Posts Tagged ‘Board Games’

The Fifth Path (14/30)

November 15, 2016

Nabua’s Journal Entry for Iyar 13th

Finally figured out that Bel cursed riddle. Got enough info in port town to solve. Needed to know parables. Also needed to know local history. Been learning much of both. Will need to write book when get chance. Learned so much here. Would be terrible to lose gained knowledge. Guide is a hero. Or maybe a heroes. He is legendary. Literally. People tell legends about him. People do not believe he is real. He is also crazy old. More than one hundred. Feel less bad about losing always in Xiwan. Can say almost beat master a few times. Better than most. To list accomplishments would take too much paper. Even with proof belief can be hard. Old man ended two wars. He defeated armies. He discovered lost treasures. He traveled many islands on this side of Green Sea. He slew giant beast. He solved ancient riddles. He toppled governments. He was known as Han the Seeker for long time. Then Han the Slayer. Then Han the Great. Then Han the Terrible. Then just Han. Full name is Ri Xu Han. Need to talk of other things or run out of paper. Very cool guy. Really interesting story.

Walking back from capital faster then walking to. Still too much walking. Fun to meet some bandits and not get stabbed. Seemed like nice people overall. Guess its hard to tell. Would not have been nice if they had actually robbed us. One played Xiwan. Managed to go even. Bandit impressed. Tried to learn story of Han in bandit group. Seems bandit group originally soldiers. Did not get paid after short war. Had weapons and training so paid selves. Famine in land so food hard to find. Han helped out at first because was responsible for soldiers. Left when food problem got better but stayed as bandits. Led group to successful attacks on storage places for food for rich. Sounded accurate.

When got to town found Eric. Had managed to sell all of stuff few days before. Getting bored. Ready to move out again. Enjoyed story of travels. Had some money left at end. Decided to spend most of it because could not convert back. Spent final night in town. Eric went on ahead. Decided to start loading his boat with goods he had bought and preparing for journey. Had been able to get boat fixed with part of money made. Said final goodbye to Han. Had figured out riddle during day. Was able to say goodbye using name. Smiled. Will miss him.

Now come to interesting part of story. We try and leave port. Wave wands over us. Say we can not leave. Question why. Say we have negative money and can not take out of kingdom. Seems very strange. We had gotten little negative money since first day. Had been able to enter town. True we had spent much of money but had still much more positive then negative. Asked them to show us money. Wand pointed to Anatu. Says she is negative by very large amount. Decide to search her for coins. Has very few. Use wand to locate source of negative money. Stored deep within her bag. Large green coin. Anatu very surprised. Guards look scared. Confused. Both talk at once. Hold up hands. Listen to one at time. Anatu says got coin before arriving Xexan. Lady in first port town in Hashim island gave her. Been carrying since. Thought Xexan coins seemed familiar. Guards talk. Say coin is very old. Known as cursed coin. From early days of negative money. Very high denomination coins. Made taking things from people dangerous. Could lose whole fortune in moment if given wrong coin. Now only have small value negative coins. But cursed coins still have their own value. Situation precarious.

Negative value of coin more than what we can make up with current possessions unless sell everything. Most of remaining money spent or went to pay our guide for all help. Can not leave to get things on boat because can not go on dock with negative money. Eric can not come back to give us help either cause he only allowed once and is now not allowed back. Look at agreement signed with leaders. Provisions for reentry? Nothing till Xexan expedition goes to homeland. Try to figure solution.

Need to give coin to someone or get enough positive coin to cancel out. Have little to bargain with. Old man left last night. Said had business in near town. Know it was to play Xiwan. Think hard. Ask to see legal code on law of negative money and leaving kingdom. Very long. Hard to read. Do best. Others can do little with out language. Tried to explain coin came from out of land but not believe. Few ways to leave even if negative. Can be dead. Can be king. Can be hero of the phoenix. Look up last one. Some kind of legend with Huang. Brighten up. Maybe someone who sees them? No. Need much more than that. Whole big list of accomplishments to be hero of the phoenix. Maybe Han could do it but is not here. Turn to section on negative money.

