New on Desk #91 — The Risk of Conquest

This is the newsletter extra penance midweek special on account of my tardiness a few Sundays back. Some more stuff that I’ve been wasting time with lately. Hopefully writing this helps me get out of the rut and back into the other rut, that of productive writing.

Introducing Conquest

Today I’m going to be writing about strategy in the well-known game of Risk (also known as Conquest of the World among the truly dedicated). For context, though, let me tell you about one of the world’s best game designers, Sean O’Connor.

I find that Wikipedia gives me a disambiguation page with some politicians, sportsmen and comedians by that name. No matter, the one relevant to gamers is this guy. He’s an indie computer game creator with a penchant for abstract games. Been in the business since the ’90s, and I frankly don’t know much more about him, because I’m not the sort to really spy on people.

I notice now that Mr. O’Connor has set up a Patreon page, so that’s probably what to read for more on what his deal is. His own website is delightfully retro.

O’Connor has created a fair number of original games (I particularly obsess over Slay myself, perhaps we’ll discuss that another time), but the day’s specific topic is Conquest, his Risk clone. I’ve been playing it recently as an alternative to hating myself, and it’s not exactly the first time over the years.

Conquest runs on the Risk rules, and it’s not like the Internet isn’t full of Risk clones, but it has some features that make it the Risk clone of choice for my particular brand of gaming OCD. Check it out:

No bullshit: O’Connor is the designer’s game designer. The game’s extremely stripped down, it does not attempt to woo you with audiovisuals or advertise at you. Just the game, and by game I mean the bare bones structural system that underlies the stuff normal people play.

Strong AI: The entire point of single-player Risk is presumably to experience the zero-sum multiplayer game in action. The exercise is pointless if the enemy makes elementary mistakes. Not so in Conquest, O’Connor has put some elbow-grease into the AI. A human can still exploit it to win from even starting positions, but it’ll take you a while to see through the logic.

Fast: Human tabletop Risk is fairly unplayable (except by children and morons, I guess), but when you remove the handling and replace the other players with AI, it’s possible to run the three-digit turn count games that are required to follow the game’s logic to the end.

Random starting positions: The only real way to play Risk as far as I’m concerned; just scatter the pieces in there, randomize the start and leave me to evaluate the position in peace.

Map editor: Conquest maps are vector graphic files with associated XML. Simple to make your own, which means that the game has a rich collection of alternate maps to really allow you to consider Risk in arbitrary battle-spaces.

So that’s a fair bit of what I’ve been doing with my autumn melancholy, playing computer Risk. I would recommend O’Connor’s take specifically for its above-mentioned strengths, but do prepare to work with the screen setup; the old WIN32 executable runs in static window size, and if you don’t know what the implications of that are, maybe stay away, or check out the remakes that O’Connor has been putting out recently.

Introduction to Risk

So that’s the version of Risk I’m playing. More generally, Risk is a classic Ameritrash boardgame from the 1950s, probably familiar to many gen X kids from when it was popular back in the day. The game is generally considered to not hold up well as it ages, with new and better games stealing its cultural cachet. A bit like Monopoly, another Ameritrash game that used to be popular (with kids and families), but is not taken seriously today.

The specific fatal flaws of Risk are that it’s slow to handle, is repetitive, has player elimination, and has a slow end-game. Any adult who’s played a complete game can tell you that it’s just a fairly problematic experience all in all. The historical significance, though, is great: Risk is the first mainstream wargame, first family boardgame without a progress track structure (having the wargame map instead), and perhaps most importantly, the first boardgame with the fundamental Ameritrash boardgame feature of zero-sum resource sacrifice multiplayer gameplay. Or, in other words: in Risk the players can choose which of the other players they will shit on, moment to moment, only limited by respective asset exposure in board position. You are playing against everybody else in the game (like in Monopoly), and you’re doing it by choosing moment to moment who to play against (not at all like Monopoly).

