Izublog #1: Dominic 

This is part of a series of posts that covers Imbroglio’s Izu mode. It will go up on either the 2nd or 3rd day of the Izu.

This was a below average pool and building a board that could get into the 200s was difficult. The most obvious things to do are to place a Forbidden Scroll in the serpent corner and to use all 4 Bog Hands to make up for the low damage of the other tiles. An open question I had was whether to use a “conservative” build that had Jagged Saws in the center, or to be greedier and put Vampiric Spears there instead. My first good score was with a compromise build, since I couldn’t decide.


Unfortunately, I woke up the next morning to see JackMule had beaten my score by a fair bit with this board:


Jack makes a few notable innovations that I started skeptical about, but gradually saw the wisdom of after banging my head against his high score. 

First, he moves the Scroll to the far corner. This was counterintuitive to me since it’s weak if you get trapped in the corner with a 4 diamond Wasp. But it’s quite strong in the sense that you can power level it to level 1 and then ignore it for the rest of the game. If you place it 1 to the right, as I have done, it wastes space later in the game. Also, Dominic’s powerful stun ability makes him less concerned about getting trapped anyway. 

Second, he uses Repercussion Drums. I had written them off as weak due to the powered up serpents putting pressure on Dominic’s diamonds, especially before they get to max level. However, as the only way to do 4 damage, it seems like they were still worth it.

Third, he plays a very greedy build with no Jagged Saws at all. I wasn’t quite ready to throw away my early game that much, but I knew I had to weaken my early game (resulting in more failed starts) and strengthen my late game to compete. This meant moving the Saws to the edges and corners, replacing them with Spears.

I internalized these lessons and after a lot of gnashing of teeth, I barely beat JackMule’s score. For now, at least, this is the top board:


In addition to the improvements mentioned above, I also did the following:

– Got rid of the Bows. If these aren’t fully leveled by late game, they’re a huge liability and can get you indefinitely trapped, doing 1 heart damage to 4 health monsters.

– Rearranged the Bog Hands to “point at” the Serpent corner. When I parked on one of the lower Vampiric Spears in the late game, my old layout would have Serpents flanking me. Although it’s harder to level than before, it’s a much stronger formation against Serpents later.

– Added a Forbidden Scroll to the Cube corner. My logic here is that in the late game I often can’t afford to step off of a Vampiric Spear to do diamond damage, making Cubes take two hits and slow me down. Of course, you need Cubes to level up your Bog Hands, so I ignored the tile until these were close to fully leveled.

Some notes on playing the board, if you want to try it out:

– Rush xp onto the Serpent Scroll early. It’s OK to burn 2 moves but I wouldn’t waste more.

– If you you can, prioritize the lower Bog Hands (don’t waste many moves), since they’re harder to get to.

– If it’s safe, kill Serpents with Bog Hands early to help level them.

– Ignore the Cube scroll until you are highly leveled. It’s bad to level it early and will only somewhat help you later. 

Overall I’m happy about what I learned, and look forward to using these lessons in future Izus.

Avoid Making the Player Proofread in your Strategy Games

Meet Hector. He’s a powerful jerk in Fire Emblem Heroes and is mostly balanced out by his low movement speed. However, when given the Wings of Mercy ability, Hector can unexpectedly teleport across the screen and ruin your day. This is a serious game design article, but please also enjoy this low-quality meme (source):

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A careful player can notice that Hector has this (non-standard) ability and plan accordingly. Some might argue this is good for the game, since it increases its skill cap. I’d argue it’s a negative, because it’s replacing strategical thought with something less satisfying. For the purposes of this article, let’s call it “proofreading”.

Players begin to proofread when the game state isn’t clear. This forces the player to either spend mental energy nitpicking through the game state himself, or suffer an in-game penalty.

