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November 7, 2012

Unpredictability and control in turn-based combat: an examination

Unpredictability makes art interesting. Twists of plot, unconventional characterizations, and surprising character development engage a reader’s imagination; unique instrumentation, sudden shifts in time signature, or an unexpected chord progression delight the ear.

So is it with games. Exploration, experimentation, discovery: all of these depend upon unpredictability, on gaps in the player’s familiarity with the game. Challenge exists only where the player cannot know exactly how a scenario is going to play out ahead of time. This is the sort of unpredictability we are going to talk about today: since it concerns game mechanics, let’s call it mechanical unpredictability.

Real-time games, as a general rule, have an easy time fostering mechanical unpredictability. Spatial navigation requires accuracy and timing; a real-time attack could miss or hit depending on a player’s physical input. The chance of making a mistake in the heat of the moment adds uncertainty, and thus tension.

Without this sort of real-time interaction, turn-based games must look elsewhere for their mechanical unpredictability. Many developers working on turn-based games mistakenly believe that unpredictability is necessarily bound up in randomness. Indeed, there is an assumption prevalent in the design community that any turn-based game without randomness will feel stale, predictable, devoid of tension.

This is a misapprehension, however. Randomness creates uncertainty, it is true, but so do other elements. This piece will examine a variety of tension-building elements, from the basic die roll to other methods that—quite undeservedly—receive less attention and respect. Each method has its benefits and its costs, though some entail a higher cost than others. We’ll begin with the most obvious, then discuss it in comparison to other methods that tend to get overlooked.

 

Randomized results

Randomized results are the very first thing any game developer thinks of when trying to add unpredictability to a turn-based combat system, so let’s talk about that technique first.

Randomized results are what happens when you interpose chance between a player’s chosen action and the results of that action. The results are determined by recourse to randomly chosen numbers: hence, “randomized results.”

If you have played RPGs for any length of time, you are already intimately familiar with randomized results. The ubiquitous “chance to hit” is a perfect example of a randomized result; so is variable attack damage. These implementations have proven incredibly popular with game developers ever since students first started cloning Dungeons and Dragons mechanics on a PLATO mainframe.

Aside from the fact that these mechanics have a long tradition, the simple fact is that randomizing results is the easiest possible way to add unpredictability to a turn-based combat system. “I ordered my character to attack, but I cannot know if the attack will actually land.” This takes very little effort to implement, but it still hides information from the player, and therefore builds tension fairly effectively.

However, the use of randomized results comes at a cost. As I’ve discussed in the past, excessive reliance on randomized results tends to produce two big problems:

  1. Excessively randomized results obscure the likely outcome of individual player actions, resulting in more opaque mechanics.
  2. Excessively randomized results take control away from the player, creating a watered-down sense of player responsibility for the outcome of battles. (“That was a bad die roll!” “The random number generator screwed me!” etc.)

In a well-designed real-time game, the player is willing to accept defeat over and over again if the controls are tight and responsive. The player knows that she and she alone is in control of her character. If she dies, it is because of some combination of three factors: (1) she wasn’t fast enough, (2) she wasn’t clever enough, or (3) she wasn’t accurate enough in responding to what was happening on the screen. It’s her fault, and she is likely to accept that fact, soldiering on with renewed determination. Game developers working on action games focus on the importance of tight controls for precisely this reason: because it means the difference between commitment and frustration, between the player taking responsibility for her failure or concluding that the game itself is flawed.

This same principle applies to turn-based games as well, though the “control” at issue is of a different sort. As with real-time games, turn-based games must respond predictably to chosen actions; without that connection, the player will not feel responsible for the outcome.

While predictability hinges on responsiveness in real-time games, in turn-based games, it is largely a matter of determinism. Many turn-based games (particularly those with combat systems built to imitate the D&D model) feature battles in which the player can engage in the same preparation and use the same tactics, but nonetheless get vastly different results based on invisible, randomized numbers outside of the player’s control. Thus, although randomized results create uncertainty, they can also sabotage the sense that a player is responsible for her failures, which is bad.

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A simplistic example illustrates the point:

Suppose that Bob is playing an RPG where he controls a party of five characters facing off against a troll. None of his characters have any guaranteed-hit attacks available. Suppose that Bob needs three of his five characters to hit the troll to kill it; also suppose that the troll will almost certainly kill one of Bob’s characters if the troll is not killed on this turn. Bob commands the party to attack.

In a deterministic system, when Bob commands all five characters to attack the enemy, they will all hit. His choices were entirely responsible for his victory over the enemy, and so he is 100% responsible for his ensuing victory.

But let’s say that we have a system with randomized results; let’s say that each character has an 80% chance to strike the troll. In this scenario, four or more characters might miss their attacks despite the fact that probability strongly favors a better result. While unlikely, let us suppose that four or five characters miss. The troll survives the turn, and one of Bob’s characters is slain.

Did Bob command his characters to miss? Of course not; the game chose to nullify his chosen actions on the basis of invisible, randomly selected numbers. Nor can we say that Bob made a poor tactical decision; he made his choice based on what was by far the most likely numerical result (namely, that at least three of his characters would strike the enemy). In all likelihood, Bob can reload his previous saved game, replay this scenario, make the exact same decision, and nonetheless get a completely different outcome. Bob is not responsible for the fact that the enemy survived here, and will be quite justified in assigning at least partial credit for this failure to factors outside his control.

This is one of the perverse realities of probability: although the probability of missing five 80% chance-to-hit attacks in a row is far less than 1%, each individual “die roll” is independent of the others. So in reality, there is actually an entirely probable 1-in-5 chance of missing each individual attack, no matter whether the ones before it hit or missed.

Randomized attack damage, featured by Dungeons and Dragons and many of its closer imitators, just amplifies the problem.

Let’s take our Bob example again. Suppose that each character deals 1d6 damage; if all five characters hit, the total damage will be the sum of five six-sided die rolls. As a general rule when rolling multiple dice, the most likely result is always just a little bit higher than half the maximum possible roll. For example: when rolling two 6-sided dice, the most likely sum is not 6 (half of 12, the maximum possible roll)—the most likely sum is actually 7. Likewise, when rolling five 6-sided dice, the most likely sums are 17 and 18, not 15.

Now, let’s say that the troll has 17 health points left. Let’s also say that the five characters’ attack rolls add up to 16. What were the chances of rolling beneath both of the most likely sums? The answer: just over 39%.

So far, not too bad. But let’s get a little crazy. Let’s say that the troll has only 11 health left. We’d have to have fantastically bad luck to roll 10 or lower on 5d6, wouldn’t we? It seems that we would: the probability of getting a sum of 10 or lower across five rolls is only 1.620%! Couldn’t happen, right?