The only important choice a player makes in Risk beyond trivial (as in, solvable) tactics is the choice of who to bash, if anybody. Choosing to injure another player’s position basically weakens you both by the same amount of resource count. Each player’s position determines how much resource they recover per round. You lose when your resource gain goes to zero. You win when everybody else has lost. This is the pure kernel of the zero-sum multiplayer game, a structure that is at the heart of modern boardgame design.

Risk, as it’s owned by Devil Inc., has had its name plastered on roughly ten thousand variants sold in boardgame sections the world over. As these variants ply you with rules cruft that does not add anything to the fundamental core nature of the game, it is generally wisdom to ignore them: if Risk is to be a worthwhile game to consider, it must stand on its own simple legs. Turn starts, place your income in pawns. Attack to gain cards. End turn. Watch other players play their turns, then repeat. Of these simple ingredients is an empire wrought.

Risk in the depths of the well

As in, the well of experience that you dig for yourself by spending hundreds of hours running the game. Some basic observations:

Attacker is slightly advantaged: The Risk dice mechanics grant the attacker a small but real advantage in casualties. You need three armies minimum to attack (I’m simplifying because attacking with less is always the wrong move), but as long as you have that, it’s better to be the attacker than the defender. This is very much the core of the game, and there arguably would not be a game otherwise, as Risk is entirely about brinkmanship: the defender’s advantage is that you’re not committing your forces to die. Being forced to attack a strong position is always a net loss for yourself, only possibly offset by the slightly lesser loss the enemy takes (and the ephemeral advantage of possessing territory), which in a multiplayer game is unlikely to be worth it for you. If, in addition to this obvious strategic weakness of attacking, that you lose armies by doing so, defender would also have the force multiplier on their side, I’d expect the game to break down entirely.

Festung positions are key: You win in Risk by other players choosing to attack somebody else than yourself. The only real reason for them to do so is because your positions are too expensive to attack. The only way to make this happen is by accumulating more armies on each of your held territories than those territories are worth. As long as another player is not racing ahead in army income (by holding too much of the board and losing too few armies while fighting other players), you are only winning every turn you take the income and sit tight. Turtle like a boss, in other words.

Reinforcement cards are an illusion: The O’Connor AI believes in attacking every turn, perhaps to gain reinforcement cards. The way their math works out, though, is that you will only ever benefit from collecting those cards if the losses you take are less than the bonus armies you gain from this “aggression perk”. The specific reinforcement rules do not matter; I play with fixed reinforcements myself in Conquest, but with scaling reinforcements the turtle player just holds onto a set of cards without cashing it in, allowing other players to drag the value of the set up, opportunistically trading in when forced by the requirements of safety.

Diplomacy is an illusion: People often have delusions about this, but Risk is not somehow fixed by above-board diplomatic dealings. It’s just players trying to control the complicated calculus of zero-sum resource expenditure. Strong-willed players whispering in the ears of the weak is not “diplomacy” so much as it is the dreaded/appreciated “talking action” of boardgaming lore. There is no viable diplomatic position to be had in the game of Risk, because there are no common interests. There is only the calculus of the zero-sum advantage, and the coordination of the weak against the strong.

I don’t know if the game works with human players: I have some fair insight into how the game works with computer players making consistently optimal local moves, but there could ostensibly be a higher-order metagame that better intelligence could uncover. The problem is that human players are so dumb that what you’d get with them is more chaos rather than more intelligence.

To be clear, life-long experience with boardgames has taught me that it is fairly impossible to get half a dozen human players around any zero-sum multiplayer game and expect them to consistently calculate board position correctly to identify the leader, and then decide to attack that leader alongside other weaklings, in appropriate proportion to their own strength such that they may still expect to improve their relative position in the zero-sum game.

The AI can’t really do this level of meta coordination either, but at least it plays optimal moves for personal short-term position (albeit overly valuing reinforcement cards), which makes it somewhat manageable. If the AI attacks you and therefore throws the game to another AI player, at least you know that it’s because you made it too cheap for them.