To clarify what I mean, here are a few examples:

Fire Emblem: Heroes

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Fire Emblem

Fire Emblem mostly has a good, clean interface, but scanning for abilities is an annoying exception. A given character can have different abilities, and these can only be noticed by proofreading the tiny ABC circles in the upper right corner. If you don’t immediately recognize an icon, you need to longpress it to see what it does.

A recent patch allowed players to customize their own characters, which will make the PVP arena much more annoying than it was. Those wanting to maximize their chances there will have to click on each enemy unit and doublecheck that their opponent hasn’t given them something nasty.

Hoplite

hoplite
This wizard can attack 5 squares in every direction. Yikes!!

Hoplite has a lot of neat things going for it, but proofreading is a major weakness. The entire board is filled with monsters that can attack from varying ranges. For instance, the wizard in the screenshot can attack 5 hexes in any direction! Tracking one or two of these guys is manageable, but as you progress further into the dungeons, the game becomes a proofreading nightmare. When I was playing, I would first find every spot that I could move to without getting hit. Only *then* would I start thinking about the tactical considerations of each safe square.

This “proofread safe squares” -> “find best move” -> “proofread safe squares” loop ended up pretty tedious, and was one reason why I could never get into the game as much as I would have liked.

Hearthstone – I have lethal!

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Can you spot lethal?

Hearthstone has an amazing interface, but there’s one issue that hasn’t been solved yet. A lot of losses in the game occur because the player forgets to count up the damage he has on the board, and misses a situation where he can kill his opponent that turn. This makes for some entertaining (and humiliating) moments in streamed tournaments, but is fairly annoying as a player. Remembering to do some basic arithmetic isn’t an exciting skill to test.

Avoiding proofreading

Once a “proofreading” situation has been recognized, implementing a solution is seldom straightforward. Often it requires a massive reworking of the basic game system to fix the issue, which is why these sorts of situations show up so much, even in games with AAA user interfaces like Hearthstone or Fire Emblem: Heroes.

That said, there are a few good guidelines that can help avoid a lot of potential proofreading situations:

  • Try to avoid having long-distance interaction unless it adds a lot to your game. Make pieces more like Go, where stones can only affect adjacent spaces, than Chess, where a Bishop can threaten a square from across the board. If you do want a Bishop-like character, try to have the squares it threatens show up as dangerous in the UI, rather than forcing the player to trace all of its paths himself.
  • Try to make sure all commonly relevant information about an object can be found by glancing at the object itself. If a player is frequently rooting through subpanels to find relevant info, your UI is probably not pulling its weight.
  • If the sum of a bunch of numbers is frequently important, add them up for the player and display it somewhere on the UI rather than making the player calculate it himself.

Above all, remember that games are supposed to be fun places to strategize. The less proofreading that gets in the way, the better.

A guide to Imbroglio boardbuilding

There’s a few guidelines I use when I’m building an Imbroglio board. These aren’t always correct, but they’re good rules to keep in mind. If you break them, you should have a good reason.

Rule 1: Keep the “heat map” in mind

Imagine the Imbroglio board as a “heat map” for your character, where high traffic areas you pass through often are red and low traffic areas are blue. What do you think it should look like?

It would roughly look like this:

board_building_1

The center has 4 possible connections, edges have 3, and corners have just 2. This has two effects:

  • If you pick up a star with a monster nearby, you are much more likely to be trapped in a corner than anywhere else.
  • To gather new stars, you’re constantly moving through the center. After that, the edges, and then the corners, where it requires unusual wall setups to ever have to pass through.

Because of these two differences, these three places have different weapon requirements.

If you put something in the center, it should have these properties:

  • Benefits from leveling up, since you’ll be killing a lot of monsters with it.
  • Becomes strong in combat. In the late game, it should be something you can rely on to kill a lot of monsters.
  • Examples: Echo Harp, Menacing Cleaver

If you put something in the corners it should ideally have these properties:

  • Starts out strong. It won’t be getting many levels, since you’ll be using it rarely.
  • Gives some insurance against getting trapped. There are many possible ways to do this. Dwindling Brazier kills the monster outright. Arcane Hourglass banishes it and lets you take care of it later. Blink Dagger lets you escape.

