Sunday, January 29, 2012

Theory: Hidden Games and What They Tell Us

Here's a thought experiment for you. Imagine a game. It can be a sport, card game, if you're imaginative enough you could even imagine doing homework or advancing in the business world as a modeled game. Now, for whatever you're imagining, imagine how a perfect robot with 100% comprehension of the game would play in order to maximize its chances to win.

If you are like me you are not actually stopping to think right now, and I want you to, so I am going to include a couple of pictures to break up the text and try to make your brain think!




The reason that I find this so fascinating is that when you look at games at the highest level with the toughest players they are often so different as to become different games. Take Scrabble as an obvious example. A beginning scrabble player is going to spend all their time and energy trying to find the best words. The entire game is "make words worth lots of points". For quite a while progress is going to be down this path, learning that you can make words like "QI" and "ZA" to take advantage of the high-scoring letters, learning all the two-letter words to help with making long words down the sides of other words to score extra points, etc.

If you have two computers play Scrabble against each other the process of discovering every possible word that they can play takes less than a second, but the game is far far from over. When you set two computers against each other in such a way (or two extremely talented Scrabble-playing humans) the game stops being about playing the best word right now and the massive massive strategical element of the game shines through. Scrabble turns out to actually be almost impossibly tactically and strategically complex. If you have access to every available word for your turn you are still going to get outplayed by a better player over and over again, because there is so much more that you need to know to play the game excellently.

What tiles does your opponent hold? You need to calculate what her best moves on the next turn are likely to be, and work out if scoring fewer points yourself is worth it to hinder her ability to score points next turn. You can theoretically gather an awful lot of information towards what tiles your opponent could have, in much the same way that you can gather information about what might be in your opponent's hand in Magic - how long did she take to play her last turn, how many tiles did she use, did she miss any obvious possibilities (say, playing "TILE" in one place when if she had an "S" she could've played "TILES" in another, much better place), what tiles are already on the board or on your rack, etc.

What possibilities will you have next turn? If your opponent is likely to play a word which opens up high-scoring opportunities perhaps you should hold letters like "S", "T", and "E" this turn so that you will have a better chance of having a long word available next turn, or perhaps you should hold letters like "Z" and "Q" because next turn there will be a higher chance of placing them on a Triple Letter tile.

The list of variables goes on for a long long time and, in Scrabble, little effort seems to have been put into developing algorithms to address those further variables. It's easy to program a computer to quickly see two different possibilities which will score it 50 points, but very very difficult to program it to understand which of those would be better for it to play.

I think Scrabble is an example of a game which is hidden by entry-barrier. That is to say, if all people had spent two years learning to recognize word possibilities on a Scrabble board, I think the way the game was played and understood would be unrecognizable to how it is approached right now. Many other games are hidden in such a way, as are many processes in the everyday world. Understanding of games in politics - political campaigns, passing legislation, etc. - is often hindered by a lack of knowledge of how such things work, what the exact goal is, who the politicians involved are and what their motivations are. Investment is heavily underdeveloped (in my opinion) because so much of it depends simply on having enough money to start investing, which is usually either unattainable or so difficult that it takes up too much time to dedicate much energy to actually understanding investment.

Next let's talk about Chess. Chess is a game which is certainly hidden by entry-barrier. I am a terrible chess player, and there are lines that even I know up to move 20. That is to say, against certain moves by my opponents, I know the (well, a. There are often multiple possible responses) theoretically correct response move, and in some games my opponent and I trade theoretically correct moves for 20 moves before either of us actually thinks for himself. The reason that I find Chess particularly interesting is that even with the entry-barrier out of the way playing Chess is still very very very difficult. In Scrabble a slight oversight could give your opponent an extra few points. In Chess failing to see one move which could be played ten moves from now could instantly end the game in your opponent's favor. In yesterday's action at the Tata Steel supertournament, which features fourteen of the best players in the world, David Navara fell from a technically winning position to an almost losing one by missing one such seemingly innocuous move that was only two moves away.


The game of chess, I would argue, is hidden by complexity, or perhaps hidden by lack of confidence. This seems odd to say, because the point of the game, as with many other games, is that it is elegantly complex. That is what makes it a compelling game. What I am trying to say more specifically is that, were two extremely powerful computers to play each other (or even two of the world's current best players) they would quite rarely fail to see something which would allow the game to suddenly swing from winning to losing in one move. However, even for those two extremely powerful players, the lack of clarity in many positions is going to drive the game. It isn't possible to check every variation for every move, and so a potentially weaker move which contains less chance of failure will often be the one chosen.