I suspect that Risk played correctly (as in, with optimal strategy) is unsolvable because it’s always better to let another player be the attacker, hopefully against somebody other than yourself. With the hypothetical table of players who were both human-intelligent and had the infinite patience to actually play correctly (say, if I played against myself — now there’s an idea), I’d expect a strategic equilibrium to form such that no player can benefit from attacking anybody else.

If that is the case, though, where does that leave the veritable host of other zero-sum multiplayer games? Do they resolve successfully due to forced plays caused by the specific structure of the individual game? Or is it because humans are incapable of playing optimally? Or am I wrong about turtling being the only rational move?

Risk is interesting because it’s such a basic presentation of the zero-sum multiplayer game. And as far as I can see, the winning move is to wait and see if other players make any mistakes that might allow you to win. There is no active strategic paradigm that would resolve to your advantage, victory is always caused by another player A attacking another player B, allowing you to swoop in and exploit.

Fixing Risk to be playable

To take this Risk exploration beyond Conquest, would mean having to put up with the tedious dance of pawns and dice, and other people who probably thought that they were signing up for something fun when I asked them to play Risk with me. I particularly imagine that the latter would rise up in revolt somewhere between turns 150–200. It’s an interesting question whether you could make the game flow better with some slight streamlining of rules and procedure.

This is strictly conjectural right now, but the following are some ideas for how to make the game go faster:

Randomize the start: Like I’m doing on the computer, I love skipping the vapid army placement thing. I would randomize all placement rather than just the territories (which is apparently popular in the Risk scene: randomize territories but control army placement); it should not fundamentally matter much where players start, assuming they’re playing a high quality game. The positions can be massaged through early game movement, and while some will have stronger positions and others weaker, accounting for that should be trivial in a multiplayer game that allows players to team up against the leader.

No diplomacy: Or rather, no talking to influence other players’ moves. This may be surprising from me, as I am generally a proponent of talking in zero-sum multiplayer games to improve the quality of play (basically, let the stronger players check the moves of the weaker players and point out the major errors to keep them in play), but Risk is so simple and transparent that I don’t think it’s very meaningful. I might spring for some formalized bare set of allowed communication cues, like saying “player X is in the lead” to indicate an implicit offer of focusing on a leader takedown. The game should work just fine without, though, and discouraging blather and resulting revenge plays seems worth the silence.

Formalize the dice-rolling: I feel that bullshit around the dicing takes unnecessary time. The attacker should roll all dice (both attack and defense), as they’re the only party making choices. Give them a dice cup, let them process it in silence until they exhaust the defense or retreat. Don’t distract them, don’t encourage flashy vertical dice rolls, etc. Just drop the dice, pair them to indicate kills, remove pieces, repeat.

Mandatory attacks: Just a thought, one step further than the thing the Conquest AI does. (The AI is capable of choosing to not attack, it just does it every time it can conquer a territory regardless of if it’s a smart move to make.) This isn’t really a streamlining move so much as it is an observation that the turtling gridlock I speculate about could be maneuvered into resolution if there was forced attack. It’s a bit of a skilled dance to force the attack-happy AI to choose to attack each other, and it might not be the worst game ever if similar game-play could happen in human Risk. Otherwise the game ends, I confidently predict, in players each having 50, 60 and 70 armies staring at each other, with the player who attacks last winning.

Turn timer: It might be ultimately necessary to limit players to 10 second turns to really speed things up. The way this would work is that a banker declares your income out loud, passes you the pawns, and starts the timer. You must place the armies and indicate an attack before the 10 seconds are up, or the turn ends without an attack (you still get to finish placing the armies, preferably while the next player is already playing their turn). The timer can be reset after the attack by any other player, and you again have to make your next attack within 10 seconds or the turn ends. Should make for a pleasantly focused pace for the game as players are encouraged to think about their next move in advance. The bane of all boardgaming, that luxury of only thinking on your own turn.