Printed only in capital. Can be destroyed only together with equal amount positive money or under small list of exceptions. Making gift to kingdom of greater value. Saving life of king or general. Eaten by huge serpent creature. None seem useful. Ask about how long to earn money enough. Long time. Could maybe go to capital and ask council or king for help. Long time to travel and maybe pushing luck. King might not willing to release if has good to reason to keep. Think about just breaking through and fighting way out. Maybe possible but probably ruin deal with leaders. Explain situation to companions. Hard time seeing way out. Unlucky. Ask about only some leaving. Say that after Baal leaves, any remaining become illegal. So we can leave Baal behind but if leaves us then maybe stuck here forever. Consider. Ask about people who horde negative money taking it all cause no need to leave town. Laws that make very dangerous. Possible to be imprisoned or killed if debt too high for too long. Giving money to people about to die? Can not be buried without debt paid. Without burial soul can not go to heaven. No one would accept. Sometimes other way around. People take old people money so they can die in peace.

Look at rules for people leaving and entering kingdom. Very few exceptions. Citizens can leave and enter somewhat freely. Even then there are limits. Journeys applied for in advance. Transfer of funds limited. Minimum and maximum trip durations. Others face more severe restrictions. Ways to become citizens few. Could marry a local but still takes a year to become after wedding. Could earn in military but takes long time. Could pass citizen test of language and culture. Hmm. Maybe possible. Ask about. Say only get one try. Taken to building to take test. Angry looking old woman scowls at me. Start test. Starts with language. Very hard. Think get low points. History and culture next. Know much about some nothing about others. Not sure how well done. Culture practical exam. Game of Xiwan.

Face off against old lady. Plays like old man. Have to step up game. Think like him. Remember games against him. Remember response to different situations. She still better. Losing. See long shot. Rely on underestimation. Done nothing too smart yet. Has shot. Make moves toward different objective. Pretend to screw up pattern. Set up attack at real target through apparent errors. Watch ladies face change expressions. Not sure what initial is and not sure what final means. Take lead but unable to finish. Lady starts to take seriously. Begins move seen old man do. Think about how develops. Try to find flaw. Can not see. Know normal response fails. Try something completely different. See own shape in woman position. Start pattern old man used against me. Strikes fear into lady. Backs down from plan that would have killed me. Begins to play defensive. Set up old man plays all over board. No idea what to do with them after first few turns but scares woman again. Press advantage into enemy side. Do stuff that makes no sense. Lady overestimates. Fears because does not understand that with no meaning. Push for victory. Board is a mess. Nothing pretty about game. Makes me cringe.

With victory though comes enough points to pass exam. Barely. Become official citizen of Xexan. Immigration policy gives me three trips abroad to bring stuff back to Xexan. Use first to go get enough stuff from boat to buy coins to make positive. Use second to leave Xexan and continue journey with companions. Maybe even come back some day. Good to visit king and Han if still alive when return. Thanked by companions. Handshake by Baal. Against Bel for Baal to shake hands with Hishtu. Maybe being corrupted from Bel? Hug from Anatu. Also violates Bel rules. Journey changes people. Is Hishtu only one to remember commandments of Bel? Not even part of Bel religion. Strange. All companions becoming heretics and hedonists. Not mind. Wonder why though. Anatu even seems sad to switch back to homeland clothes. Speaking of clothes. Figured out how special thin cloth made. Created from stuff like spider webs but from worms. Very strange. Bought a lot of fabric to take with though. Very comfortable.