If you put something on the edge, it is usually either a combat weapon that doesn’t need much XP (Rimeclaws), *or* a “tech” weapon that needs lots of XP but is weak for actual combat (Ixxthl’s Ring). The edge is fairly flexible, though.

Rule 2: Mix your reds and blues

To simplify things, let’s say you only have weapons that do 1 heart (red) or 1 diamond of damage. You arrange them like this:

board_building_2

It should be apparent that this is a poor way of arranging your board. For instance, if you are on B1, and a Cube (4 heart, 1 diamond) monster is on C1, you almost certainly will want to use one of your blue weapons on it. But this requires a *minimum* of two moves (more if there are walls in the way) to be able to use one.

All else being equal, the optimal board is this:

board_building_3

If you are on a red square and need to move to a blue one, no matter what, it will only take you 1 move as long as you are not completely blocked from moving. Imbroglio puts you on a “timer” where monsters come out faster and faster as you take more and more turns, so minimizing the number of “wasted” moves is key to getting a high score in Imbroglio. This checkerboard pattern is the best way to do that as a general rule. Or, at least it would be, if it weren’t for Rule 3.

Rule 3: Pay attention to where monsters come out!

The last general wrinkle to consider in board creation is that every type of monster only ever comes out of one corner. Going back to a “heat map” analogy, the heat map for a Cube monster looks like this:

board_building_4

Cubes spawn at A1. They’re guaranteed to go there every time! By comparison, it takes a minimum of 6 moves to get to D4, so they will almost never show up there.

The practical implications of this are as follows:

  • Both Cubes and Snakes are weak to blue weapons.  As a rule, you should have more blue weapons on the left side. This consideration is especially important for the tiles that border the lefthand corners: A2, B1, C1 and D2. You will find yourself standing on these vs. a freshly spawned Cube/Snake quite often, so it is better if they are blue.
  • Both Wasps and Chimeras are weak to red weapons. As a general rule, put more red weapons on the right side. This consideration is especially important for the tiles that border the righthand corners: A3, B4, C4 and D3. You will find yourself standing on these vs. a freshly spawned Wasp/Chimera quite often, so it is better if they are red.

As a note, these guidelines are contradict Rule 2. Let’s refer again to the “checkerboard” formation:

board_building_3

Notice that the squares bordering D1 are both red, and the squares bordering D4 are both blue. This is the opposite of what you ideally want, since it will make dealing with Snakes and Wasps difficult. In practice, boards are often a compromise between the checkerboard pattern, and clumping relevant weapons around the four corners.

Board Analysis

Let’s analyze a board I recently used to clear the game with Masina:

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This board revolves around the synergy between Plague Totem, Reaper’s Scythe and Necromancer’s Mask. When the combo is fully assembled, it’s hard to lose (the tough part is getting that far). Reaper’s Scythes are weak against Cubes and Snakes, so I added Echo Harps (and their eternal love, Whetstones) to help with that.

Plague Totem is a strong corner weapon. If you pick up a star in the corner, you’re normally worried about getting trapped by a monster you can’t kill. For Plague Totems, however, a single monster will be cursed and immediately turn into a ghost. The classic weakness of Plague Totems is that you sometimes can’t afford to take the diamond damage. Being in the corners helps with that (you can often avoid stepping on them if you don’t want to), but I added an Ixxthl’s Ring to help as well.

Every board has a certain “XP load”: the amount of XP you need before your board is functioning as intended. In this case, I want my Whetstones maxed, my Scythes at level 2, at least 1 Necromancer’s Mask fully leveled, and the Ixxthl’s Ring mostly leveled. That’s a high XP load, so the Vampiric Spears are included mostly because they only need 1 level to be pretty good. Masina has issues dying early because she has no “parity” control (ability to pause for a turn to get the first hit in), and the life gain from the Spears helps with that. I also considered using Blight Broadswords, but think they’re overall less useful. Masina’s hero power already lets you boost weapons, so the 2 damage from a broadsword isn’t too relevant here compared to the lifegain.