Some variant notes

I am a very boring person, so my thoughts on Risk variants I’d be interested in trying are all bone-dry math stuff. It goes without saying that I’m happy with alternate maps, so let’s skip that and look at some core rules stuff:

Variable defense: It could be interesting if everybody was forced to defend with one die only unless your territory has a fortress, in which case you’d defend with two. A fortress would be something that you can build at the cost of a single army at the start of turn. Every starting territory would start fortified. I think the impact of this change could be pretty interesting. For further twist consider directed fortifications: each fortress only safeguards a specific border; you might be limited to building just one per turn per territory.

Variable offense: If the number of dice you could use in attack depended on the number of territories you control around the target territory (sort of representing how your armies converge on the target from different directions), that would also be interesting, and simple to execute. (For added complication you could also track where the actual attacking armies come from, which would curtail and complicate rampage attack runs severely.) So if you control two neighbours, your attack is allowed to use two dice, etc. This rule would presumably be coupled to a principle wherein the defender can only ever use at most as many dice as the attacker (so just one die when the attacker is attacking from a single territory), so as to not make single-connection territories too powerful in defense.

Committed attacks: Players pre-commit a given force to an attack. The force can break off the attack, but if they conquer the territory, the entire force has to move into it. This is more like how Conquest plays in practice (or rather, you’ll just attack with the entire stack every time), and it’s not a big change most of the time (you can just use the move action to split back part of the force), but it does make moving armies around a bit more complicated.

Defensive retreat: It might be pretty interesting if a defensive force “broke” and retreated after suffering 50% casualties. The defender would distribute the retreating forces into any friendly neighboring territories. Forces without route of retreat would fight till the bitter end. A simple change that might do a lot to freshen up the gameplay in various basic patterns, so would be interesting to try out.

Note as a general observation that Risk rules do not inherently break by further advantaging the attacker; the canonical attacker advantage is like ~10% (that is, for every 10 dead attackers 11 defenders die, on average), but the fundamental nature of the game would probably be pretty similar even if the advantage was more like two to one or whatever. You’re still taking losses by choosing to attack, but you’re also controlling the board position by doing it, which is ultimately the entire idea of the game. If anything, rules variation that further favours the attack would probably make the game clearer, easier to play, by making turtling strategies tactically more difficult. Wouldn’t change the fundamental truths, but you wouldn’t just lose quite so easily with aggressive play.

Favouring the defense more, on the other hand, could easily make the game entirely trivial. As it is, you can still win with aggressive play with a bit of luck and non-perfect opposition play. The more defense is favoured in the basic math, the further this dream of winning by being the first to commit recedes.

Monday: Coup de Main #63

As this is a midweek makeover special newsletter, we’re still back in the distant past: this is the game report from last week’s Monday. I expect that I’ll have a report on this week by Sunday, one way or another. This one’s again by Peitsa.

Present in the Knights Temp:
Sven the Reaver, 4th level Barbarian, avec Stone Battlecreek, his 2nd level bruiser buddy.
Bob the Mundane, 3rd level Commoner.
Kermit the Hermit, a 2nd level Savage of learned mien.
Ælfstan the Monk, a 3rd level psion from afar.
(+ 7 mercenaries of solid moral fibre)

I like the moral fibre, reminds me of this highly technical WWII isekai serial I’ve been reading. More on that in the next newsletter, but the gist of it is that apparently RAF (the British air force) used to diagnose PTSD as “lack of moral fibre” back in the day. LMF had symptoms such as not being willing to climb into a flying death-trap to, well, go die. Treated similar to conscientious objectors, ie. by punishing.

In fact, here’s Wikipedia on the conceit. Fortunately the Knights Temp do not suffer from a lack of moral fibre. Their fibre is just fine. Solid.