Once on boat talk about next destination. Take out maps I bought. Eric wants to go to near port to sell new goods acquired. Turn into lighter goods. Look for route around Green Sea. Do not want to go through again. Unlikely be saved by tornado again. Upper route looks promising. Take few months but brings us close to end goal of journey. Can continue with original plan after that skipping islands we missed on other side of Green Sea then returning home using original plan. Takes us close to several near ports to try and sell goods. With Xexan identification card will make trading easier near Xexan. Eric worried about pirates. Does not understand Xexan well but kept hearing word for pirates many times while selling. Go out to ask port authority about. Indeed many pirates in these times. New pirate leader unites them. Should be very careful. Also warns of sea serpents and whirlpools. Tell everyone might be attacked by pirates. Engine should be faster than pirates. Everyone still worried. Nothing for it now though. Not just going to stay here. Have to keep moving. Consider buying weapon but after talking to port authority think it not good idea. Hard to carry weapons out of country. Fear of selling to pirates or rival nations.

We go anyways. Hope for the best. Watch out for other ships. Try to speed past as much as can. Baal asks to teach Xiwan to him. Wants to beat Anatu. Seen both play. Baal plays better against me then her. Plays with no fear against me even though win always. Seems afraid to lose and has no aggression against her. Explain this to him. Facial expression changes. Wish knew what meant. Say can help some. Teach for while. Of course no space on boat so Anatu joins in too. Baal not tell her is training to beat her so soon she learning too. Eric drops by with few tips. Not know he played. Says will play game next day. Got to do a lot of work with boat for today. Engine not fixed completely. Have Anatu and Uras play against each other. Nag him not to be wimp. Does better. Still loses. Tell to keep trying. Want to start writing about Xexan culture. Do that all night.

Next day Eric says pirates following us. Slow chase. Could take all day. Something to do with wind. Engine not fixed yet. Everyone plans. Still time. Bored. Write.

The Fifth Path (12/30)

November 13, 2016

The First Draft of the Autobiography of Baal Uras, Soon to be 28th King of the True Land

Running Title: A King’s Awakening: Walking the Fifth Path to Understanding

Composed Aru 7th In the 59th Year of Baal Shamas

Chapter 10: The Palace of Xexan

I did not sleep well after the second assassination attempt. The first time we had captured the assassin and Anatu had been watching over her. At this point I trust Anatu completely and totally, so that assassin was not a problem any more. The second one escaped though. That they had been skilled enough to not get caught after Anatu had blocked their initial attack also worried me a bit. Thus far in our journey my Protector’s prowess at fighting had been so far above anything that we have faced that it made physical danger seem much less of a threat. In the very heart of a kingdom just as large as the true lands however, it might be conceivable that their would exist those who could at least match her. And potentially whoever was targeting me had enough resources to employ such skilled servants. My Scholar’s news that two of the council had potential motive for my elimination was about what I was expecting, but it was still disheartening.

For most people, I think, the prospect of negotiating an alliance with an isolationist power while sharing no common language with its rulers would be challenge enough. For me and my companions though, assassination attempts had to be thrown into the mix. So now I had to solve some kind of complicated plot in a city known for its complicated nature while not knowing the language of any of the citizens. Add in existential fear of assassins actually bursting into my room and ending my life, and I think, gentle reader, you can forgive me some tossing and turning. Still, I was not too tired when I awoke, and the bitter beverage that was served at all times of day in this land seemed to have some of the same awakening properties of the coffee of the true land. So by the time our morning meeting got going I was ready and raring to go.

The meeting went well enough. It was however, just as strange to me as all of the meetings since getting into the capital city have been for me. The natural order of all decisions throughout the journey thus far has been the natural order of all meetings between a Baal and their servants. I lead the discussions, and bring in suggestions and ideas from my companions. Sometimes my companions can be dismissive of my initial suggestions and we end up going with something nothing at all like I had originally planned, but each step is still a decision by me. Now however, that has shifted. While no one is subverting my authority, neither are they deferring only to it. There seems to be no real leader in terms of direction of discussion, with it moving from topic to topic based on stuff brought up. And while I can still make the final decision on each step, this has two caveats. One, Anatu can also have the final say. If we are discussing something, some times she just makes a statement about a decision and we move on to the next topic. Secondly, and this has only happened once, so maybe this is all in my head, I was once about to make a decision on a topic, and Anatu caught my eye, arched an eyebrow at me, and I just automatically stopped, and waited for her decision instead. Its a strange feeling. No matter how I look at it, I can’t seem to see my power being usurped exactly in any way. The social dynamic just changed. Its not necessarily a bad thing, as again, I trust my Protector’s judgment, but it feels weird. Perhaps this effect will fade as we move further in time away from the period where my Protector had to make all the decisions. It doesn’t feel that way though. It would seem that this Awakening is changing not only me, but my companions as well. Hopefully everyone can keep their minds free from the corruption of the false world.

