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Min-Maxing

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There Will Be Games

When I play board games with my games group, I'm usually more competitive than I would otherwise be. I want to win and try to find the most efficient way to get the most points. However, I know that I'm not usually very good at spotting where the points in a game come from, unless maybe when the theme of the game is really good and guides me to victory. At the same time, others in my games group are usually very good and seem to approach games in a very analytical and victory points focused way. In this article, I want to look at how this type of approach might work and see if it'll help me learn anything from it.

So I looked at game theory, which is a huge field of study that tries to model the behaviour of players in games. It assumes that all players are always making the best choices to get the most points, or the best outcome for themselves. It usually focuses on two players, but in theory could be extended to an infinite number of players.

Game theory is basically all about building decision trees and recording the resulting victory points the players would have after each decision they make. A full decision tree would represent every possible decision of every player and the victory point scores. You could then go to the top of the tree to see which path gives you the most points.

In reality, that tree would become very wide very quickly, even in a two-player game. Also, some games include an element of randomness which will widen the decision tree even further. If you wanted a full tree you'd have to create a branch for every possible random outcome.

Game theory can't be fully applied in a live board game with friends, unless you have very patient friends who are happy for you to map everything out, but it does offer some lessons. It does teach us to look at our options, map each one to a victory point score, then look at the next player's options, map their victory points score and so on around the table. If a path looks like it's giving you the highest victory point gain when compared to the other players, then it's probably a good choice.

The problem for me though is working out what victory points players would get for each choice they have. In some games it's easy, because victory points are mapped directly, but in other games they are abstracted into resources, money or similar, which usually are further converted into other resources or more money, and only at the end of the game do these translate into victory points.

I also often think that some games don't want you to go for victory points straight away, but invest in resources or other things first, because in the long run they will give you bigger benefits and more victory points, which will allow you to overtake other players who simply choose to get a small amount of victory points from the start.

So my next port of call was constant-sum game theory, of which zero-sum game theory is one example. This theory looks at games where there is a shared victory point pool. So in a two-player game for example, when one player gains victory points, the other player loses the same amount of victory points. I think it's quickly clear that the sort of games I play aren't constant-sum games. Chess is a constant-sum game, because either player 1 wins or player 2 or both draw. Poker is another example, because the total amount of money stays the same throughout the game and is just redistributed between players.

By the way, the minmax theorem, which this article's title references, is found in constant-sum game theory.

Leaving constant-sum game theory behind, I then looked at variable-sum game theory, which seems more aligned with the sort of games I play. It is a fascinating theory and discusses things like the prisoner's dilemma. Yet, it still relies on being able to somehow work out the benefit for every player to be able to decide what the best choice is.

The more I looked at game theory, the more I came to realize that my lack of being able to identify where the most victory points in a given game could be found is what is holding me back.

I think that's actually fine and not a bad thing. Making gut decisions is all right and even though it might mean I won't win many games, it doesn't stop me from having fun when playing. If I can find games that have a great theme that meshes well with the rules and guides players to making victory points, then I will have a good chance of winning them.

So what is your approach to making victory points in games? Are you a very analytical player? Do you math everything out? Do you prefer to play whatever feels right? Please share your thoughts and experiences in the comments below. I'd love to hear how other people approach playing board games.

There Will Be Games
Oliver Kinne
Oliver Kinne
Associate Writer

Oliver Kinne aims to publish two new articles every week on his blog, Tabletop Games Blog, and also release both in podcast form. He reviews board games and writes about tabletop games related topics.

Oliver is also the co-host of the Tabletop Inquisition podcast, which releases a new episode every three to four weeks and tackles different issues facing board games, the people who play them and maybe their industry.

Articles by Oliver Kinne

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hotseatgames's Avatar
hotseatgames replied the topic: #314092 15 Sep 2020 08:53
Great article! I don't often win games, and that's fine. I play primarily for fun, and if I win, great, if I don't, did I at least stop Tim from winning?

I don't enjoy the mental gymnastics required to plot out tons of options and repercussions. I usually focus on my short term goal in a game, with a long term goal in the background. I then will try to ascertain the goals of other players, and then decide if pursuing my own goals is more valuable than trying to stop their goals.

Games like Lords of Hellas and Root highlight this kind of play. I have felt like every other turn in Root has to be spent on ruining someone else's day.