For placement, the Reaper’s Scythes are my “bread and butter” weapon. They are extremely powerful once operational, especially when boosted by Whetstone and Necromancer’s Mask. That’s why they’re in the center. Ideally I would put the Harps in the center as well, but the recent Whetstone nerf requires them to go there instead.

On the edges, all of my blue tech weapons are on the left so that I’ll be able to level those up quickly. The masks are together because I don’t need both to be maxed – the second mask is more of a luxury than a requirement. This way, I can focus on one, and then level the other one more leisurely. The ring is far away from the masks because I don’t want it competing with the masks for XP; it needs to be leveled up quickly.

Overall, it’s a powerful board, but somewhat inconsistent in the early game due to Masina’s lack of parity control.

Conclusion

Hopefully this guide helps to explain some of the logic behind why I build my boards the way I do. If you’d like me to analyze more boards, let me know either here or on twitter.

Imbroglio’s Izu Mode is the way forward for deckbuilding

Deckbuilding games have a long and successful history. People love customizing their experience and trying to find the best possible deck. If you look at the most popular strategy games today, a huge portion have customization. The best, in my mind, is Imbroglio’s Izu mode.

As most game designers know, the “classic” MTG model has a large weakness in the post-internet era. Players copy other players’ decks, making small improvements. This iterative process from the “hive-mind”  rapidly solves a format, to the point that a game like Magic needs incredible amounts of content to stay fresh. Even with hundreds and hundreds of new cards being printed, formats still get noticeably stale in between releases.

Not everyone can afford to vomit content in the same way that Wizards of the Coast does to maintain Magic. Designers wanting to create smaller customize-able games need more economical solutions. One solution, of course, is to simply refuse to create customizable games. Depending on your taste, this is perfectly valid! But for people that enjoy the process of fine-tuning a “deck”, what’s the best way forward?

A major breakthrough was made in 2008 with Donald X. Vaccarino’s Dominion. It randomized a “bank” of available cards, then had players build a deck from this limited subset. This approach has been tremendously popular, and is on the right track. Unfortunately, it had some basic flaws that prevented it from obsoleting the MTG model in the way Vaccarino had intended:

  1. Everyone started with the same boring deck. Boring!
  2. Making customization in-game limited how different final decks could end up. In Dominion, your final deck ended up being maybe 20 cards, with a few cards different from your opponents. This is a far cry from the level of customization available in a game like MTG, where two players can start turn 1 with completely different 60-card decks.
  3. Part of the fun of a customizable game is discussing “builds” among players. When the bank is randomized each game, it’s hard for a community to build around the game to talk about building things together. Usually at most you could only talk about general power levels, which isn’t as fun as showing off a cool deck you just made.

A great compromise I’ve found has been Imbroglio’s Izu mode. It’s the way forward for customizable games.

Michael Brough’s Imbroglio released to some fanfare last year. In it, players would construct “boards” to take into battle and compete on a global leaderboard. Unfortunately, it suffered the same problem as most customizable games. People iterated on each other’s boards and quickly arrived at working “solutions”, and soon mostly identical boards were populating the top of the leaderboard. The fact that the game released with 8 different characters helped with this somewhat, but within a month or two, every character had a working solution. At this point, there wasn’t much reason to try innovating, and players lost interest.

As a result, it’s sad but perhaps understandable that a comparatively smaller amount of attention was paid to Imbroglio’s follow-up expansion, Ossuary. In it, Brough added “Izu mode”, which has considerably helped with the game’s longevity.

