Playing with Probability

I have occasional discourses on probability. Here is Professor Munger having one upon the recent event that the Michigan Daily 4 lottery drew the same number two drawings in a row. The odds of that happening, of course, are exactly the same odds of your winning or of any given number being drawn once: 1/10,000. (If your intuition tells you it should be 1/100,000,000, remember that there are 10,000 ways it could happen.)

I haven’t checked his math on the all-year, many-states extension, but that’s the next piece on which to train your intuition: 1/10,000 events that have a chance to happen many times per day should happen pretty frequently. If you want the extended version of that, the post links to a piece adapted from a book subtitled, “Why Coincidences, Miracles, and Rare Events Happen Every Day.” Because in a world of seven billion people, one-in-a-million events happen seven thousand times a day.

Big, foundational ideas in probability theory were based on analysis of lottery and dice games like this. It is perhaps no wonder that we have trouble with designed more complicated games if our intuition has trouble with something as simple as drawing numbers from a hat.

: Zubon

Quick Review: Spoiler Alert

A conceptually amusing platformer with mixed execution. Playing part of the first world is worth the time; probably not worth buying or playing through the whole thing. I played around 45 minutes to get 100% completion.

You start at the end, defeating the end boss and running away with the princess. Then you go in reverse, from right to left, bouncing off enemies’ heads to wake them back up, returning coins, and catching fireballs. That’s the “conceptually amusing,” a reversed platformer. Not all the coins were collected nor all the enemies stomped on the run through the game you are unwinding, so the challenge is frequently to collect particular coins and avoid bouncing off certain enemies.

This is entertaining for a small number of levels. There are 100 levels. Most of the levels are very short. A perfect run through the game would take about 15 minutes. That is helpful, because stomping an enemy you were not supposed to creates a “paradox,” start over. Some levels are a couple of easy jumps, and you will never see them again. Others require pixel-perfect jumping or timing that you need to memorize because you need to react to some things before they come on screen.

That is, the jump is a fixed height and width, so if you need to make three jumps in a row, you need to know exactly where to start the third one so you can start the first one at the right spot, and the third one will be off-screen. That’s bad design. Many other design decisions are good. For example, when a new enemy is introduced, you have an entire level that is nothing but dodging that attack pattern with no complications, more or less just showing you how this enemy moves.

One design decision initially annoyed me, but I decided it was a good thing. You get a perfect score on a map by beating it with no deaths or paradoxes. You cannot start over in the event of death or paradox, or perhaps you could by quitting to menu, but there was no quick restart I saw. The level restarts automatically upon paradox, and it keeps doing so until you get the whole level perfect in a single run-through. Then you get your score. If you want your perfect score, you need to do that, then start over and do it without failing. In effect, you need to be able to beat the level perfectly twice in a row. I like that. Once can be a fluke (and perfect on the first try still counts); if you just failed it 10 times in a row to get it once, you need to do it again to demonstrate that you actually know what you’re doing. It reminds me of a nice bit in Ender’s Game when Ender has his troops repeat a maneuver three times to prove to themselves that they have mastered it (but only three to avoid having it become a repetitive drill).

: Zubon

Attention to Detail

2015-01-15_00001 Fist of Jesus is a game in the latest Humble Bundle. It is a beat-em-up distinguished only by cartoonish blasphemy; none of the reviews give me hope that the gameplay improves, but if the idea of “play Double Dragon as Jesus and Judas versus Lazarus’ horde of zombies” sounds entertaining, it is currently $5+ for this and four other games (or $8+ for another two, including an actual Double Dragon).

The level of attention to detail in the game is perhaps best attested by the typo in literally the first screen once you start the game.

: Zubon

Difficulty and Creativity

Lower difficulty accommodates a broader range of playstyles and options. Higher difficulty increasingly demands optimization and can make every fight a puzzle boss.

There are more and less effective ways of accomplishing goals in games. For many people, theorycrafting and metagaming are the game, and the real fun comes from figuring out how to manipulate rules and situations for optimal effectiveness. There is a lot to be said for this approach to fun. If you enjoy strategy games, this is probably what you enjoy. Wringing the most value out of every move and option is the heart of strategy gaming.