Of course it can. Remember, every die roll is independent of the others. Every roll carries an even chance of rolling any number on the die, and a greater than 33% chance of rolling a 2 or lower. The 1.620% figure only accounts for the numbers you haven’t rolled yet. So once you roll three 1s and a 3, you still have a dead even chance of rolling 3 or lower on your last roll and getting a sum total of 9. Ultimately, it does not matter that the entire sequence of events at first seemed wildly unlikely.

And though it may be fairly uncommon for your players to get totally screwed in this fashion, this is actually not an especially good argument in favor of randomized results. The fact that it seems so improbable just means that when it does happen, it will feel like the game equivalent of getting struck by lightning out of a clear sky: arbitrary and painful.

The simple fact is that adding yet another layer of randomness in between a player’s tactical choices and the outcome of those choices further distances the player’s input from what happens on the screen. The player thus becomes even more likely to grow frustrated when the game fails to respond predictably to her choices. Although randomized results add unpredictability, they do so while (1) decreasing player control and (2) incurring a corresponding increase in player antipathy. This phenomenon is especially problematic in high-stakes situations, where randomized results can cause the player to face serious consequences (e.g. permadeath) even if he makes the most optimal move.

On top of all of this, excessive use of randomized results also renders a game’s mechanics more opaque. Think back to the discussion about the probabilities of various die rolls that we just had above. Did you find all of that clear and elegant, or did you find it sort of confusing and unintuitive? More to the point: how many of your players do you suppose will understand what’s happening there?

The more you rely upon randomized results, the more your players will have to engage in analysis like this to understand your game’s mechanics. I don’t think it will be too controversial for me to say that it is not exactly desirable for us to force higher order math on players who wish to understand how to make good decisions in our games. There must be a better way to generate unpredictability.

Tactical complexity and second party uncertainty

Luckily, unpredictability is not just a spark that flickers into existence for the moment between issuing a command and watching the game’s onscreen interpretation of it. Unpredictability can also exist on a much broader level. Developers can employ a combination of clever AI and tactical depth to keep turn-based combat unpredictable and wrought with tension.

Chess and Go are a fine example for us to look at. As we know, Chess and Go do not have an ounce of randomness in them. Every last move is 100% deterministic in its effects. It is never unclear what happens if your knight moves onto a pawn’s space: the knight takes the pawn. Period. End of story. Likewise, you’ll never sit there biting your nails, wondering what happens when you surround a group of enemy pieces in Go. The pieces are either taken or not taken based on a simple, unchanging rule. The results of the move are entirely predictable.

And yet, matches of Chess and Go can positively drip tension, the end results of any given match wildly uncertain. How is that possible? The answer lies not in what happens after the player selects a move, but rather in what happens beforehand. In Chess and Go, the player faces a black box full of dangerous and unpredictable moves. This is possible only because each of these games sports two characteristics: (1) a thinking opponent and (2) a large possibility space.

As you no doubt divined, the clever opponent is the primary source of unpredictability here. A clever opponent will go out of its way to seize on weaknesses in a player’s plan. The player never knows for certain which move such an opponent will opt for, and therefore has to tread carefully to avoid having her own moves exploited. In order to succeed, the player has to try to guess the opponent’s likely response to each move from among multiple viable options: in short, to outwit him. This is a huge source of unpredictability—and thus, tension.

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However, a sufficiently large possibility space is essential to make this work well. I’ll quote Ian Bogost here for a definition of “possibility space”:

In a video game, the possibility space refers to the myriad configurations the player might construct to see the ways the processes inscribed in the system work.

This is somewhat similar to what programmers refer to as the state space, meaning the number of possible states the game can exist in from a game’s start until completion.

A cunning opponent can be hamstrung by an overly simplistic combat system. Consider Tic-Tac-Toe, a deterministic game with (as games go) a tiny possibility space. Every turn past the first presents only a single optimal move. The only option for a clever opponent is to fight the player to a draw. (As Randall Munroe of XKCD puts it: “The only winning move is to play, perfectly, waiting for your opponent to make a mistake.”) Because the optimal counter to every move is predictable, there is no tension in fighting a clever opponent in a game of Tic-Tac-Toe.

Chess and Go, by contrast, have massive possibility spaces. On any given turn, there are numerous viable moves; if there exists a single optimal move, it is obscured by the massive number of choices on offer and the unique state of the playing field. This renders the game unpredictable.

I choose to call this phenomenon second party uncertainty, since it concerns uncertainty about what the second party—the opponent—will do. Second party uncertainty differs fundamentally from the uncertainty imposed by randomized results, in that its tension arises not from whether the game will choose to nullify your commands, but from whether those commands are themselves good enough. To analogize to real-time games for a moment: second party uncertainty is the equivalent of playing a hotly contested match of Super Street Fighter IV and feeling out your opponent for weaknesses while trying desperately not to slip up. Randomized results are the equivalent of knowing that the game is going to occasionally not register your button presses. Both offer tension and unpredictability, but one is of a clearly superior variety.

The uses of randomized results

Having just argued so strongly against the use of randomized results, you may surprised to hear that I am now going to discuss reasons to use randomized results.

Much of my design philosophy over the past six years has been a reaction against the widespread overreliance on randomized results I saw in RPGs and turn-based strategy games. My goal was simple: put control back in the hands of the player. A good strategy will work; a bad strategy will not. Period. No more wasting time reloading the game because your characters missed too many attacks in a row.

To that end, I did away with randomized results beginning with Telepath RPG Chapter 2. From that game onward, the Telepath combat system was almost entirely deterministic: attacks always hit, and they almost always did the same damage. Targets with elemental resistance took less damage and backstabbed targets took more, but the damage always changed according to a fixed percentage, entirely predictable to the experienced player.

Recently, I’ve been looking for ways to deepen the system, and that has led me to question whether pure determinism is really the best way to go.

Arguably, the biggest problem with the choice to rely exclusively on tactical uncertainty to promote unpredictability is that the AI must be truly clever and varied, or else the player is eventually going to figure out how it thinks. Once that happens, the player will be able to beat the AI consistently and without difficulty. When the only uncertainty in a battle consists of the choices the AI will make, definitionally, there can be no uncertainty left once the AI becomes predictable.

I first encountered this argument after releasing Telepath Psy Arena 2. It’s a clever argument, but really this is an argument for better AI, not an argument for randomized results. Making attacks randomly hit or miss, or making them randomly deal 1-6 damage instead of just 6 damage, is the proverbial finger in the dyke. It is a cheap solution that does little to fix a glaring structural weakness in the game; a game of craps attempting to stand in for a clever and unpredictable opponent.

A second potential issue is personality-based. For some, failure in a game bruises their sense of themselves as competent people. In their minds, they didn’t just lose because they tried a strategy that didn’t work; they lost because they are intrinsically not smart enough, not good enough. The ego is much too tightly wrapped up in the results of particular challenges, producing a personalization of loss that can be emotionally crushing. The mediation of the dice provides an “out,” a way of walking away from a loss without feeling totally responsible. In short, it’s the flip side of my argument above: determinism promotes a feeling of player responsibility, but perhaps some players don’t want to feel wholly responsible.