Izu mode works as a sort of hybrid between the Dominion and MTG models. Every 4 days, a new “bank” of available options is generated from a larger pool of tiles for players to construct boards with. They then compete for highscores, which also reset every 4 days. This provides a good compromise of providing customization while still ensuring that the game remains relatively unsolved. It does not take long to find the best board with a given amount of options. However, it takes considerably longer to find the best board for every subset of options, and Izu mode exploits this well.

At the beginning of the period, several viable decks are tried out, and you can see a number of different approaches at the top of the leaderboard. At the end, a specific variant has been found to be the best, and users start adopting this board more and more. Fortunately, this is right around the time when the mode gets reset and players must reoptimize.

Usually, there’s a tension in games between “variety” and “quality”. Do you give a lot of low-quality content to improve variety, or do you add a small amount of quality content, but settle for low variety? Imbroglio finds a healthy mix of letting its “quality-minded” content go far in terms of providing the player with a large variety of game states.

It’s easy to see how a MTG-style game could benefit from taking a similar approach. Rather than trying to race player tendency to solve formats with more and more content, simply randomizing a “bank” of cards for players to construct decks in a given week would allow for a “customizable” game to go farther on a much smaller amount of content.

Survival Games need Difficulty Levels

Survival Game: Games where the goal is to live as long as possible. Often (but not always), this involves plowing through ever increasing hordes of monsters until you eventually succumb to them.

Difficulty Levels: For the purposes of this article, anything that adjusts the difficulty of the game counts. This could take the form of skipping early levels, or making early levels harder.

Pure survival-based videogames were tremendously popular in the 1980’s arcade era: they practically were what people thought of when someone said “videogame.” They declined in the console era, but are resurgent these days; partly from the iOS gaming boom, and partly as game designers slowly realize the strengths of the framework. Survival games tend to be light on cruft, focusing not on more and more content but immediate and brutal challenge. While completion-based games often seem best suited for passive, cinematic gameplay, survival games focus instead on self-improvement in the face of ever-increasing challenge.

However, survival games have a key flaw best illustrated by analogy. Imagine an inept math teacher who only instructs through tests. He gives his student arithmetic tests to start. At first, the student fails the tests repeatedly. However, she slowly figures out the rules of arithmetic, and begins passing some of them. Whenever she passes an arithmetic test, the math teacher immediately gives her an algebra test, which she promptly fails. After she fails, the math teacher starts the loop over by giving her another arithmetic test.

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Soon, she has mastered arithmetic and now routinely alternates between arithmetic tests (which she passes) and algebra tests (which she fails). Eventually, she masters algebra, and begins passing those tests as well. Her teacher rewards her with a new and exciting calculus test. She fails, of course, and soon she falls into a cycle of arithmetic tests (which hold very little value), algebra tests (which still hold some value, but not much), and calculus tests (which are what the student really should be working on).

At first, the style is reasonable, even optimal–test their skills until you find their limit, then go back to the basics and work your way up. However, as the student becomes more and more proficient at mathematics, the math teacher’s method becomes increasingly inefficient. By the time the student wants to learn graduate level mathematics (say, convergence of nonparametric regression techniques), her learning will be severely slowed by the remedial tests she has to grind through before she can even begin learning something new, let alone mastering high-level concepts she’s only seen a couple of times so far.

Survival games carry this exact flaw. As the player slowly masters the game, she progresses further and further on each playthrough. However, whenever she dies and starts over, she’ll have to start again at the exact same spot she did as a beginner. The early parts of the game inevitably become a grind as her skills trivialize their relatively low difficulty.

For this reason, survival strategy games need difficulty levels. The level of challenge appropriate for a beginner is far removed from that of an expert, but a survival game without difficulty levels ineptly presents the same challenges to both players. Without the ability to skip trivialized sections, your game is doomed to be abandoned — not because your player has mastered the game, but because her skills have advanced to the point where she no longer wants to play through increasingly long periods of trivial gameplay to get to a worthy challenge.

