on a blog instead of in a lounge. The second one kinda makes sense; it's like getting postcards from someone I knew 13 years ago. That's almost a normal thing to have happen I would think. But the last guy, well, there's really no rational explanation for why I cared about when his baby takes naps. Read the post about moustaches and then move on is what should have happened. Vicariously live a house husbands life by reading blog posts for several hours when I probably should have been sleeping? Not a lot of sense there, I don't think.

I reread all my old posts (ok, I skimmed the outdated stuff about WoW quest chains) and don't feel like what I had was really good enough to have someone from any of those three camps read it and enjoy it. However, I think it could get to that point if I actually work at it. I want people I hang out with now to leave comments and have discussions on random things I may post. I want old friends who may randomly stumble across the blog to think "Hey, I knew that guy! What has he been up to?". And I even think I want random strangers to stumble in and find my ramblings interesting enough to waste an evening reading them.

I think I'm a cyber-voyeur. And I want to be a cyber-exhibitionist. Man, I'm really screwed up...


One thing I noticed is this site is butt ugly. I'm sure I had a good reason for picking this heinous colour scheme in the first place but I'm going to have to mess around with the templates at some point and fix it. This blog has been up for four and a half years (though not active for most of that time) and it's only gotten two comments. I'm pretty sure being painful to look at probably caused some of that.

Another is that I made too many typoes in the first place. I know the initial scope was to try to curb my anal retentive perfectionism and not edit anything at all but that's just not good enough. I intend to at least use spell check this time around! Huzzah!

I'm not sure what the focus is really going to be at this point but I'm going to see what I can do to spruce the place up and get actual posts running. I can probably cobble together a WBC 2009 recap, though with the long delay (again) it'll be just as mediocre as the last two! Maybe this year I'll still be posting come August so I'll get it done in a timely manner. One can only hope...