Waking up in Harrowmoor Keep, the party was pretty hung over from last night’s feasting but in good spirits as they made their way back to Prigworth. While the men were otherwise ready to go, a powerful storm broke out for a couple of days and the Temps decided to rather booze it up in the city instead. Ælfstan had caught up with them there, having stayed behind on other business for a couple of weeks, and spent the rainy days training acrobatics with Sven as plans were laid for the next push. Options were stormed between going for the throat through a secret entrance that should lead right into the midst of the monks in the cellars, or perhaps taking it a bit slower through the main ruins and maybe even conversing with the monks first.

When the heavens finally settled, the dirty dozen rode forth. As they came upon the ruined monastery once more, Kermit and Ælfstan spotted a circling flock of birds high above the area. Could it be the spirit gloam? Hoping to avoid notice, horses were left with two tenders under the canopy cover of the forest while the men would sneak into the main hall in smaller groups. As no immediate sign of attack came, the descent into darkness began once more.

The entrance was sealed with floating candles and rubble once again, eliciting groans from the less mystically minded in the party. With a heave and a ho, the rubble pile was pushed back enough to let one man pass through at a time, but as expected this was too much for the magical barrier and the flames were snuffed as the candles crashed down to the floor. No-one seemed to mind this, at least immediately, and the group pressed on.

The northern fork of the water channels were supposed to control access to the treasury vaults of the monastery, making them a natural target for the mercenaries’ investigation. Coming upon steps down into partially flooded passages, Kermit and Ælfstan shed their shirts and waded into the waist deep murk.

While the mural covered hallway initially seemed peaceful, water flowing gently into the darkness, as Ælfstan turned a corned he was immediately greeted by a scaly head, like that of a giant reptile, looking silently back at him from some distance away. Ducking back behind the corner, everything was oddly calm enough for a second. This bugged the monk enough to take another quick peek around the bend instead of retreating immediately. This time, the head was much, much closer.

Some classic monster interaction imagery there. I also like how the party chose to send the ascetic duo of Elfstone and Kermit wading shirtless in the murk. The kungfu monk and the unwashed crazy-coot forest hermit make for natural allies. I wish them the best, I’m sure the story of encountering the sewer alligator continues happily from here.

Everything erupted into chaos and fury in the blink of an eye. Kermit swam back towards the open stairs as a hideous, seven-headed monster the size of a cottage burst into view and filled the room from floor to the ceiling as it reared in aggression. Boars, reptiles, fair maidens and upturn’d bovines could be found in the chaotic mess now facing the Temps.

Ælfstan sped away, his martial prowess on full display as he launched himself to safety by kicking off from the monster as it tried to snatch him in a snake’s maw (though he did get poisoned through a scratch and fell unconscious immediately after on the stairs in Kermit’s arms as he sprang to haul the fallen comrade out of harm’s way).

Meanwhile Sven had ordered the men into a protective spear wall, himself shooting arrows into the beast’s eyes to buy time for Kermit and Ælfstan to retreat. As the chimeric monstrosity lunged forwards, it impaled itself badly on the spikes to the cheers of the warriors. Though gravely injured, the fell creature had only began its rampage. While it was thrashing around with venomous fangs and sharp horns, so too did it belch noxious smog and one of its heads screeched in unearthly horror that laid waste to the group’s sanity. Some fell on their knees clutching their ears, some stood slackjawed in stupor while some launched themselves towards any real or imagined foes they could find.

Utter confusion reigned as thus confused Kermit tried to bash poor unconscious Ælfstan to death against the floor, Stone chopped up one of the armsmen and so while Bob, the poor bastard, simply slipped into the channel through mundane fumbling as he tried to get choppy with his magic axe.

Oh, Bob, you’re so precious. A Chaos Hydra screams, your allies turn to murder the shit out of each other, and your biggest problem is walking and swinging an axe at the same time. Shine on.