Personally, I’m not convinced that this is a good reason to add in heavy randomization. If you aren’t responsible for your loss because the dice intervened in the outcome, then what does that say about the moment when you actually win? Is that victory as meaningful? Insofar as such a thing can be stated objectively, I feel comfortable in saying that beating someone in chess is objectively a greater accomplishment than beating them in Mario Party—or in Risk, for that matter. The more luck victory requires, the less you can say to have achieved victory solely through your own wits.

There are more arguments to look at. David White, lead developer of Battle for Wesnoth, wrote a lengthy post back in 2008 justifying the game’s heavy use of randomized results. (Interestingly, the developers apparently received so many complaints about the randomized results in their game that they felt obliged to stick a link to this post in their game’s official FAQ!)

White’s defense is spirited but flawed. For one thing, White assumes that losing units due to unlucky die rolls is somehow superior to losing units due to poor planning and unit placement. However, if determinism combined with a competent AI makes the loss of units inevitable, then randomized results combined with competent AI makes the loss of units arbitrary. It is the job of the designer to tune the difficulty of battles—randomization of results cannot do the job for him.

Worse, White outright dismisses the interesting tactical situations that a deterministic system can offer. Determinism does not necessarily mean little tactical complexity, and it certainly doesn’t mean that the player won’t have to work out a good strategy. Nor, conversely, do random results equate to tactical complexity: if your game is simplistic, adding randomized results is not going to improve the situation. Tic-Tac-Toe is not going to suddenly become a tactically rich experience if we throw die rolls into the mix.

But then again…maybe there’s something there. What about a game that is already tactically rich but entirely deterministic? Could a game like that be deepened if we placed a wreath of randomized results upon its brow?

To some extent, I think the answer is actually “yes.” Consider this: in a purely deterministic game, the player’s contingency plans will hinge solely upon possible enemy responses. There is never a moment where the player has to plan for the risk that his or her own strategy will fail. The possibility space actually shrinks, in other words, because there are fewer possible results when a player implements her plan of action.

That sort of consideration comes about only through randomized results. Therefore, although randomized results are most certainly not a panacea for an otherwise dull turn-based combat system, they can expand the possibility space somewhat by offering up another dimension of tactical considerations for the player to mull over.

The design challenge therefore becomes finding a good balance, one that (1) forces the player to form extra contingency plans while (2) not sabotaging her sense of control. This means implementing randomized results in a very controlled and deliberate way atop an otherwise deterministic base.

It is no trivial matter to tinker with a successful, well-balanced deterministic combat system in this way. I have been thinking for months now about how to do so successfully in my latest title, Telepath Tactics. For the sake of providing an example, I will now talk about the areas in which I have added randomized results to the Telepath combat system, and discuss my rationales for doing so.

     Use #1: Negative status effects

The most conspicuous of my concessions to randomized results lies in the use of negative status effects. Negative status effects are a common feature in turn-based combat systems. They lend depth to RPG combat by creating secondary objectives (e.g. cure poison as soon as possible to minimize damage) or by changing the resources at various player’s disposal (e.g. muted characters cannot use magic until cured).

Despite their utility, negative status effects have been almost entirely absent from Telepath titles up until now. “Craig,” you ask, “why would you create a strategy RPG that excludes such a useful and obvious tool for increasing tactical depth?” The reason, quite simply, is that previous Telepath games employed a combat system that was almost 100% deterministic. Most negative status effects, in turn, are simply too powerful to use in such a deterministic environment!

Consider an attack that imparts “Frozen” status, for instance. If this status effect hit 100% of the time, Cryokineticists and Frost Spriggats would become game-breakingly powerful. Imagine going up against an opponent with an army composed entirely of characters that freeze your units solid for 2-3 turns on their first attack; there would be almost no way to successfully engage them. This same problem applies to Sleep, Stun, or any sort of common RPG status effect which prevents a character from acting.

Even a milder status effect, like “blind,” would become overpowered in a deterministic system. Not only it would take effect 100% of the time, it would necessarily cause the hit rate on physical attacks to drop all the way to 0%! Blind would essentially become an automatic Render Physical Attacker Completely Useless card.

The solution I chose was to make negative status effects take hold only some of the time. This limited application of randomized results turns negative status effects from a way of automatically crippling the enemy into a gambit you can try–and for which you had best have a contingency plan in case of failure!

     Use #2: Dodge chance

The second concession I made to randomized results concerns the ability of characters to dodge attacks. I did this as a way to help balance the units, enforce specialization, and raise the stakes when dealing with a few, particular classes. The Assassin, for example, is specialized in getting behind enemy lines and taking down weaker characters. Without a chance to dodge, the Assassin would be dispatched quickly almost every single time; giving the Assassin a significant dodge chance makes dealing with one much more of a tactical challenge.

I also give units an automatic, very high dodge chance when an attacker is blinded; this represents a compromise scenario with the Blind status effect, a negative status that would otherwise be overpowered, as we discussed above.

This is significantly different from most RPG combat systems. Most combat systems with a chance to hit impose a substantial probability of missing attacks against all enemies. Further, even those which do not force characters to frequently miss attacks will oftentimes set a maximum attack accuracy somewhere around 95% to account for the chance of a “critical miss.” (In practice, all this accuracy limit does is institute a chance of missing so low that it calls to mind our lightning strike scenario: the player will have no reason to expect it, and he will be profoundly unhappy when it occurs.)

The implementation I use in Telepath Tactics is far more circumscribed. Rather than a typical “chance to miss” system, it is a “dodge chance system.” The difference lies in the game’s base-line assumptions. There is no such thing as missing in the game–by default, any character’s attack will always hit the target. It is deterministic by default. This use of randomized results is a deliberate exception, representing particularized tactical dilemmas to spice up the game at key moments rather than simply dumping randomized results into every combat interaction in the game.

Just as importantly, the game provides several ways of circumventing dodge entirely. Blinding the target or slowing the target will prevent it from dodging (although, of course, there is always a chance that these status effects will themselves not succeed). Mental attacks, in turn, can never be dodged under any circumstances.

Much as with status effects, the use of units with dodge is merely a gambit: a player must be prepared in case the gambit fails, and the opponent should plan ahead by availing him or herself of strategies to counteract it. In this way, it deepens the tactical experience without significantly undermining player control.

     Use #3: Line-of-sight, gun-based systems

That about covers it for Telepath Tactics. However, there is a pretty big elephant in the room here, folks. There are some combat systems that consistently need to rely on randomized results for–at a bare minimum–hit and miss calculations. I am thinking specifically of line-of-sight combat systems with highly lethal projectile weaponry. (Think Fallout, Jagged Alliance or X-Com.) A deterministic core would very quickly turn these systems into a mess because of the lethality of the attacks involved. Everything I said about negative status effects being overpowered in a deterministic system applies here as well. These games get a pass.