Playing with people who over-think it (analysis paralysis) is SO not fun... winning the game is just not worth destroying everyone else's enjoyment.
Shellhead's Avatar
Shellhead replied the topic: #314096 15 Sep 2020 10:26
Games that are won with victory points that can be obtained from multiple sources are sometimes called "point salad games." If you own a copy of a given point salad game, you could take some time to analyze the math behind each source of VP. What are the probabilities of obtaining a given type of VP, and what are the related costs in terms of resources or turns or risks? In some games, you may find that certain VP are more easily scored than others, and you should focus on those VP. Unless it becomes obvious to other players, in which case that should be factored into your estimates, possibly making less popular forms of VP now more reasonable. In other games, it may turn out that all the various sources of VP are well-balanced against each other, in which case you should pay closer attention to what your opponents are doing each game. Some of the classic euros have been analyzed to death on BGG, so you can possibly speed your analysis along by reading some discussion threads about strategy.
jason10mm's Avatar
jason10mm replied the topic: #314101 15 Sep 2020 15:07
Stone Age is a victim of this, as you can thematically starve your villagers to death (or rather, force them to subsist off of stone, brick, sticks and gold) to focus on point earning huts and cards and win. But then you also have to have at least some awareness of what other players are doing lest someone score all the culture cards. Seven Wonders uses the drafting mechanism wonderfully to promote self interest versus denying an opponent a good card.

Puerto Rico has such an optimized path that I've played with folks who get very agitated when you DON'T pick the obviously best role card (best role for you and letting them anticipate the round and their pick as well) and instead pick a card that marginally helps another player more or serves your own goals in a sub optimal way. They will screech "kingmaker!!!" and wring their hands but really it is just a player living more in the moment than they.

Some games MUST be played this way though, like all those Friedmann Friese math games, as the game optimization aspects ARE the game, and efficiency engine building is basically the sole goal. Making a pretty city arraignment in Power Grid is meaningless.

Min-maxing is most objectionable (to me anyway) when it compromises a storytelling game or a RPG. Things like dump stats, picking weapons, items, or spells purely for their in game effects, or wonky skill choices that seem to be contradictory just to push a bonus as high as possible. Some of those games may have a "winner" to justify this behavior but usually the games are more about the trip instead of the destination, it is the players mindset to "win" at all costs.
Shellhead's Avatar
Shellhead replied the topic: #314102 15 Sep 2020 15:23
By coincidence, I started reading Chapter 17 of the fan-written Book of Learning for Magic Realm. Magic Realm is an incredibly complex board game that is also a point salad game. Unlike most point salad games, Magic Realm requires the player to secretly select their VP goals from five possible categories: Gold, Spells, Great Treasures, Fame, and Notoriety, before starting the first turn. Failing to hit a given VP target earns you negative points in that category, while points in a category that you didn't choose aren't as valuable.

Chapter 17 gives specific recommendations for VP goals for each of the 16 characters. For example, the Druid can read magic and is immune to curses, so he should prioritize VP from Spells. The White Knight is a monster killing machine who should emphasize VP from Fame. The Black Knight is very effective against human opponents, so he should focus on Notoriety. And yet all characters should seek points in more than just one category, because it's difficult to score high enough with just one category. But all of this advice is conditional, possibly affected by number of players in the game, map layout, and specific characters played by opponents.
jason10mm's Avatar
jason10mm replied the topic: #314103 15 Sep 2020 15:28
Stuff like that should just be baked into the game IMHO. Require those classes to take some specific end goals and fewer electives if it is that obvious.

Certainly some games are broken with just a few vastly superior strategies but for most there are optimal ways to play but enough chance in the system that anyone could still win with a baseline amount of competence.
Shellhead's Avatar
Shellhead replied the topic: #314108 15 Sep 2020 17:27
I have only played Magic Realm once so far, but it does seem reasonable to either make specific VP goals inherent to each different character, or else give players the freedom to opportunistically pursue any flavor of VP that is available. The real mistake is that the Magic Realm VP calculation is horribly complex. You assign five points to the five categories of VP at the beginning. At the end of the game, you compare your goals with your actual results, except that the goals are expressed in small whole numbers, while your actual results are initially calculated in numbers that need to be converted to compare with your goals.