Review: Five Card Quest

Five Card Quest is the latest game from Rocketcat, who previously made the excellent Wayward Souls. It’s a turn-based FTL-like card game, where you battle through procedurally generated dungeons and kill a boss at the end. I’m quite partial to these sorts of games and Touch Arcade rated it five stars, so I got it, even though the linked review ominously read, “I don’t usually prejudge games before playing them, but…”

First things first: the game is obscenely buggy. Some of the bugs are reproducible and just another thing to learn, but others appear random and act as an unwanted dice roll. It’s pretty bad right now, so if you’re interested in the game, I’d recommend waiting for a patch or two. Anyway, that’s not too interesting to write about. What about the game design?!

The first sticking point is an interesting one. Rocketcat have made their name making excellent real-time games, and those work well with almost no tutorial. Wayward Souls didn’t tell you what monsters did, or the exact damage on your various weapons… and I’d argue it didn’t matter! In a real-time game, it’s *fun* to figure out the basic rules of the system – figuring out exactly what the enemies do, how many hits it takes to kill them, etc. For a real-time game like Wayward Souls, telling you the rules of the game is largely pointless – “this monster fires a fireball 10 pixels wide every 4 seconds that travels 10 pixels per second” is technically lots of actionable info but in practice you’d learn faster just watching the fireballs fly across the screen. As a whole, Wayward Soul’s refusal to tell you many of the rules ultimately doesn’t matter and even helps the accessibility of the game.

Five Card Quest is much worse off, though. Turn-based games, I’d argue, challenge a different part of your brain, and for reasons I’m not entirely sure of, that part of your brain *hates* even slightly ambiguous rules. As an example, one ability reads, “can interrupt some lightly armored foes.” Um, which ones? There’s no “lightly armored” characteristic anywhere, so in practice you have to spam the ability on various monsters to see whether they get stunned or not. This vagueness, combined with the bugginess, makes learning the game a nightmare. It’s one of the most unnecessarily obtuse games I’ve learned in a while.

Lastly, the game is just too damn easy. It has the typical card balance issues that you see in a lot of card games, and people with some experience are going to hone in on those pretty quick. Not surprisingly, a card that can draw 2 cards, do damage, prevent damage, and is FREE ends up being pretty good in this game. Once you start chaining free actions together it gets pretty easy, particularly given the overly forgiving rules regarding death (dead characters just revive next fight with a small amount of health).

So, the game sucks? Not quite! I’ve been ragging on Five Card Quest up until now, but one thing that is genuinely praiseworthy is the card system itself. You have monsters and your characters aligned in three “lanes”, and in general units can only attack the enemy across from them. So there’s some interesting positioning that happens as a result, in addition to the usual RPG tropes. This, combined with the FTL-like mechanics and lack of variance, made it an okay buy for me. After 5 (long-ish) playthroughs, I feel like I’ve seen most of what the game has to offer, but I had an okay time after the initial game 1 annoyances.

It’s about a 6/10.

Don’t mix Risk Management and Competitive Highscores

Games with Risk Management ask players to choose between low variance (or “safe, but low payout”) and high variance (or “risky, but high payout”) strategies.

Single-player games with Competitive Highscores present highscore as the sole goal of the game. Most of these have an online leaderboard.

Game designers combine the two on a continual basis, which I’ve come to believe is a critical mistake. But first, I need to rewind a bit and explain why risk management is a valuable thing to include in games.

Let’s analyze Pass the Pigs, a simple game that happens to beautifully illustrate what this “risk management” thing is all about. Briefly, the rules are as follows:

1) Players take turns rolling adorable pig-shaped dice. One player usually rolls multiple times on his turn.
2) Most rolls score you points.
3) One particular roll, called “Pig Out”, ends your turn and cancels all points you scored that turn.
4) A player rolls until he chooses to stop (at which point he scores the points earned) or gets a Pig Out.
5) First person to 100 points wins.
6) There is actually a different rule where you can lose *all* of your points, but for simplification, let’s pretend it doesn’t exist.​

Your only real decision each turn is to figure out when to stop and take your points.