Randomization beyond results

Randomized results are not the only potential use of randomization in a game. Randomization can also be a valuable tool to build tension by creating unpredictable starting states for various scenarios. Card games provide a great example of this principle. Even if you know your opponent’s deck, you will never know what cards lie in his or her hand. The deck is shuffled: the hand is chosen at random. Consequently, the player faces some uncertainty about the options available to her opponent. This builds tension and makes a turn-based encounter more gripping.

In a spatial turn-based combat system, unpredictable enemy unit composition and positioning under a fog of war mimics much of the effect of a randomized hand of cards. The player must scout, or else take the risk inherent to issuing orders with incomplete information about what enemy characters the opponent has at its disposal. Other elements of the battlefield can be randomized as well: loot drops, spaces with healing or defense bonuses, and environmental hazards, to name a few.

Crucially, these each add unpredictability to the scenarios the player faces, and not to the results of individual player commands. The player is never compromised in his ability to control his characters; any random chance the player confronts in this way, the player has the opportunity to respond to and circumvent.

There is one other, major way that randomization can be used to foster unpredictability. You may recall me mentioning earlier the dangers of relying exclusively on clever AI to provide unpredictability in a game. No matter how clever an AI’s programming, if its decision-making process is consistent from game to game, sooner or later the player is going to figure out how it thinks and learn to outwit it over and over again. The opponent will become predictable, in other words, and the game’s tension will plummet.

This is a great place to employ randomization: add a random modifier to some of the AI’s heuristics that change its priorities from battle to battle, or even from turn to turn. Also good: add a random coefficient to the scores the AI assigns to attack targets: small enough that the AI won’t make ridiculous decisions, but big enough that its target priorities will be difficult to predict from attack to attack.

I could go on, but I’ll stop here. Though this might seem like a lot of stuff, I’m sure that I’m just scratching the surface. After all, randomized results occur at a very specific moment: randomization can occur literally anywhere else in the game. As long as (1) the randomized elements impact the player’s optimal strategy, and (2) the arrangement of those elements is not immediately revealed to the player, you have an implementation of randomization that is ripe for tension-building.

Conclusion

There is a whole world of tools for building unpredictability. I would like to see turn-based combat systems–particularly those in RPGs–start focusing on a greater variety of these, and stop using randomized results as a crutch. Randomized results have their role, but I’d like to see them used more deliberately. Like special sauce on a burger, randomized results can add spice; just make sure the player still gets to taste the meat.

Craig Stern is an indie developer currently working on the turn-based tactics game Telepath Tactics. He is the founder of IndieRPGs.com, and can often be found rambling in short, 140-character bursts on Twitter.

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  • Neil Brown

    Interesting article. I wrote the XCOM one you linked to, and in a follow-up, I talked a bit about this issue (see the latter half of http://sinepost.wordpress.com/2012/10/30/probability-and-people/ ). I’m beginning to agree with one commenter that this use of simple independent events can be seen as laziness on the part of game designers. “Let’s have some uncertainty, so each unit has an 80% chance to hit the troll, job done”. I wonder if the game mechanics should take a different approach to “realistic” probability. Instead of independent events, use a lookup table against the number of chances. With 3 warriors, you have only a 40% chance to kill the troll. With 4, it’s an 80% chance, with 5 it’s 100%. What do you do — go for the guaranteed hit, or risk it with less? Now the chance depends more on how many men you will commit, and you can eliminate uncertainty, at a cost. The difference between 100% chance to hit and 99% chance is a lot bigger tactically than I think many designers realise.

  • http://www.handsometrustworthy.com/ Armaan Khan

    I was thinking about a similar system after I read your XCOM article as well. In the military, we learned that the more people who fire on a target, the more likely that target was going to die. Not because one person was more accurate than another, but because everyone was working together. A similar system would actually be awesome in a tactical game, for the reasons you describe.

  • EmpireForge

    Great, now I have to rewrite the combat system for Forge of Legends… :p

  • Kyle Gibbons

    Great article, though I think it missed a great point, with randomness you can set up a great strategy, have everything just “perfect” and something goes wrong beyond your control. This can be good or bad depending on who you are, the inexperienced would probably mostly call this bad yet when you play a game (or a series that uses the same or similar mechanics throughout the series) enough you begin to master what to do. Winning 100% of the time is never fun so I have found that when there is the chance that you lose based off of pure luck you retain some of that tension even when you know that you should win. An example of this would be Fire Emblem, this is the series that first got me into this style of gameplay and as such I’ve played all the (English translated) games multiple times, regretfully after a while things get predictable. So when I set up a strategy for beating the current map I have to be careful and not assume that everything will go according to plan, basically I have to compensate for the fact that not everything goes right, so I will for example not put an unit that will get killed in one more hit in harms way unless the chances that it gets hit are at the “lightning strike” level. So if I get a run of bad luck I will have to change my tactics to keep the unit alive. While the system is not perfect (I’ve lost units merely because of a critical hit that had 5% or so chance of occurring, though Fire Emblem’s crit system isn’t exactly amazing to begin with.) it does mean that I can’t look into the future with 100% accuracy. While you did hint at this (and even say a few points I made) I didn’t feel as though you mentioned my overarching point, that randomness will make an experienced player still have a feeling of tension. I do agree that this can be difficult for the newbie but honestly if you’re new to a game then there should be a learning curve. If you can jump right into something and be a master at it then there is no challenge and without challenge then what is the point of strategy games? Thanks for reading this rather long comment.

  • CraigStern

    Hey Kyle, what you’re talking about right here is actually *exactly* what I mean when I say that “[t]here is never a moment where the player has to plan for the risk that his or her own strategy will fail” in a pure deterministic system. So you’re basically reiterating my argument in favor of adding in some random results. :)

  • Devon Scott-Tunkin

    Hey Craig. I think you make a very good argument, but I think some players actually enjoy the risk of the lightning strike event whether it’s good or bad (myself included). I get really bored knowing 100% that I I’m going to be able to defeat something, at that point it becomes another kind of grinding where I’m wondering why the game even has me chase down a weak unit and kill it. It’s just a waste of my time. Chess gets a pass here because the end goal is not simply eliminating all the other player’s pieces (which I think would make Chess terribly dull) but rather having to trap the king, which usually requires a good emergent strategy involving two or more pieces and gives at least the illusion that a losing player will have some chance to still win the game. Shoots and Ladders does the same thing with chance by having you have to land exactly on the end square. Another aspect of the random vs deterministic argument you didn’t mention is realism. Some players and game designers enjoy simulation over competition, and while simple randomness is often likely to be an intellectually lazy way to add realism to a game, you would need many dozens of deterministic heuristics to achieve a similar feeling of simulation that well-designed probabilities can provide.