Sven, quick on his feet as ever, resisted the foul magics and leapt on top of the beast casting aside his bow. With Herja in his hands, he wrestled a grasp on the beast’s back and struck deep in one of its necks. Blood and stained water spattered everywhere as the spiteful blade was drawn across the screecher’s throat. Roaring in triumph, Sven ripped the head off and stuffed it into another maw that struggled to gain purchase on him. Unfortunately, Bob was struck far harder by another head, something in his leg giving away as he too fell to the waters. With the aid of the bravest of the mercenary Joes, Sven brought the thrashing beast down in ruin before more esoteric bullshit could be vomited forth from its mutated form.

In the immediate aftermath, maybe half an hour was spent in more or less silent vigil as Sven either slapped some sense or wrestled into submission those members who still hadn’t gotten their wits in order. As their heads cleared and no immediate follow-up threats emerged, more men stumbled to their feet and began assessing the situation. Most of the mercenaries were dead, Ælfstan sleeping deeply as if cursed, Bob’s leg busted through and any hope of pressing on at this point rather sordid. While the laughing, gore-covered barbarian was snacking on the hydra’s heart, Kermit tried to wake Ælfstan with foul smelling offal from the carcass of the beast to no avail. They would clearly have to fall back soon, but first the team took a last look at the machinery in the den of the beast. Clearly, there was some sort of a water wheel that the Archimandrite had told would control the doors to the vault. The place was somewhat flooded, but not so much that there was no drainage at all. If they could stop the water flow from the pool upstairs, maybe it could be cleaned enough to try if the mechanism still worked? A table might be enough, next time.

Hauling the casualties and equipment up, it was soon apparent that the circling birds were gone. So were their horses, panicked and driven into the woods. Never ones to despair, the Temps fashioned some stretchers for the wounded and started the long march back to Prigworth. As fates would have it, the two Joes left to guard the horses were still alive and well there, recounting a bit shamefully how they’d broken and fled immediately when the birds had attacked the horses. Not that anyone really blamed them, knowing what they faced. On their own, they’d only ended up as bird feed had they stood their ground. There was a brief crisis of morale in the ranks, but Sven’s boundless martial confidence soon swayed their mind. Besides there being more in it for everyone of them now, had they not already proved themselves as warriors? They had beaten the crow, the dead and the beast: surely, they would beat whatever else tried to stand in their way now that the vault lay in sight!

Hopefully father Rewalt could do something about Ælfstan’s situation, given the monk still hadn’t woken up…

That lack of moral fibre case at the end surely opened my eyes about Peitsa’s impartiality as a narrator. Nice end-capping there. Did you see how ostensibly epic his character Sven was in that fight, single-handedly slaying the hydra and saving everybody?

Aside from that, though, that place seems like it must have some great treasures in its vaults. To recap, the archimandrite’s ghost told the adventurers earlier that the monastery has a treasure vault, and then they find the treasure vault’s locking mechanism “incidentally” guarded by a Chaos Hydra. Imagine the adventure author who’d put an empty vault behind that kind of foreshadowing!

This could well be the break that Knights Temp need to break into mid-levels for good.

State of the Productive Facilities

No developments since the weekend, I’m afraid… Well, to tell the truth I’m actually writing this on Monday morning, so do I really know that I wouldn’t have gotten anything done before midweek? Maybe I’ve actually gotten my correspondence into order, there’s a couple of people I really should reply to. And write something, too, of course.

2 thoughts on “New on Desk #91 — The Risk of Conquest”

  1. A very interesting analysis of Risk.
    I remember that scaling reinforcements naturally led to the end of our Risk games. Dunno if we played by the rules as written but scaling was ever steeper (exponential?) so that players alternately swept almost the entire board until one such sweep succeeded.
    (Probably not a solution to the problem, as it would become a game of when to cash in, as you point out.)

    1. Yeah, that’s the standard rule. It’s a bit of a controversial fix for the game in that the ever-larger reinforcements don’t really solve the game so much as they encourage bad play. “Rampage across the board” is often mentioned as the core experience with Risk, which is a bit of a problem for how it’s not actually a way to win the game. It’s sedative game design in that it strives to hide the ultimate conclusions with theatrics. I prefer to play with fixed reinforcements (6–12 units depending on the combination you turn in) in my solo play, as while the game is slower that way, it’s also less arbitrary and luck-based.