In any event, my Scholar was once again sent out alone, the only one of us able to effectively act away from our guide due to the language problem. His rapid improvements in the language are impressive and have proved extremely useful. He was sent to follow the money trail, as apparently there are extensive records of payments and money changing hands withing the palace, for the scanners allow the wealth one is carrying with them to be checked very easily. It was not something I would have thought of, but our guide mentioned the records after Anatu made some comment about the gentlemen with the scanners always laughing about something every time they scanned her. Once my Scholar heard about this, he lit up, and he explained his plan. Then he explained it two more times until we all mostly understood. We would know who is paying who and by how much by the end of the day.

Meanwhile, the rest of us had two goals for that day. One was to continue the negotiate with the council, and the second was to make an attempt at an alliance with the negative money printing council member who’s name was thankfully pronounceable. Our ability to actually do anything about the assassin sender even if we figured out who he was was limited as foreigners. We needed someone with a lot of political clout to fight our battles for us on that front. Depending on how long these two things took, we might get a chance to explore the city a little more as well. The first day’s exploration had been clouded by the incredible, mind numbing, bureaucracy we had to endure, and yesterday we were too busy because of all the ceremonies I mentioned before.

There was about an hour left before the meeting with the council after the meeting concluded and my Scholar practically danced his way out of the room and towards the records office. I spent that time learning a few greetings and formalities of Xexan from our guide. While I had no hope of becoming anywhere close to conversational in the short time we had here, I had learned a lot of languages in my life, and the least I could do was learn enough to greet others and be polite. Such things could go a long way I knew. As such, when the meeting finally started, I was able to greet each of the eight council members with the proper greetings and titles, which earned me a respectful head bow from each one, which, according to our guide, was about the equivalent to a standing ovation in this situation. I was happy my memorizing skills had not failed me, and glad my tongue was finally managing to wrap around these new sounds.

The negotiations that day were exceptionally fun. Not only were we finally getting into the phase where decisions could finally start to get made, but I was also using my questions in suggestions, not just as valuable parts of the negotiations, but also as signals that might draw out emotional responses from the council members. It seemed likely they were all skilled at hiding their facial expressions, but the off chance of a reaction that might actually tell me something meant it was an important thing to try. As such, my suggestions and answers were a bit more blunt then they would be if I was putting all of my effort into diplomacy, in hopes that rapid shifts in tone might shake one of the council members up. It slowed down the negotiations, but as we finally neared the end of the meeting, I could see it start to work. The council members were starting to get more distracted by thoughts of what they would be doing later as we got close to the end, and thus paying less attention to the flow of my words, or rather the flow of my guides words. As such, it was more possible to surprise them by shifting tone rapidly. What the small amount of info I was able to gain told me was strange however. Based on the way they reacted, both of the council members who had been pegged as potential assassin buyers seemed actually interested in the success of this deal, reacting positively as it moved forward, and seeming distraught if the negotiations hit a snag. The other strange bit of info I was able to gain was also not expected. One of the members in charge of the port authority, and thus standing to gain the most from additional trade, seemed incentivised to slow the process down, seeming worried when it sped up, and, after I started looking at it, intentionally bringing up points and things that would serve to take up time. We would have to look into him. In the end the meeting ended well enough, with some progress made, but still, potentially, a ways to go. I said the appropriate goodbyes, and we exited the room.