  • CraigStern

    Hey Devon! Knowing 100% you’re going to beat your opponent means the match is predictable. This is the first argument discussed in the “The uses of randomized results” section near the end of the article: you can address this with randomized results, you can address it with stronger and more unpredictable AI, and you can address it with less predictable scenarios with key information hidden from the player. Randomized results are just one approach.

    I totally get the argument for realism–this goes all the way back to that struggle in the design of Kriegsspiel about whether it’s more realistic to let dice decide the results of encounters, right? I’m not really talking about sims here, though. In my view, realism is a separate consideration from designing a game to be balanced or enjoyable.

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  • KKairos

    IIRC, Chrono Cross did this on an individual basis, at least in a way. In addition to spells, characters in that game had three basic attacks, weak, medium and strong. And the chances of hitting were, of course, highest for the weakest attacks. It doesn’t quite eliminate uncertainty, but it added a choice in probability to the game that isn’t always there with other games.

  • lapce

    “The player knows that she and she alone”
    “Suppose that Bob is playing an RPG where he controls a party”

    What is this nonsense ? Either you are a rabid loopy feminist or you arent. Be consistent, dammit.

    “There are some combat systems that consistently need to rely on
    randomized results for–at a bare minimum–hit and miss calculations. I am
    thinking specifically of line-of-sight combat systems with highly
    lethal projectile weaponry.”

    This is ridiculous. So a shot in the guts would be “highly lethal”, yet a sword slash isn’t ? Isnt it the other way around ? Frozen Synapse, for example, gets by without any need for ridiculous “to hit chance” being implemented. Moreover, if we’re talking Fallout – “to hit chance” might as well not be there, so its a bad example from the getgo.

    I would argue, that “highly lethal projectile weaponry” games ESPECIALLY, dont need “to hit” chance. That finally opens the doors to some real planning. Where to attack, when, from which side to approach, plan how to perform a combination attacks to put the enemy in crossfire, and so many more.

    On a more personal note, i am currently developing a giant robot strategy game where all aiming is done by a pilot-operated computer. What i did is put a delay between ordering to fire and actual firing. With a 100% deterministic (and a full friendly-fire) system it means that you will always hit a motionless target, but the faster it moves – the less of your shots will land. What that means is you get immediate advantages from thinking tactically, i.e. : tailing your target so it doesnt matter how fast he moves, binding the enemy in combat so it slows down, crossfiring, setting ambushes, immobilizing weaponry, using formations so you can use area attacks, synchronized actions…Zeus, it just boggles the mind how none of this would work with a randomized “to hit chance”.

  • CraigStern

    Frozen Synapse is a special exception, since the actual “turns” are modeled in real-time. The highly granular timing and positioning requirements to get a successful shot add unpredictability in a way more reminiscent of real-time games than of typical turn-based systems.

    I like the idea of breaking up an attack into a succession of smaller hits that can be deemed successful as needed based on circumstances, without randomized resolution. If implemented well, I could see that successfully replacing randomized to-hit calculations.

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  • http://twitter.com/antoniodamala Antonio

    Thanks, man, that was just what i needed to decide when and how to use randomization in my turn-based game. I’ve been struggling with randomization for quite a long time, now i’m finally free of it.

  • Matt

    I’m one of those stodgy old-timers who loves the random outcomes in games, just to put my bias out front.

    While I agree it is annoying to be down to that “we have to kill the troll this round or else someone dies” situation, I think that once you’ve allowed that situation to occur you already have done something wrong as a player. If you are looking at permanent death in the game, then typically battles will be skewed in favor of the player. They become games of risk management, where the player must constantly determine the most highly probably positive outcome actions to take, while avoiding the most highly probable negative outcomes. If the player has that high a chance to lose a party member against the trolls… should they have really even taken on that fight to begin with?
    It’s also not really sensible to compare DnD to Chess or Go. In those board games you’ve mentioned, every player always has the same pieces no matter what. D&D and similar games have an “equipment and ability management phase”, for lack of a better term. Part of the gameplay is examining and preparing each combatant long before any fighting takes place, to assure they are equipped properly and coherently. If you’ve done your job of equipping your troops, learning their abilities, and choosing a quest of appropriate challenge level, then the odds are very good that you will succeed. The randomized results add a little spice into what is a battle stacked in the player’s favor. The player still enjoys their victory, because they made a series of correct decisions in order to make sure they came out on top.
    The way to fix the problems you have with the random outcomes is to make it more finely grained. Instead of the 80% chance to hit all-or-nothing type rolls, you could get a little more granular. If you can get more dice involved per action, the outcomes will trend in a more predictable fashion instead of being all or nothing. If you’ve ever played tabletop warhammer, you know all about this. When two units face off, each side may be rolling upwards of 20 dice, and the outcome is usually fairly close to what probability would suggest (usually).
    So, how to do this with a single sword attack against a target? Call it “intensity of hit”. You’ll have full hit, partial hit (1/2 damage), and grazing hit (1/3 damage) or somesuch. Against a semi-skilled opponent you have a 60% chance for full hit, 80% for partial, 100% for grazing. So you’ll always graze them, but a good portion of the time you do full damage. What won’t happen with this system is the dreaded 95% chance to hit, then missing for no damage. In the case of a 95% chance to full hit, you’d always at least score a partial hit for 1/2 damage.

  • http://twitter.com/CoreTechsGame CoreTechs – C.McLeod

    Excellent article Craig. Way to rebel against the ever-popular, tactical randomness staves off boredom ideology. I couldn’t agree more.

    In a similar vein, I do want to bring up a part of deterministic design that I’m not a huge fan of. Things like % damage reduction based on particular damage types seem to serve only to get the player to do quick mental math over and over again. Although these types of calculations are often rooted in strategy games, the learned skill is simply doing those calculations frequently that they become second nature. It ends up feeling like the hacking “pipe-dream” game from Bioshock. I’d prefer my players have their minds focused on other strategy elements.

    On randomness, I quite like your negative effects usages. In your game, when do those effects occur? Does the player know his unit is blinded one turn, and then it may or may not be blind the next turn? As in, for 5 turns, the unit has a 25% chance of being blind.

    I also find myself drawn to your dodge blindness dynamics, but would have a hard time employing those type of ideas in my game. We’re going the card route with expansion releases, so unless we’re going to have say ‘dodge and blind’ stick around as abilities throughout the build, we’re going to have to break down abilities as more atomic units. This seems like you’ve already done that with psychic abilities being un-dodgeable. I’d be very curious as to how you’ve broken down your system. Do all abilities have types but units do not? I’m looking forward to having some time to check your games out.

