Tools for analysis

[awall]

I'm curious: What do players who draft out their plays use to help them analyze the possibilities? Exdeath mentioned that he uses a whiteboard, and this strikes me as the ideal tool for working through the possibilities, but I don't have one, and I'm really not a paper sort of person. Right now, I'm using a text-editor to write out possible gesture chains and work through what'd happen, but working with matrices is a pain in the butt.

Does anybody have any recommendations for software that could be used to build some kind of tree-like graph? What tools do other people use for their analysis? I may just have to go ahead and get a small whiteboard or something, but I prefer electronic stuff when possible, as it's easier to save your work and look back at it later (i.e. if the same situation arises in a later game).

[Slartucker]

I use a text editor for relatively uninvolved decision points I need to think out, or for matrixes where the significant part of the result involves something tangible (i.e., dying or not dying) rather than gestures. For anything more I use pen and paper, which is significantly easier both for matrixes and for trees of possible turns.

I recently put together a binder in which I keep some of my more general analyses, one to a page with several relevant dividers. I did this after getting frustrated by a particularly convoluted but also useful series of email exchanges with Taliesin, which I came back to after a month and had to spend over an hour trying to understand again. At the moment it mostly contains explorations of different opening match-ups.

[Rycchus]

I use a text editor if I can't reach to a pen and paper, otherwise I use pen and paper.
I've been trying the whiteboard thing though. It's not half bad.

[zugzwang]

So has anyone (and I'm looking particularly at you, Slarty) come up with a decent notation for analysing positions? Finding a way to record the results of such an analysis which is compact, understandable, and contains all the relevant details seems a pretty challenging problem to me, and one I've never successfully solved.

My analyses, if such they deserve to be called, tend to be ad hoc combinations of writing out likely consequences, with frequent applications of the rubber to explore different paths, and the occasional matrix (rarely more than 2 by 2) with most pertinant details kept only in my head. Quick and reasonably effective, but no use as a permanent record.

So any tips? And: I don't suppose you feel like scanning in the contents of that magic ring-binder, Slarty? I'd be fascinated to see it.

[Slartucker]

I rarely write out 2x2 matrixes, as those are pretty easy to keep track of in my head. The matrixes I do write out are more likely to be something like 3x4 (in-game) or 6x8 (general analysis of openings, say). For the latter type, I'll cross out an entire row or column if I'm convinced it's totally, or near totally, suboptimal. But I don't make those assumptions when I begin, as sometimes there can be several esoteric possibilities that nudge the general picture from what I expect.

I'm not sure what you have in mind with this notation. The most compact way to cover "all the relevant details" is just to scribe the relevant turns of spellflow. I suppose you could reduce a matrix to text and produce something standardized that includes a list of relevant options and a brief description of pros and cons.

[zugzwang]

I'm impressed that you can calculate 2x2s in your head; I know the arithmetic is pretty simple, but just holding 4 numbers in my head at once is beyond my pathetic brain's capabilities...

Hmm, though what do you mean when you talk of matrices? Do you actually mean, as I do, estimating numerically the utility of each possible position and calculating the minimax equilibrium - or do you just mean cataloguing the possibilities in the hopes that staring at it will provide insights?

In any case, you're probably right that the complexity couldn't be martialled by any amount of fancy notation. You just have to recursively analyse as many possible paths as you can as deep as you can; hoping to find dominated strategies you can rule out early, and situations where the direction and degree of advantage is clear enough to estimate.

Sounds like a pretty mammoth undertaking - are you finding your results so far useful in actual play?

[Slartucker]

I seem to remember having an extended debate with you in the spring of last year as to whether or not your numerical abstractions were useful. I don't use numbers in matrixes and I never do math. (Neither did the other matrix advocate, Yaron, and he was a mathematician!)

It may be useful to use numbers for probability when you are dealing with a black-and-white situation. Taliesin and Rycchus recently did this very professionally for a particular strand of FOD -- that will be in the refuge update. However, I find that numerical estimations of utility miss the point entirely most of the time.