Now we needed to try and get the attention of our potential benefactor. The scheme was relatively simple, but I was happy to have come up with it. With my usual leadership role being less important in the discussions, it had felt like I needed to contribute more on the idea front. We started by asking a completely different member of the council where the mint for the positive money was. Then, we would head there, then through conversation and happenstance we would decide to check out the negative money mint and just happen to bump into our target. From my Scholar’s work yesterday we knew he was always at the mint to check on it in the early evening, so we planned everything in order to get us there at the right time, and have a good reason to be invited in to his private office and have a chat.

Things went smoothly up to the point where we were visiting the positive mint. Unfortunately the owner of that mint had a big problem with our target, so it became very difficult to bring up the idea of visiting the other mint without offending our host. Thankfully our guide managed to play on the mint owner’s feelings of superiority, and we got him to talk about it in the context of his mint being better. From there we managed to get the location and a pretext for visiting it easily enough. As we were traveling across town to our real destination however, we passed through a dense crowd surrounding a sale on fish, just brought from the port. While I was walking through, one of the many frenzied shoppers suddenly turned, large knife in hand and stabbed me, or at least tried to. I managed to jerk away just in time to avoid being skewered, but the blade still managed to cut through my clothes and put a gash in my chest. My protector was on the man in a moment, but something startled the crowd, people started running into us, and the man managed to escape in the confusion. Needless to say, I was a bit frazzled. Unfortunately this put a bit of a snag in our plan. It would not seem natural at all for us to keep going to visit a mint we supposedly only have a passing interest in right after I got stabbed. Going anywhere but a hospital or back to the palace would be very suspicious. But, we were able to adapt.

Since we actually knew where our target council member lived and what time he was expected to arrive at his mint, we were able to head towards the palace, but do so in such a way that there would be a good shot we would run into him on the road. And seeing me bleeding in the street it would be only appropriate for him to stop and offer us a ride. And that was just what happened. We all entered into his carriage, and he took us to a doctor he knew well to treat my wounds. And in the short bit of time we had in the privacy of the carriage, we sought to bring him into our confidence, explaining about the assassination attempts, and expressing a fear that it was the work of another council member. His response was strange. He acted shocked by the attempts on my life, but it seemed feigned, and he seemed disinclined to get involved in the situation at all. It didn’t seem likely that he was the attacker, but, I realized, it did seem that he likely knew who was, and was scared of them. This did not bode well. We had not considered the possibility of a complicated net of loyalties within the council, or the possibility of some members being manipulated by others. So it was with a great deal of concern that I sat, thinking about the possibilities even as I was stitched up, and my wound cleaned.

It seemed foolish to wander the city after such an attack in broad daylight, so we returned back to our rooms in the palace. I had the strange experience of walking in to my room and finding my former assassin making my bed. Whatever had driven this girl to try and kill me seemed to have vanished completely, at least as far as Anatu was concerned. I still had my reservations, but if my Protector, the person sworn to defend my life with hers, believed in her, I wouldn’t fight it. What could have possibly transpired that inspired that trust is a mystery to me, especially considering the complete inability for the two to talk to one another. Anatu and I took the time to learn a board game from our guide, the same one he had wasted several hours on during our first day of traveling. It had a lot of depth to it, and I could see how one might value a good game of it quite highly. Once we got the rules down, our guide bested both of us a few times, then set us up against each other. It was an interesting contest. We both ended up winning a few games. I had more experience with board games in general, but she was better at seeing some of the attack angles in the game.

We kept playing until Nabua returned. He was dead tired, and dropped a bunch of names connected to each other with reasoning in front of us, muttered something about not knowing anyone’s name, then passed out in his room. It seems we had forgotten that our Scholar didn’t know the names of anyone except the council members, so while he had been able to make connections he didn’t know who they were really between. Our guide chuckled and took the papers into his room, mentioning that he’d try and make sense of the names in the morning. Anatu and I played a few more games, but I started to get tired and made some dumb mistakes in all of them, allowing her to win each one. I was a little annoyed and wanted to win one before I slept, but after the third loss I realized it was not happening that night. I said a sulky goodnight to my protector then passed out.