    Great blog. Thanks for the good work

  • Quirk

    Another thing Frozen Synapse does, though it’s far from the first game to do so, is to utilise simultaneous turn submission.This is, I think, an extremely useful way to introduce randomness without randomness: you can predict precisely what the outcome will be of any move pair made by you and your opponent, but not how your opponent will move. I used to play a lot of an otherwise deterministic multiplayer strategy game which incorporated this feature. While having a statespace far smaller than Frozen Synapse’s (I think approximately 27 possibilities per player per move), nonetheless the game was lent a great deal of longevity, to the point that it took probably half a decade to more or less crack strategically by a community of a few hundred players. If had it been purely deterministic, it would never have been able to hold out as long. Incidentally, it supported a pretty sound ELO system which seemed to work pretty much as well as say, chess – I played about 70 games with someone three or four hundred ELO below me, and lost once at most. On any individual move it was possible to lose the exchange to a weaker player, but over a couple of dozen moves things averaged out.

    Generally, the purpose of non-determinism is to slow player progress towards the best strategy. Statespace alone does not confer depth; consider noughts and crosses/tic-tac-toe being played on a grid of infinite size. Hence devising a purely deterministic game for which no simple winning strategy exists is hard and needs much testing, and throwing more possibilities into the mix often only increases the likelihood of some of them being imbalanced – and once you’ve got a game with seriously non-trivial strategies, it’s very tricky to design an AI capable of outwitting a human. Things get harder still in an RPG where players expect to win every encounter and preserve their characters intact. Non-determinism hence serves as a fig leaf for both weak AI and poor tactical depth, providing variety in the encounters and a little challenge without overly punishing players who’re terrible at tactical thinking; the trade-off is that occasionally the dice rolls go wild and reloading has to happen.

  • CraigStern

    “Non-determinism hence serves as a fig leaf for both weak AI and poor tactical depth”

    Yup. Not sure how that’s an argument in favor, though.

  • Droopy

    That argument about hypothetical win-or-lose situations only occuring because of poor risk management beforehand always crops up in any discussion of randomisation, and it’s a really annoying.

    The first thing you should learn about risk management is if you can’t eleminate the risk completely the worst will happen, it’s just a question of when. “If the player has that high a chance to lose a party member against the
    trolls… should they have really even taken on that fight to begin
    with?” In the example above there was less than 1% chance of failing to kill the troll at the start, but if a few thousand players enter that scenario you’ll probably have a few dozen of unhappy players at the end. Heck, change the trolls certain to kill to 10% chance to crit and kill, and you’ll probably still find a few players shouting at the screen having lost a character. Managing risk well doesn’t stop you losing forever, it just staves if off for longer.

    And if you are in a system where it’s possible to elimnate risk entirely, why not just go the whole hog and start off deterministic to start with? Since the riskless strategy will be the optimum one anyway it’s just needless obfuscation.

  • Matt

    ” In the example above there was less than 1% chance of failing to kill the troll at the start, but if a few thousand players enter that scenario you’ll probably have a few dozen of unhappy players at the end.”

    Strangely, this straw-man of a game seems to be one with permanent death and no save/load features. Most players, upon receiving horrible dice rolls in a CRPG, will recognize that this has happened and reload the battle. Players take care of the outlier situations on their own, by hitting “load game” and saying “that’s not what really happened”.

    “And if you are in a system where it’s possible to elimnate risk entirely, why not just go the whole hog and start off deterministic to start with? Since the riskless strategy will be the optimum one anyway it’s just needless obfuscation.”

    The system I am talking about would create far more outcomes than just “hit” or “miss”. Going back to the example, your 80% chance to hit the troll would convert to a 100% to at least do a partial hit. So this would eliminate the chances of everyone whiffing. But note, you are not choosing the 100% option, you are still just rolling a single time, and applying the best result. The 100% result is simply the worst outcome that could happen, so there’s an 80% chance that a single character could kill the troll.

    Another example of what this type of system could look like…

    Two equally skilled opponents face off. Each is using the same type of weapon etc. On any given attack, the hit table is like this…

    -10% (critical hit x2 dmg) 20%(solid hit x1.5 dmg) 50%(normal hit x1 dmg) 70% (partial hit x1/2 dmg) 90% (grazing hit x1/3 dmg)

    So first thing, since these two opponents are so close together in skill critical hits are out. In this system, critical hits are reserved for quickly dispatching something far beneath skill level.. or perhaps they come into play when debuffs/buffs boost your chance to hit, or if your target is laying on the ground or something. A normal system would have a “miss” in the 50-70 range, whereas in this system two such “misses” add up to a normal hit. It’s a lot less “all or nothing”. Purely deterministic would resolve these equal opponents this way… attacker A attacks, hits, does 5 damage. Attacker B attacks, hits, does 5 damage. Attacker A attacks, hits, does 5 damage…. etc. Spoiler, attacker A wins because he went first. It’s just a lot less interesting, and you don’t get any of the back-and-forth swings.

    “And though it may be fairly uncommon for your players to get totally screwed in this fashion, this is actually not an especially good argument in favor of randomized results. The fact that it seems so improbable just means that when it does happen, it will feel like the game equivalent of getting struck by lightning out of a clear sky: arbitrary and painful.”

    And yet, somehow players of such games live on. Possibly because of the “Load” button. It’s really not a big deal to expect players to occasionally discard outlier results, they do it all the time. To somewhat appropriately quote Dennis Leary, “Life’s tough get a f@cking helmet.” (Appropriate because helmets prevent critical hits, everyone knows this) To me, playing a purely deterministic turn based strategy game is arbitrary and painful, but to each his own.

  • Mark

    I think that the solution lies in combining deterministic interactive mechanics with non-deterministic automatic content generation.

  • Droopy

    Straw man is a handy term sometimes, but since we’re all discussing the same example and no-one’s misrepresented it, it’s not really applicable here. (Aside – Not heard of roguelikes then? Check ‘em out, I think you’d like them.)

    Saving/loading isn’t discussed because this isn’t about how to enjoy a game with randomized results as a player, but wether randomization is good from a design viewpoint. From that perspective, saying players should disregard the game’s results and go out of the game to save/load until an appropriate one is obtained is pretty damning evidence of bad design. If that’s what they’re supposed to do, why not just have the game discard “outlier” results automatically? What’s unlikely enough to be defined as an “outlier” in the first place? Why not just smooth things over and give the most probable result every time?

    Wasn’t intending to dicuss how making things more finely grained or enforcing none-zero minimums doesn’t fix things, but since I’m here again why not. There’s two ways a scenario can go with your system, either it’s possible to win the scenario with clever play even if every one of your attacks does minimum damage and every one of the enemy’s does maximum damage (I.E. Risk elimination). In which case you aim to construct a plan that meets those guidelines because a zero risk strategy is always going to be best. But then as soon as you or your opponent don’t get the worst result that you planned for, the difficulty level goes right out the window such that it’s either really hard or mindlessly easy depending on what the randomized results give you. So smart players end up playing it like a deterministic game anyway but with randomized results making the difficulty level wildly inconsistent.