The classic example is their PSD vs my WP and ogre. I'll assume an environment free from any complicating factors, and for simplicity's sake I'll ignore the possibility of a PSDP or PSDS dummy. Of the four possibilities, two are great (PSD is countered), one is good (PSDF hits) and one is horrible (PSDD hits). However, the difference between the great and good possibilities is totally irrelevant. Obviously it's better not to be charmed; but the charmed position remains one I know I can win from, assuming I don't make mistakes and am not outplayed. So unless I'm playing someone who has is likely to do so, I'm never going to counter myself -- no amount of great positions are worth even one horrible one. But if you do it numerically and assign a lower value to the charmed position, you'll get the result that you need to counter yourself some percentage of the time. It doesn't matter how much you're ahead, it just matters that you're ahead, and if you put vectors into matrixes, as opposed to just directionalities, this fact gets distorted.

As for my out-of-game analysis, a lot of it just confirms things I already knew or suspected, but some of it has led me to some highly useful tricks, including several opening variants I've never seen played before.

[zugzwang]

Ah, I was thinking that your talk of matrices meant that I'd won that debate. Well, this probably isn't the place to rehash it in depth, but just briefly:

Yes, if you believe that you outclass your opponent to such a degree that you can win with absolute certainty from a particular position, then it would be foolish to risk anything to get to a seemingly better position. However, if you consider your opponent to be of approximately equal ability, then it might well be that getting to the "good" position leaves you with less than 100% chance of winning, while that "great" position will leave you with a higher chance. From there, unless you want to bring in psychological concerns, logic dictates that you indeed should risk a worse position - even an instant death - for a chance at getting a better position if it leaves you with a better chance of winning overall.

Warlocks is a simultaneous move game, hence inevitably probabilistic... you can ignore that fact, but it won't go away!

Though no, I'm not really convinced that exact computation of matrices with largely arbitrary entries is a practically useful way to deal with it except in the most clearcut cases.

[Slartucker]

It's not about outclassing ability. If Yaron and I played each other and one of us was given an ogre at the start of the game, whoever began with the ogre would very likely win. We were quite equal in playing ability, therefore a material advantage would make all the difference.

In warlocks, when both players are equal in ability, a small advantage will tend to multiply itself into gradually greater advantages until one wins. You need an advantage of a certain size to rise above the natural ebb and flow of initiative, so a goblin usually won't do it, but an ogre will. So I would really say that, in the example above, the successful ogre defense is closer to winning than the charmed player result is, but they are both on the road to winning; and the latter result is less likely only in the sense that there are more chances for me to screw up or my opponent to trick me.

What I'm saying is that simultaneous movement is not inevitably probabilistic, not all of the time. There are certainly times when it is, but just as frequently either (1) one player is in a dominating position regardless of choices made on a turn, or (2) the plurality of probabilities becomes a big brown puddle, in which sorting out the individual colors of contributing probabilities is both difficult and irrelevant.

[zugzwang]

OK, perhaps in that specific example the 'good' situation really is as close to 100% chance of winning as makes no difference worth worrying about. Then indeed you should take no risks. But this isn't always the case - for example, near the start of the game it really might be worth taking a risk for a small gain, even if the risk is of letting Yaron get an ogre and a sure win.

[taliesin]

I think I'm going to throw the cat among the pigeons here, but I don't usually use matrices at all. I use a simple text editor.

Why? My play style relies heavily on worst case analysis. I start with a position, and make moves turn about, assuming my opponent knows what I'm doing and will stop me. I'll go back and explore other possibilities, looking for something still worse. I have a plan, of course, but I'm always concerned with the best possible foiling of that plan. I am in effect focused on finding the row of the matrix which provides the best worst case, not caring about the other rows, and I pour my time into deepening my knowledge of the line I currently believe superior.

Sometimes all bets are off; say, for instance, I have a monster and potentially consecutive counterspells but I'm facing double charms. I normally play this kind of situation by gut, because while some paths may be better than others, my opponent will know these paths are better than others, and his probability of taking the options that do most to defeat these paths rises. Calculating in your opponent's probability of following a given option is something better left to instinct than mathematically assigned, and naturally assigning numbers to the pay-offs is almost certain to mislead you.

Lastly, I will take risks, but most of them are mild risks. If I am ahead, I may take a gamble that will reduce me roughly to equality if it fails, but stands to win the game if it succeeds; if I am against the wall, I probably won't do anything that will kill me, but will be more daring in a bid to beat my adversary's predictions of my play style. If I'm equal, I'll often bet on my preferred spellflow being superior.