      (To be clear, for real-world purposes I absolutely do recommend the standard reinforcements rule. It’s the humane thing to do if a sane person has to play Risk, and the kids will love it because you get big piles of armies and get to roll lots of dice. The game will probably even end pretty quick, as rampaging will indeed work fairly well if there are no turtles in play.)

      What proponents of the game usually claim is that the rampaging behavior works because the goal is player elimination; by eliminating another player you can take their reinforcement cards, allowing you to hopefully cash in another set and thus recoup the expense of destroying said player. This domino effect could then help you reach an unassailably dominant position and thus win the game. Because reinforcements scale faster than default income (3 armies per round), rampage beats turtle.

      The problem in all this (your decision to react to getting +20 armies by going on a rampage, and your decision to seek player elimination) is that player elimination will only ever have a positive income effect for you if the other players allow it: a player who is your neighbour will have to have chosen to a) have all of their territories contiguous with yours such that they’re in easy reach for elimination, and b) to not cash in their own reinforcements yet, so as to make eliminating them affordable. In other words, you can only ever eliminate somebody from the game because they have remarkably bad luck, or because they’re playing badly. With many players eliminations will of course happen to start simply due to dice luck, but by the time you’re at say four or three players remaining, why would one of those players have amassed an unassailable position that the others couldn’t rebalance between them by judicious expenditure of their resources?

      To be entirely explicit about what I view to be the optimal strategy in Risk: in the early game, when nobody has enough forces to actually prevent relatively free movement across the board, pick two festung positions to fortify yourself in. They should be on different sides of the board, in places that are non-objectionable to the other players and out of the way of their likely struggles for continent domination (a fool’s errand in itself early on). On every turn place your reinforcements in the two festungs and attack a single neighboring territory for a reinforcement card if an empty (single-army) target territory is available. Retain a big hand, try to keep reinforcements available so you can react if somebody nevertheless decides to try for a mutual kill by attacking you; the reinforcements will help your recovery. When you’re forced to take reinforcements due to the hand limit, just place those in your festungs normally. Keep doing this until the suboptimal play of the other players has resulted in your festung armies being so large that you can afford to split expeditionary forces that are themselves invulnerable to challenge, at which point you can start slowly conquering the board territory by territory without your opponents being able to do anything about it. Interfere as necessary (minimizing the expense to your festungs) to prevent the other players in their stupidity from allowing one among them to rise to a position that allows them to produce more than you do.

      The dilemma of Risk, and arguably all other Ameritrash zero-sum multiplayer boardgames with fairly free attack vectors (that is, the game doesn’t prevent you from expending resources against another player fairly freely) is that the turtling strategy seems to be locally hegemonic: it wins against any other strategies. Particularly, if you’re the only turtle in the game, it should be fairly guaranteed that the players who are actually expending their forces in futile struggle (you don’t actually gain anything in Risk from attacking other players beyond the questionably valuable reinforcement cards) will be outpaced by the players who save up their strength (turtle). However, if there are several turtles, particularly if there are three or more of them, the game doesn’t seem to end. At least the turtle’s strategic doctrine, above, says that two turtles would just keep amassing forces until the infinity.

      (If you had just two turtles and no third player, the situation would be resolved by the slight advantage attacker holds in the dicing. You’d want to amass a very large army, say a hundred units, and then attack the enemy’s equivalent hundred-unit stack. You should end up with about 10 armies in advantage from the exchange, which would suffice in a two-player situation to secure victory afterwards. Thing is, Risk will never end up in a two-player situation as far as I can see, if played competently. If there’s a third player, you winning a big fight 100-90 against one of your two opponents just means that your other opponent wins the game when they attack your remaining 10 armies with their own 100. Thus, with three turtles in the game you should never attack, and thus the game never ends.)

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