Perhaps surprisingly, this game is not trivial to play optimally. The dice are unique–they’re pig-shaped–so calculating the probabilities directly is infeasible. Fortunately, we can gather empirical data instead. Amusingly, John C. Kern actually used statistics to analyze Pass the Pigs in the Journal of Statistics Education. Never underestimate science!

In the paper, Kern first rolled the two pigs 6,000 times to get reasonable point estimates on the chance that you’d get each roll. Among other things, he calculated that:

– Your chance of scoring points is 79%, while your chance of a “Pig Out” is about 21%.
– Once you have accumulated 22 points in a turn, rolling again has negative expected value. By that, I mean that that on average, the number of additional points you can win will be outweighed by the 22 points you will lose if you “Pig Out.”
This paper finds that if we roll on 21 and stop at 22, we can expect to go out after about 10 turns.
– If we carry out an “extreme-conservative” strategy of always stopping after one roll, we can expect to “go out” (score 100 points) after 24 turns.
– If we carry out an “extreme-risk” strategy of rolling until we get 100 points, we can expect to go out after 100 turns.​

So the game is solved, now, right? Just roll until you get 22 or more, and then stop every time?

The problem here is that maximizing points is not the actual goal of Pass the Pigs. The goal is to win by going out, and once you factor in your opponent’s score, risk management comes into play. Consider the extreme example of having 0 points versus your opponent’s 99 points. In this situation, your opponent is going to win if he doesn’t Pig Out on his first roll next turn. Your chances of winning are… pretty low. But how do you maximize them?

If you default to the “best” strategy and stop each time you score 22 points, you can expect to go out after 10 turns. Assuming this average run, this means your opponent needs to not pig out 9 times in a row. The chances of this happening are *astronomically* low: less than 0.00001%!

As it turns out, your best strategy in this case is to adopt the normally terrible “extreme-risk” strategy. Your chances of going out immediately are about 1%, which is already several orders of magnitude higher than using the “best” strategy of stopping at 22 points. In fact, extreme-risk’s chance of winning here is slightly higher than 1%; if you fail to go out on the first try, your opponent might whiff his 80% roll once or twice. But either way, the normally awful “extreme-risk” strategy becomes the best option available to you.

This is the core of what risk management is about. Your strategy depends not just on what maximizes points, but your position in points relative to your opponent’s. When you are ahead, you should try to reduce your risk, opting to stop at rolls less than 22. When you’re behind, it’s time to turn on the gambol. In a good risk management game, you often have two equally puzzling challenges: what is the plan that maximizes resources, and what can you afford to risk to carry out this plan?

How does adding players affect optimal strategy? Raising the number of players also increases your inclination to take risks. With each player added, your chance of winning the game goes down, no matter what strategy you use. Similar to how you’re more inclined to bet your wallet if there’s less in it, you should be more inclined to use high risk strategies when your expected chance of winning the game (“equity,” as game theorists say) is low.

If you’re in a game with one other player using the “extreme-risk” strategy, you can easily win almost no matter what you do. Even the terrible “extreme-conservative” strategy will easily beat him, on average. But add in 99 other players doing that, and there’s a pretty good chance you won’t get to see your second turn! At that stage, you need to employ the extreme-risk strategy yourself to even have a chance.

You might think I’ve forgotten about my original thesis, that high-score competition trivializes risk management decisions. But actually, creating a risk-management game where players compete on a global leaderboard functionally increases the number of players to an arbitrarily large number. Just as how the winner of a 100 player game of Pass the Pigs is most likely the one who decided to employ “extreme-risk” and happened to get lucky, if you have risk management in a high-score competition, there is a virtual guarantee that the players on the leaderboard got there by employing an extreme-risk strategy. This, in turn, trivializes the intricacies of risk-management play.

Credit goes to DisquisitorSam for many of the ideas in this post.

Also thanks to Evizaer for looking over this. ^_^