It was the next day when everything came to a head. The guide was out and about in the morning connecting names with faces and figuring out who everyone was. Meanwhile my Scholar was busy writing. So once again that left Anatu and I to play the board game. I was pretty determined to win the first one, and after a hard fought battle, I did. But she picked up the next few, and it soon became apparent that my experience was being caught up to, and I needed to improve if I didn’t want to keep losing. The grin my Protector was wearing was getting dangerously smug. I could feel my mind returning slowly to the place it had been earlier in regards to my Protector, and I knew I should quit before the effect increased, but my pride wouldn’t let me. As I kept losing, the tone of our conversation shifted, falling into the rhythm of those nights. It was a good thing that our guide burst in when he did, exclaiming that we were all in deep trouble, because I was on the borderline of being able to think about the outside world at that point. I managed to shake myself out of it by the time my Scholar was fetched, and the guide started explaining the situation. My Protector sat down next to me and apologized for going too far. I shook my head, telling her it was my fault. Then we both listened.

I must confess I did not follow all of the reasoning. Some of it was exceedingly complex financially, and some had to do with local culture, but the end result of it was that the money paying for these assassins seemed to be coming from the royal treasury, which could only be accessed by the vote of the whole group, or by the young king. Since the whole group negotiating with us while trying to assassinate me at the same time seemed pretty silly, it somehow had to be the young king, or someone acting as him setting up the assassination attempts. We decided that I would go to the next meeting with the council while at the same time Nabua would try and talk to the young king, see if he could figure something out.

In the end the mystery was solved in a rather anti-climactic fashion. While I was continuing the negotiations, my Scholar managed to get an audience with the king. It then soon become apparent that the king had indeed sent the assassins but mostly because he had liked Nabua from first impressions and he didn’t want him to leave right away. Nabua apparently gave the kid a quick lesson on morality and explained that he was doing something important right now and wanted to keep traveling, but would be willing to hang out until he had to leave. Once the news of this reached the council room, the one council member who had been slowing me down stopped trying to do so, apparently having been under orders from the young king. The negotiations progress smoothly from there, and it reaches the point where I think one more day might be enough. I don’t of course know the reason for this until I meet up with my Scholar later that day. With the assassin threat gone, we finally get to explore the city a bit, and release our ex-assassin servant from our rooms. She decides to stick around until we leave though. While we are out and about, I purchase a copy of the board game that the guide bought us.

We all celebrate not getting assassinated with a lot of food and games that night. Anatu and I show Nabua how to play the game, but when we play him, he ends up winning his first game against both of us. We keep playing him and he seems to be getting better at an alarming rate. After he destroys us for the fifth or sixth time he starts breaking down laughing. Apparently he and the old guide had been playing it together basically since we met the guide, and he was just pretending to be new at it. Anatu smacks him, but he just keeps laughing. We all have a good time and then fall asleep.

How a Computer plays a Game

July 21, 2016

When you hear about a computer thinking a hundred moves ahead, or twenty or whatever, what exactly do you imagine that it is doing? How does knowing all the possible moves help it win? Even if the computer knows what all the possible moves are from a given move, how does this help it decide what to do? There are a lot of possible answers to these questions, but a lot of them make use of an algorithm called MinMax. Said algorithm is going to be the topic of discussion today.

The principle idea of MinMax is incredibly simple. The title says it all. The MinMax algorithm will choose the choice which minimizes the maximum possible value for your opponent. That is to say, you make the move that will make your opponents best move as bad as possible. You look at what the game is like after each different move you could make, and you choose the move that gives the opponent the worst options. If the game only lasts two moves, one move for you and one move for them, then this is easy, but if its like most games, and lasts longer than two moves, then we need some way of figuring out what the opponents best move is. Thankfully, we have this great algorithm called MinMax that can help us out with that. So, in order to find out what the opponents best move is, we assume the opponent is also using MinMax, and that the best move for them, is the one that leaves us with the worst possible best move.