    Or the only hope you have of winning is working probability such that as long as you don’t get too many “outlier” results you should win, which has all the same drawbacks as the randomized system already discussed.

    As for the perfectly equal attacker A and B scenario, that’s even more simple than tic-tac-toe and it’s already been discusssed how a better response is to give the player more options to work with (chess), rather than randomizing fewer options (coin toss). What exactly does adding randomization to that scenario add anyway? Your only option is still to attack the other player, so it doesn’t change your plan. The spoiler just becomes “Whoever gets the best random numbers wins (with a slight bias towards A if things aren’t simultaneous)”

  • Quirk

    Firstly, it’s an argument in favour from the perspective that it makes RPG development possible.

    Imagine having to develop deterministic mechanics which provided the tactical depth of say, draughts/checkers when designing a game turn based combat engine. With a small number of game testers, paths could be gone down for months before it was realised that trivially game-breaking strategies existed. Even after devising a tactically rich statespace, AI is an incredibly thorny problem. Fail to spot a tactic which will be spotted almost instantly by some member of the public after release, and your AI becomes trivial to beat for anyone who reads an FAQ or message board; devise an AI which is a little too competent and a large portion of your playerbase will find the game unbeatable. Scaling the challenge is hard, and by the time you’ve perfected it, you have a turn-based strategy game which is exceptional in its own right, and will sell to gamers with the patience to get really good at it. Spending another couple of man-years producing RPG content for it gains you very little, as the breed of gamer who will purchase RPGs is usually looking for the comfortable illusion of strategy, in which they get to tinker and try various things until the dice let them proceed, rather than the occasional cliff-face of conceptual novelty that the chess or go player has to scale.

    Secondly, a little well-chosen non-determinism can vastly increase the effective statespace of a game. The positions people play from are less constrained than they would be if both players were following optimal lines of play. For instance, chess opening theory will stay with you past the first half-dozen moves, but if the pieces were randomised behind the pawns before starting play (as per Fischer’s suggestion) or some variant allowed players to order their pieces as they liked on the first rank before knowing their opponent’s layout, it would be simply impossible to have an optimal gameplan memorised. In this case non-determinism would be rather better than a fig leaf, a potent weapon hacking apart pre-planned strategies.

    I am broadly empathetic to your aims, here, as a former competitive chess player who’s fairly bored of RPG combat. I feel that creating purely deterministic games with depth is hard, though, and would classify it as probably too high a goal for a genre which usually can’t even be bothered recreating the interesting tactical elements of real combat (for example, relatively few turn-based melee games seem to address the positional implications of weapon length; spear or dagger, it’s all the same).

  • CraigStern

    *shrug* I’ve done it. It’s hard, sure, but so is anything worth doing. Check out Telepath RPG: Servants of God; the combat starts out fairly simple, then grows more and more complex as you progress.

    Anyway, I’m a one-man team and I’ve managed it. I refuse to believe that I’m some kind of superhuman RPG developer, and that no one else could pull off good deterministic combat in a computer role-playing game.

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  • Lenny

    I identify two types of randomization in games:

    1) “Vertical” randomness, where the result of the randomness determines whether the outcome is good or bad and to what degree (eg, dodge chance, chance to hit, variable damage).

    2)”Horizontal” randomness, where the result of the randomness determines which of a selection of equally “good” or “bad” options is selected. Eg, A character in an RPG gives you a random magic item as a reward. The result is always “good” and to approximately the same degree, but the random factor introduces variety; there are many possible items with different properties you could receive. Random enemies, random loot (although that tends to use vertical randomness as well), procedurally generated content in general are all random factors which increase variety and possibility space while not arbitrarily giving good or bad outcomes to the player.

    So my principle would be to always aim for horizontal randomization to increase possibility space and minimize vertical randomization for the reasons described in the article.

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  • http://www.facebook.com/justin.prazak.9 Justin Prazak

    Hello,

    I just want to start by saying I recently found out
    about Telepath Tactics through Kickstarter, I think it will be great
    when it’s finished, and I’m glad you are giving it a second go. I’m also
    really glad that you are making posts like this and having this
    conversation with the TRPG community.

    Now, about the randomized results.

    The
    post is very well done and I’m very glad you came over to the design
    position you have arrived at. I think the specific instances of
    randomized results you mention are great. However, I would like to make a
    small case for the intrinsic value of randomized results as a baseline
    for attack success or failure.

    I hate the game Risk because it
    is too random. I love Fire Emblem because it is regularly random
    (absolute misses and absolute hits are possible, but most attacks fall
    in the range of probabilities between).

    It would seem that aside
    from the Assasin’s dodge ability attacks success is almost always a
    guarantee in Telepath Tactics. I do think it will be loads of fun, but
    was I took a bit of a pause when I initially read that about the game
    design.

    At first I thought it was simply a matter of familiarity
    (Fire Emblem, FF Tactics, Dark Wizard, Vandal Hearts, etc, etc,) all
    have regular use of randomized results in the combat engine. I kept
    thinking about your points and weighing whether I my initial reaction
    was out of apprehension of change or a legitimate merit of randomized
    results and their use in games.

    In general I don’t think that
    they remove control from the gamer, they just give the gamer one more
    uncertainty to consider. They add uncertainty to outcomes, but that
    doesn’t mean they are not tactical decisions or not in the player’s
    control.

    The example you used with the troll is
    not bad because of randomized results, but what sounds like either bad
    game design (designing a game in which there are really good odds that
    the player will lose a character in that fight, stacked against the
    player party) or a failure on the player’s part to effectively up-level
    his characters, equip them, or master their uses before they arrived at
    that fight (maybe he’s using his b-squad entirely). Other possibilities
    and questions would obviously linger; why did the player move all of his
    five characters within striking range of the troll? Is it impossible to
    have avoided this scenario in the fictional example? Are they all
    injured characters or is the Troll just so strong that he can kill any
    character “almost certainly” one hit? Again it seems like either bad
    game design (too powerful troll) or bad long term player choices
    (inadequate leveling decisions or positional choices) would have led to
    this circumstance.

    Conversely I lost a character to permadeath
    very recently in my copy of Path of Radiance. The character was at full
    health and being used by me to assist in accomplishing a secondary
    objective (clearing a path for another character to be used in stealing
    an item I wanted). The character in question had a very good chance of
    being hit by the enemy but only a moderately decent chance of receiving a
    critical hit and thus sustaining enough damage to be killed. It happened though.