Perfectly played chess would be impossibly beautiful, but even the best players in the world are forced to admit their imperfection with "safe" decisions, and face their imperfection against unsound attacks. The game becomes about preparing perfectly for the opening, studying rigorously for the end game, and doing as well as you can in the middle game. The most exciting games are ones in which a player studies a new move which, while not the best move, may not have been extensively prepared for by their opponent, leading to dangerous improvisational play in which one player backs their preparation at home against their opponent's ability to exploit a theoretically incorrect move.

When the best computers play there are no such crutches, and the game becomes purely about positional understanding and, well, Chess. A perfect computer will never play a weaker move just because it has calculated that it can't be extremely bad for it - it will play the strongest move and leverage any advantage it has as quickly and savagely as possible. And it will never shy away from a piece sacrifice or a dangerous tactical line because it finds the consequences unclear - it will play that move because its heuristics say it is best and trust itself to survive the explosions that follow. Basically, Chess is a game where playing the best move is often so difficult and risky to understand that it is not worth it to try, and players settle for moves which they think are simply "good enough".

The real-world "game" which strikes me as most hidden by lack of confidence or complexity is dating. The stakes are high, the rules complex, and consequences impossible to fully understand. I don't mean to say that relationships are simply a game, or that they are anything like a game, really. My point, rather, is that relationships often fail to reach their fullest, most beautiful potential, simply because the two (or more) people involved often settle into a rut of safety. How many relationships do you think suffer compared to their most ideal form because they follow basic norms instead of being the best they could possibly be at every moment? I feel that all must. It could be that one person is afraid of embarrassing themselves dancing and so the couple never tries to dance when they could have enjoyed dancing greatly if they had only given it a chance, or it could be something much more serious. Perhaps a relationship could be enhanced by open-status but neither person is willing to risk dealing with the emotions that will follow if they attempt to do so.

The last game I want to talk about is Poker. Poker is so misunderstood that people often call it gambling instead of calling it a game, or argue that it is a "game of chance" instead of a "game of skill". This is because Poker is a game which is hidden by variance. If I went to play at a casino for a few hours I might play 200 hands. If I look at any random collection of 200 hands from my Poker career the results could be just about anything. Maybe I win $200, maybe I lose $4,000. If I look at a large sample of hands though my Poker career (and that of other winning cash-game players) looks like this:


That Poker is so hidden by variance is actually a main reason that it can be so profitable. If players knew from the second they sat down at a table that they were going to lose $200 they would probably just choose not to sit down, but when players are expected to lose $200 they not only have no way to calculate that fact for sure, but there's also a chance they'll win money instead, so it can still be fun for them, and they sit down at the table, and on average they lose $200, some of which ends up in the pockets of people who are using Poker to make a living.

Unfortunately, hiding results due to variance also makes Poker hugely misunderstood. One thing that variance does is damage the way that the game is played; people make bad plays over and over again because they have no way of actually knowing that they are bad.

Whether Poker is played perfectly or not (or even well or not) is not a crucial point for humanity, but the stakes in the real world in situations hidden by variance can be much much much higher. What if instead of a hand of Poker, game theory was being applied to a war? Misunderstanding the actual consequences of actions because you are basing your understanding of them on past results which were in fact unlikely could cost countless lives. On a smaller scale, what if you have massive potential that you are not realizing because you've misread results of your actions? Maybe the girl you were meant to marry was busy the two times you called her and you thought she wasn't interested and never spoke with her again, or maybe you had a bad experience traveling to Fiji and because of it you don't travel much anymore. Humans are massively predisposed towards linking results to their actions causally and strictly, and they give far too great a weight to negative results compared to positive results in most situations. When our brains were evolving, way back when we were hunter-gatherers, a bad outcome could easily mean being eaten by a tiger, while a good outcome only meant eating for a day. In modern society we can much more easily afford to fail and don't have to suffer such absurdly heavy consequences if we do, so we should be willing to take greater risks.

As you go about your life, keep in mind that you are imperfect, and that, for whatever you are doing, even the best person in the world would be imperfect. Try to keep in mind how that might hold you back, and do your best to understand how you can maximize your potential and enjoyment of the world. Games are great fun, but life is always the most important thing, and if you're not applying what you learn from games and about game playing to your life in general you're missing out on a great source of inspiration, intuition, and wisdom.

Thursday, January 26, 2012

Draft #39: RGD 4-3-2-2

Technical problems with the last video, sorry. (I ended up losing).

Wednesday, January 25, 2012

Let's Play: Blood Bowl

You can see my walkthrough of a couple of Blood Bowl matches (the PC port by Cyanide) via the navigation link at the top-left of the page!

Monday, January 9, 2012