This might sound a bit confusing, so lets break it down with a few simple examples. Lets pretend we have a really simple game. It lasts three moves. You go, then your opponent, then you go again. The game takes place on a very simple board, with only five spaces, all in a line. Each space has a number on it. There is a single piece, and each turn the piece can be moved one space, or kept still. The piece starts in the very middle, and when the game ends, you get a number of points equal to the number on the board where the piece is. You want as many points as possible, your opponent wants you to get as few. The board looks like this [10,-10,0,-1,1]. So the piece starts on the zero square, and can move left or right each turn. The first choice then would be to either stay on zero, go to the negative ten, or go to the negative one.

So, lets start with the MinMax algorithm. We want to pick the move that minimizes our opponents best move. We need to know what our opponents best move is if you go to the -10, what it is when we go to the negative 1, and what it is when we stay on the zero. So, for each option, we pretend like we did it, then look at what our opponent would do.

If we go to -10, our opponents will then use MinMax to find the best move. The opponent’s choices are to go to the 10, stay on the -10, or go to the 0. They will choose the move that leaves us with the worst possible best move. So lets look then at their first choice, to go to 10. If they go to 10, then on our last turn we have the option of staying on 10 or going to -10. Obviously our best move would be to stay on 10. So, if they go to 10, then we get 10 points. If they stay on -10, then on our last turn we have to choose between 10, -10, 0. Again, we are going to choose 10. Finally, if the opponent moves to the 0, then our options are -10, 0, -1, which means we will pick 0. So our opponent wants to minimize our best moves value, so they will choose to go to 0, because that move makes our best move 0, while the other two moves make our best move 10.

Now we know what our opponent is going to do if we go to -10. We then repeat that procedure for staying still, and going to -1. It turns out this is a really terrible game, because our first move doesn’t matter at all. All three moves will end up having the opponent move us back to 0. As such, there is no optimal move for our first move and we can pick one arbitrarily. Then our opponent will make the best move from their position, and we end it by going to 0, which will always be the best move for us. Its a game that will always be a tie if both players play to their best, just like tic-tac-toe.

Now that we have seen an example of how it works, you can kinda see how it might work in a longer game. Assuming you have the power to check all the possibilities, the MinMax algorithm will always find the move that puts you in the best position you can get at the end of the game. The problem of course is having the computation power to do that. In our little tiny game, we only had 3 options each turn, and only 3 turns, but it still took a paragraph or so to write out all the different ways that game could play out. As the number of turns one has to look ahead increases, the computational complexity increases exponentially, making it almost impossible for even a really good computer to look more than a dozen or so moves ahead in a reasonably complex game. If you can’t look ahead to the end of the game, how do you decide which moves are good or bad in MinMax then? In our example game we were able to MinMax all the way to the final score and work our way back up from there, but if we are applying this to Chess or something, and twelve moves in the future no one has won or lost, how do you use this?

The answer is something called a heuristic. A heuristic is like a mathematical guess. Its turning a situation that you don’t understand perfectly and turning it into a number. In Chess, if you wanted a number to determine how good you were doing, you could use pieces captured as a heuristic. A game where you have taken three pawns is better than one where you have taken one. A game where you took a knight and bishop is better then one where you only took a bishop and two pawns. You can assign the captured pieces point values, and when you get as deep as you can go, maybe six or twelve moves in, then you just use the heuristic as your point value. Obviously if the game will end in the next twelve turns this will override the heuristic, and you will use the real values, but once the computer has thought as deeply as it can with MinMax, it has to pick a value to compare the different possible game positions, in order to decide what is a good place or a bad place to be. These are not perfect, and it can lead to the computer making bad decisions if the opponent understands the heuristics and could manipulate them somehow, but its generally the best that can be done.