For example, you might assign 2 points of VP goals to Fame. But every 10 points of Fame gained in the game gets divided by 10 when comparing with your goal, so you need to gain at least 20 Fame to meet your goal of 2 VP in Fame. Notoriety is divided by 20, Spells are divided by 2, and Great Treasures count on a one-for-one basis. Gold is divided by 10, after subtracting the gold cost of your starting weapon and armor. Then there is are penalty points for missing each goal and bonus points for exceeding each goal. I found an online VP calculator and use that instead of wrestling with the math.

Some Magic Realm players ignore the VP system completely, and instead use the fan-made Book of Quests. Each player picks a Quest at the start of the game, and the first player to complete their Quest wins the game. However, the Quests replace the complexity of the VP system with other rules and complications.
Sagrilarus's Avatar
Sagrilarus replied the topic: #314189 17 Sep 2020 10:21
One of the things that I personally look for in games is enough slurry in the running gear to allow you to play the game your own way, with your own personality being in the mix. Min-Max is fundamentally Mr. Spock gaming, which as far as I'm concerned is every bit as tedious as the character was.

Your personality can shine through when there are sufficient options and enough uncertainty about them that you have to play the odds a bit, or hope to convince other players to go along with your approach in order to succeed. This can be co-op or competitive, doesn't matter. But when luck is removed from the game, especially post-decision luck, Mr. Spock shows up (or, more to the point four or five Mr. Spocks show up, all sitting at the same table and all concluding the best correct move together as a committee) and at that point I can go get drinks for everyone while they decide what I do with my turn.

So "Min-Max" to me has become an epithet, a way to insult a game as not terribly engaging or thought provoking. Given the inevitable discussion of "point salad" which followed on in these comments, that design approach is an attempt to make the decision space big enough to prevent other players from having significant impact on how you proceed, in spite of there being more or less zero post-decision luck in the game.

This is about removing luck from games, particularly post-decision luck. Designers have been working their way deeper into the thin end of the envelope because they're chasing the "gamer" market. Designers that let luck happen suddenly find they can create a game where one way to earn one point -- e.g. first one across the finish line -- is sufficient for everyone to have fun. The design space opens up and things blossom from there. Plenty of games to choose from in this part of the market.
Shellhead's Avatar
Shellhead replied the topic: #314190 17 Sep 2020 10:59
Acquire uses cash instead of VP, and everybody liquidates their stocks for market value at the end of the game so it's just an exercise in counting the money. The min-maxing comes in with the disparate prices of the seven hotel stocks. Tower and Luxor are the cheapest stocks, while Imperial and Continental are the premium stocks. All other things being equal, you are better off buying shares of Imperial and Continental because they will probably be worth so much more in the endgame. Fortunately, there is more to the game than this simple min-max calculation. Companies grow or possibly get merged into other companies based on tile play, and all tiles are randomly drawn. Players hold their hand of tiles in secrecy, but must play one every turn. So it's possible that Imperial and Continental may never grow and instead keep getting merged into other corporations for small payoffs. It's also sometimes crucial to hold a controlling interest in a given stock, and that can be more valuable than the stock itself during a merger.
jason10mm's Avatar
jason10mm replied the topic: #314244 18 Sep 2020 16:14
There are plenty of games that have no luck, just pure interplayer strategy. Something like the worker placement Lord's of Waterdeep does really have any luck (unless you consider random card order to be luck) but there are multiple paths to victory both in pursuing a strategy yourself and denying an opponent points they need. I'm not sure I consider this min-maxing, just good play.

To me min-maxing is sacrificing play FUN for the sake of play optimization, though a game that forces players to make nothing but hard choices can be a valid game design as well. And there are certainly players that derive lots of fun out of wringing every last bit of game mechanic optimization out of the system regardless of in game thematic consequences. Most games probably require min maxing in order to function else a player is essentially wasting their turn (either through disinterest, novice play choices, or deliberate sabotage of another player despite knowing it is a suboptimal move for themself).
ubarose's Avatar
ubarose replied the topic: #314247 18 Sep 2020 17:27
People think I don't like games where you can math out how to get the most points because I'm bad at math. The actual reason I don't like them is because:
  1. I am good at math
  2. Arithmetic is boring
  3. You don't really have a choice, you just have the illusion of choice

As Sag points out, you need some element of the unknown to begin to make these sorts of games interesting. The best games are the ones where the other players are the primary uncontrolled variable (i.e. what other players do impacts you in a significant way).Throwing in a little randomness that can be quickly calculated or intuited with some basic knowledge of probability adds drama and fun.