Many care less about that. They have concepts they want to play, toys they want to use, or “I’m just here to have fun.” It does not matter if the flamethrower is 20% less effective per point than the shotgun; they just want to watch the world burn. At an extreme, there are those who love the difficulty of execution, and they will intentiontally make suboptimal choices to prove they can succeed under those conditions.

High levels of difficulty tend to restrict the range of viable options. In easy fights, like solo MMO play, a silly concept build works just fine, and a perfectly optimized build just saves a little time. As difficulty increases, the number of viable builds narrows (given constant player skill). Difficulty gets tuned this way: playing at the highest difficulty, you may need great execution and a great strategy and an optimized build. If not, the highest difficulty could be made even harder.

The Queen’s Gauntlet in Guild Wars 2 was a good example. You could sleepwalk through most of the fights with an optimized mesmer, and I’m told that warriors were also strong. Other classes needed to struggle and adapt more. Stronger classes and builds could keep their usual skills and talents; some people needed to switch up weapons and abilities to beat some bosses. More skilled players could do more with less, but the DPS check (X hit points, Y seconds to defeat it) limited that.

You can also optimize fun and silly builds to make them viable at higher difficulties or use optimized builds for casual play to compensate for unoptimized playstyles (inexperienced, lazy, drunk, limited physical capabilities). One of the joys of character optimization in Dungeons and Dragons 3.5 was seeing experts take mechanically weak ideas and make them viable characters rather than burdens that needed to be carried by the rest of the party. “We swapped some feats on your whip-wielding halfling cleric, and if you take these spells, you should be back up to par.” The car looks the same on the outside, but because it is souped up under the hood, it handles better when conditions get rough.

: Zubon

Mechanics, Flavor Text, and Warmongering

In Seven Wonders, the blue cards are civic structures like aqueducts and temples. They do nothing during the game but are worth victory points at the end, like victory point cards in Dominion. The red cards are military structures. At the end of each era, players compare how many “shields” of military power they and their neighbors have, and victory points are awarded accordingly (simulating battles). You see the same dynamic that you see in Civilization, where aggressive players go for red cards and compete, while others hoard blue and green (science) cards in self-contained path.

You can build a functionally identical system but change player behavior by changing the flavor text. Keep the mechanics the same but flip the names: that barracks is now a theater that produces “scrolls,” and at the end of each era players compare how much cultural influence they and their neighbors have, and victory points are awarded accordingly (simulating immigration). The former civic structure cards now all have military names, and military prowess does nothing during the game but is worth victory points at the end (which is just as coherent as having aqueducts and courthouses do nothing during the game while they could be given a mechanic showing that they promote health and justice). Better yet, let’s do a three-way trade: now science works like the civics cards did (points per scientific discovery at the end of the game) but the military works like science did; the symbols are now archery, infantry, and cavalry, and you get points for either or both of having one really strong or a complete set of combined forces.

In all those cases, the mechanics are identical. We are just changing names and colors on the cards. But I’m willing to bet that warmongers will still accumulate legions of infantry in that last example, while more peaceful players like me will gleefully compete with their neighbors culturally. It is what I loved about Civilization IV: using cultural imperialism to have enemy cities riot until they could join my empire. You can see the same thing in modded games: take the necromancer, have it summon unicorns and rainbow friendship friends instead of ghosts and demonic worms, and suddenly you have a whole new class that appeals to a different demographic. Tanto Cuore is Dominion re-skinned as a game about Japanese maids, which made it an instant must-buy for one of my friends but drove away other friends who are happy to play Dominion.

: Zubon


“The will to win is not nearly so important as the will to prepare to win.”
— attributed to dozens of coaches

While execution is crucial, the most important parts of the game can happen before you play.

