Risk strategy: which continent wins, and should you turtle?

The spreadsheet says Australia

The classic argument for a continent is a ratio: the bonus armies it pays every turn, divided by the number of territories you have to defend to keep it. Australia pays 2 armies and has one way in, through Indonesia. North America pays 5 for three border territories. South America and Africa come last on this list.

That ratio is where "take Australia" comes from. It leaves out everything that happens after the first turn: whether you can actually get the continent, whether you can keep it, and where you go next. So we played it instead.

We played it instead

The opponents in every game are Strategists: a general-purpose bot that looks at the board each turn, picks the continent that is cheapest to complete, attacks when its odds are decent, puts most of its reinforcements on the borders of what it holds and cashes in cards when it can. Its settings came out of a tuning run of 90,000 games between 40 variants.

Then we built six continent hunters. Each one is the same Strategist with one change: it commits to one continent from the very first claim and keeps going back for it until it holds it. We sat one hunter at a table of Strategists, three to five players, rotating the seats, and counted how often it won compared to a fair share (one in three at a three-player table, one in five at five).

Because the setup changes everything, we ran it three ways: the official draft where players claim territories in turn, a random deal of the territory cards, and tables where every player hunts a different continent.

The order barely moves. South America and Australia are the two best continents to go for in every setup, North America is a solid third, Africa sits just under a fair share, and Asia and Europe are traps.

Between the top two, the setup decides. In the draft, nobody stops a player from claiming all four Australian territories, and the hunter holds it in 99% of games, usually from its first turn. With dealt territories you have to conquer your continent first, and then South America comes out ahead: +58% against +24% for Australia. Australia is easier to keep (the hunter holds it 65% of its turns), but its only exit is Siam, which leads into Asia. South America has two doors, and both open onto continents worth taking.

Table size matters too. In a three-player draft, North America is the best pick (+55%, winning 52% of games) and Australia is below par. With four or five players it flips: Australia climbs to +115% and North America drops to a fair share. The more players, the more a safe corner is worth.

One level deeper: what if someone else wants it too?

Everything above assumes nobody fights you for your continent. At a real table, Australia is the first thing an experienced player looks at. So we seated two hunters after the same continent at a table of Strategists.

Every continent collapses. Two Australia hunters split the four territories and spend the early game fighting each other for them while the rest of the table walks past: each wins 48% of a fair share. Even South America, the most robust pick, drops to 57%. The best continent is the best one nobody else is going for.

Getting it, keeping it, and Asia

With dealt territories the hunters have to fight for their continent, which shows where the traps are. Asia is the extreme case. A hunter that does manage to hold Asia wins 57% of those games, but only 13% ever get there, on average in round 11.7. Twelve territories and five borders means every neighbor is in your way. Europe is easier to take than Asia but hard to keep: hunters hold it 7% of their turns.

A second check that does not depend on our hunters: in ordinary games between identical Strategists, the ones that happened to hold South America by round 5 went on to win 2.3 times their fair share, Australia 1.9 times, and Europe only 1.1 times.

Turtle or attack?

The second argument at every Risk table: do you build up and wait, or do you attack every turn? We gave the Strategist five temperaments, from a turtle that defends every border and only attacks once a turn to earn a card (it breaks out once it has 1.5 times the armies of anyone else) to a reckless bot that attacks anything at 25% odds and never stops rolling.

Against a table of Strategists, the turtle wins 39% of a fair share. It does survive: it finishes in the top two about as often as anyone (53% of games). It just almost never wins, because the players who attacked collected the continents and the cards. Being too careful costs as well (the cautious bot: -15%), and so does attacking anything that moves (reckless: -10%). The tuning run said the same thing in a different way: variants that only attacked toward a goal averaged +3% against the field, variants that attacked anything at the same odds -4%.

Doesn't turtling work when everyone else is fighting?

That is the turtle's whole theory: let the others bleed each other, then take over. So we sat the turtle at a table of aggressive bots, who attack far more than the Strategists do. It helps a little, from 39% to 50% of a fair share. Still a losing plan.

Then the reverse: what happens to the one player who attacks at a table full of turtles? It wins 3.0 times its fair share. Turtles leave the continents and the cards on the table, and the attacker takes both.

Cash in your cards right away

Set values go up for everyone each time anybody trades (4, 6, 8, 10, 12, 15, then 5 more per set), so it is tempting to sit on a set and wait. We tested a Strategist that only trades when the rules force it, at five cards. It won 3% less often than a fair share. The other way round, a Strategist that cashes in immediately at a table of holders won 4% more often than a fair share. A small edge, but a consistent one: armies now help you take a continent or a card this turn, and you have to trade at five cards anyway.

Two smaller findings. Turn order matters: in a three-player draft the first player wins 40% of games and the last 26%. And bot games are quick: on average 13.1 to 17.6 rounds depending on the number of players, because escalating card sets snowball. Our dice article has the odds for every single battle.

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How we tested

The rules engine plays classic Risk to world domination: the 42 territories and 83 borders of the standard map, starting armies by player count, territories claimed in turn (or dealt), reinforcements of territories divided by three with a minimum of three plus continent bonuses, attacks with the exact dice odds from our dice article, at least as many armies moved in as dice rolled, one fortify move between adjacent territories, one card per turn with a conquest, sets worth 4, 6, 8, 10, 12, 15 and then 5 more each, the +2 bonus for a pictured territory, forced trades at five cards and taking a defeated player's cards. Automated checks cover the map (every border listed from both sides, continent borders), reinforcement math, card sets, the dice sampling, and invariants after every turn of hundreds of test games.

All bots except a random baseline share one core with adjustable settings, so a difference in win rate comes from a setting rather than from one bot being coded better. The Strategist attacks when it has at least a 60% chance to take the territory, puts 60% of its reinforcements on the borders of continents it holds, and only attacks toward a goal: its continent, someone else's bonus, a card, or a player it can eliminate. Every configuration was played thousands of times with rotating seats and fixed random seeds, so the numbers reproduce exactly.

Limits worth knowing. Bots don't negotiate, form alliances or hold grudges, and they don't block a continent during the draft, which is why the uncontested Australia numbers are an upper bound and the rival experiment is the other end of the range. The Strategist is a decent player, not an expert, so this is the best of the strategies we tested, not optimal play. Draft results swing with the number of players (see the numbers under each chart). We used classic world domination rules: no secret missions, no two-player variant, and fortifying only between adjacent territories as in the classic rulebook. Card symbols follow a fixed pattern rather than the printed deck, which only affects the +2 bonus. More on how we test.