    It
    would have been absurd for me to feel that I wasn’t in control of it
    however. I chose to put that character in that situation, while even
    though it was not the “most likely” outcome death was a reasonably
    likely outcome. I made the tactical choice however that the uncertain
    possibility of death to that particular character (whom was a b-squader I
    chose for a special purpose in this mission), was a tactical gamble
    that was justified by my desire to acquire a stolen item. I played a
    gamble, lost something, and gained something more. While I would have
    been more excited to pull it off without the loss, the loss makes my
    tactical choice in play feel more meaningful -there was a cost from my
    choice, which could have been to never risk anything.

    So then,
    why is that good? For starters I think it’s much more realistic. Yes, I
    know you are talking about play dynamics, specifically how they make a
    game fun. For me, and many players tactical realism in a TRPG is very
    fun. Comparing TRPGs to chess loses something, I think. chess is 100%
    deterministic because it is predominantly or entirely abstract strategy.
    Yes symbolically the pieces “represent” knights, and kings, and
    bishops, but tactically it is pure abstraction. There is no tactical
    legitimacy as to why the queen is a super badass and the king can barely
    move, nor ever defend himself. for that matter why would a bishop ever
    only move in a zig-zag pattern or knights an L.

    The entire game
    is abstraction of strategy. It is a finite possibility of circumstances,
    built to be expressed in a format and world that doesn’t even feign
    realism, and abides absolutely and unflinching to a small set of
    immutable laws and rules. All that can be gained from it in terms of
    real world strategy is principles because of the highly abstract nature:
    Plan ahead, deceive and distract, be willing to sacrifice to win, etc.

    TRPGs
    while having some abstraction (because they are a game) and some
    obvious breaks with realism (because they are usually fantasy based),
    tend much more to be an avenue for more realistic and less purely
    abstract strategy. Realistic tactical details are usually considered a
    good thing in the genre, like mounted units traveling farther, arrows
    striking from a distance, mud or swamp slowing character movement, and
    certain weapons having varied effects. While still being partly abstract
    (and unrealistic) they tend to try to represent more of the real world
    of tactical considerations through environmental factors, strength/speed
    trade offs, and well, attacking with skill and weapons instead of
    jumping over one another for the kill.

    The particular role that
    the dice (or random number generator play in this is a continuation of
    realism in tactical decision making). In my younger years I was a
    military intelligence analyst in the US Army and uncertainty of outcome,
    even when the odds are in your strategic favor, do not guarantee
    knowledge of the outcome. For me the fun in many games is tied to
    weighing differing potential outcomes, contingency plans, and what ifs.

    You
    see it in life everywhere. No matter how certain one is that boxer A is
    a better fighter than boxer B, a win by boxer A cannot be guaranteed
    beforehand(aside from match fixing). The huge array of potential
    variables (mistakes, miscalculations of lefts or rights, reacting
    slightly too slow, underestimating, etc) all persist. The roll is the
    representation to account for this. You can get odds, and in games like
    fire emblem is is possible to get a guarantee, but most fights have a
    least some degree of chance.

    That chance while being more
    realistic, also provides for added thrill when you gamble with a
    strategy and come out on top. Such as getting a high critical hit
    possibility in the right place at the right time. Conversely when things
    that have odds of going right go wrong, you are forced (as sometimes
    happens in real life strategy) to recover a bad situation that odds said
    were not likely to happen – but were in fact possible.

    This
    causes players to need to be improvisational and is another area where I
    see randomization directly benefiting the player’s options of
    situational strategies innately. One reason that computers can beat
    people in chess is because it is so deterministic that computers benefit
    from being able to “memorize” the likelihood of various outcomes for
    every possible configuration and recall all of those outcomes
    immediately. Human minds are not as ready made for that and the greatest
    chess players on earth have vastly different neurological development
    from all that playing that optimizes them for such thinking. However,
    studies have shown that if you inject even small amounts of rule changes
    in the game great players become just like everyone else because all
    their strategy was highly specialized in the immutable rules of
    tournament play. They actually suffer greatly from having to face small
    “unexpected” changes.

    Improvisation is something that, unlike
    humans, computers cannot due. The best they can due is give the illusion
    of it with clever and deceptive programing. That realistic injection of
    randomized outcomes (going this way when things should have gone that
    way) gives players a way to exercise that humanly unique aspect of
    strategic decision-making, improvisation.

    “Crap, that character should have been dead by now, guess I’ll have to come up with a plan that changes everything.”

  • stinky472

    I think indeterministic results are ultimately a key to adding interest in a game, but only when the variety of results is significant enough to be amusing. If it’s merely hit/miss, it’s like playing a card game that deals one card where the player with the highest card wins (ace being best). This gets dull pretty fast and will soon turn into a grind where players are complaining that they got dealt ‘2s’ and ‘3s’ 4 times in a row.

    If we turn it into a two card game, the results get a bit more interesting. If we turn it into a 2 card game with player control to be dealt more cards, split, double, etc. we get blackjack which is amusing enough on its own (at least until we find out that there is only one mathematically optimal way to play.

    If we turn it into a 2 card game with 5 community cards and massive combinational variety and player control, we get Texas Holdem which has kept players entertained for years and years, and the results can vary from a 7 high to a royal straight flush.

    Of course with RPGs, we want a good deal of determinism. If the player felt like he was completely the victim of chance, he might as well play card games. However, if the level of variation in the results is interesting enough, I think that can add a lot to the fun factor. When we aim for a character’s eye in Fallout and manage to blind him,it never really gets old. When we shoot at a character’s arm and cripple him and make him drop his weapon, there’s a little bit of delight and excitement. If we blow his entire arm off, there’s a little jump for joy each time. And however annoying it is, when that happens to one of our characters, I think that level of unpredictability keeps people playing. Then again if it’s hit/miss and our 80% hit misses 3 times in a roll, we can’t help but be annoyed by the random number generator, not just because it’s screwing us over, but in a really uninteresting way.

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  • SperoAmicus

    I think you could consider random numbers with unequal distributions. For instance, if you were to randomize the damage inflicted by an attack as a random number, the set doesn’t have to be 1 to 10. The set could be:

    { 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10 }

    This would favor a reliable and expected outcome (6-8), while open the possibility of dealing more or less damage than expected.

    I think you should also consider three additional arguments in favor of randomness:

    – Believability. Things almost never happen with strictly predictable outcomes.

    – Surprise. Missing, or dealing extra damage, can be fun experiences when they happen with reasonable parameters.

    – Cushioning the learning curve. A difficult encounter can turn off new players before they have the chance to figure out the right strategies. Giving new players the chance to get lucky opens the door for being successful with a (slightly) sub-optimal strategy and encourages players to stick it out, and consequently, to continue working on their strategy.

    But mostly, my point is that randomness doesn’t have to be seen strictly in terms of D&D dice and with extreme outliers like 1 and 20. You can use randomness very effectively without sacrificing good game design.

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