What hardcores are doing that casuals are not is preparing to win. They are theorycrafting, studying builds, practicing skill rotations, learning maps, and generally investing time that will lead to better execution. They are not thinking on the same level as the casual player. While I am playing Starcraft and thinking, “I’ll build a drone. I’ll build another drone. I should probably get a Spawning Pool soon,” the hardcore player is already executing “6 pool” and has most of his brain left to think about how he is going to beat me. To say nothing of games where you can stockpile resources so that playing more means winning more.

Examples outside online gaming are even better. Go watch a local non-professional sporting event and pick out who has been doing her endurance training. Teams fall apart in the fourth quarter because they are tired, while the teams that ran more laps can keep going. Rote learning is actually really valuable1 because you just know things without needing to look them up, think about them, or work them out. Ender’s Game has a lovely bit from Bean’s perspective; he might be the smartest person on the planet, and he can re-derive all of geometry from Euclid, but he needs to study because he won’t have time to re-derive all of geometry on the test. Martial artists practice their kata endlessly because you have less than a second to react to that fist coming at your head.

No one has time to do this for everything. Most of us are casual for most of the things we do. Casual players are entirely reasonable when they say, “It’s just a game,” and they have more important things to do with their time. But hardcore players are just as right when they say you need to put in the hours if you want to get on their level.

: Zubon

(1) Provided what you “just know” is true.

Strategy in the Smallest Things

Do you ever lose track of which units/buildings/whatever in the game are yours? Lately, I have gotten into the habit of intentionally picking the least desired color so that there is less cognitive load from trying to remember which color I have this time. My friends argue over who gets red or black this game, but no one fights me for these Cheetos-orange pieces. Bonus points if you get your own set of meeples and use those for board games so yours are always distinct.

: Zubon


On the one hand, I don’t get the use of “casual” as an insult. “Casual” could reasonably translate to “sane,” particularly in the MMO world. They spend only a few hours a week playing? Yes, that’s a good idea. Games designed for casual players are more accessible, have a comfortable learning curve, and can be enjoyed in relatively small increments.

On the other hand, I completely get why “hardcore” players do not want casuals in their (our) games. Some games require a heavy investment to really pay off, and there are levels of play you cannot reach without practice. If I am trying to play at those levels, I will not be happy about having teammates or opponents who are just there casually. There is a difference between shooting hoops in the driveway and playing basketball in a competitive league. Relatedly, hardcore players reasonably scorn games designed for casual players because they are often shallow, with a low skill ceiling.1

“Mastery” is the concept I think I want here. Casual players are there to play, to have a bit of fun. Hardcore players are there to master the game, and that is where their fun is. Neither is a wrong way to approach playing games, although one might be ill-suited to particular game, and conflicts arise when you put both sorts of players on the same field, whether in direct competition or simple interaction from playing with the same toys.2

Many of the best games have both casual and hardcore appeal. They can be enjoyed with a minimal investment and enjoyed further with greater investment, without making the casual players feel like they are being excluded. But you know Sturgeon’s Revelation, and those relatively few games are “the best” because they capture that rare pinnacle.

: Zubon

(1) Casual players can reasonably scorn games designed for hardcore players because they are often unnecessarily complicated, with a huge investment required for limited reward beyond the cognitive dissonance that it must have been worth it.

(2) Good PvP matching systems help separate those two groups to make competitive games. Oddly, the market is one place where casuals and hardcores can interact to mutual benefit. Hardcore speculators love profiting off naive casuals, and naive casuals can immediately cash in for what they consider a decent price without even noticing that they could have gotten 12.4% more if they had researched market trends. Capitalism, ho!

Quick Review: Dear Esther

Pretty but shallow. Lovely visuals and sound, but it gains nothing from being in a game format. The story is evocative but never completely gels. I am told that there are semi-random elements, which would be an advantage of the game format except nothing makes that apparent and how many people want to walk through the game again in the chance that the verbal part will vary randomly? Also a reason why the story may not gel; it must support multiple, conflicting stories at once.

Great atmosphere, marginally worth the time (~hour), certainly not worth the price. You would be happier watching someone else play through the game, which is the same effect except for holding down the W key.

: Zubon