Actual competitive programs are generally a bit more complicated than this, with ways of modeling certain chains of moves as one move because they always play out the same, and different things like that, but the basic principles I just talked about make up the MinMax algorithm, something you can use to make a reasonably smart computer program to play any given games. As long as you can come up with a way to guess how good the board position is with a heuristic, you can use MinMax and the computer will find the best possible position according to that metric.

The only real limiting factor on the effectiveness of the MinMax algorithm, aside from the exponentially growing computation requirement, is the fact that it assumes the opponent is just as good as it is. If you have some special knowledge of ways the opponent might make a mistake, then potentially you could come out of a game better than the MinMax algorithm would have if they played the same person. Still, if you are playing on the highest level, you have to assume your opponent is going to do really close to the best thing, so it is rare that this ends up mattering. If you were convinced the opponent was literally the worst player ever, and would always make the worst move, then you could probably write the MaxMin algorithm to find the best way to play against them, maximizing the worst possible move on the assumption they will play it.

Anyways, this is just another look into the way computers can think about different problems, and while its probably a little dry, I think it can give you a method to think about games as well, and think about how computers are playing them.

Possible New Format

August 31, 2013

In conversation today, I have discovered a possible focus for this blog as apposed to the random rambling of my usual posting.  It probably won’t start for a while, but I am thinking of posting combo games.  That is to say, I will take two different board or card games, and find a fun way to use the pieces and the important parts of the rules from both games an create a new game from that.  Game design is a hobby of mine, specifically board game design and I think that this would be both incredibly interesting and also a lot more useful to potential future careers than what I am currently doing.  This would of course slow down the posting rate, as I would actually have to put time and testing into the games, but hopefully each post would potentially create a great deal of fun for people who had access to the pieces of both games.  I will begin working on a few of the potential fusion games and once I have written a few I may make that this blogs focus.  For those of you following the dungeons and dragons campaign log, I will also continue to post that as well and I suspect other random things as well when the mood strikes me, but should I actually be able to do this I will not be forcing myself to write a post about something different every night.  Hopefully this works out and is fun.

Twilight Imperium

August 30, 2013

As I am not sure if I have mentioned it before, I am a board game aficionado.  I own a high number of chess variants and such along with several more modern games like Settlers of Catan, World in Flames and Twilight Imperium.  I recently finished a game of the last member of that list and I figured I would talk about how awesome the game was.  

The backstory of twilight imperium is fairly simple.  The galaxy was ruled for many years by a race of aliens called the Lazax.  They were generally benevolent though absolute in their authority.  Eventually however their strength faded and a rebellion wiped all of the lazax off the face of their home world Mechatol Rex.  Though the Lazax were gone, the beurocrasy and political structure that they had created remained.  All of the other races in the galaxy were now in a race to become the new rulers of the galaxy.

The goal of the game is to get 10 points, but these points are largely gained through completeing various objective cards, both public and secret.  These objectives might be military in nature or economic or political or scientific.  The game is wonderful in that it allows many kinds of play.  Their are a host of different space ships for those interested in conquest, but their is also a fairly large tech tree, a voting system in which ones political strength and politcs skills can allow new rules to be added to the game, and various methods of setting up trade agreements and improving economically.  Add this to the space exploration and planet conquering that occurs in the early game, and it becomes a game that has a ton of option as far as how to win and how to play.

Their are a bunch of different races, each of which has their own backstory, special powers, starting units, starting technologies and starting planets.  The choice of race also determines the value of your trade agreements along with netting you a special technology that only you can research.  The races include the Lion looking Merchant race the Hacan, and the Turtle diplomats, the Xxcha.  You can also play as humans, space vampires, the borg, space gypsies, bug people, a sentient disease and many many more.  

I won’t get into how turn order and such works, though from a game design perspective that is also fascinating, but suffice to say, the game is designed so that even though the game can take from 6 to 12 hours to play, individual turns are quick and you have choices to make and ships to buy fairly constantly.  

All in all the game is extremely well designed and fun.  It can be a bit of logistical nightmare to get enough people together enough times to actually finish a game, but its worth the effort, and is in general an all around good time.