Master — Quoridor AI Opponent
Magnus is the master tier, one rung below the strongest bot on the roster and one above the expert tier. It is the right opponent once your losses have stopped arriving as single identifiable mistakes and started arriving as a game you were slightly behind in from move six onward. Magnus will not hand you a swindle, and it will not fall for one. What it will do is show you what a game looks like when neither side is making errors and the whole thing turns on which player counted more carefully.
Two things only become visible at this tier: how the bot decides which move to play out of several that all look fine, and how it decides which positions are worth thinking about at all. The second one is worth stealing.
The move it plays is the one it kept coming back to
Magnus spreads tens of thousands of playouts unevenly across the moves available on this turn (how the engine scores a move), and when the budget is spent it does not play the move with the highest win rate. It plays the move that received the most playouts.
That distinction matters more than it sounds. A move only accumulates playouts by continuing to look good as the search keeps returning to it. A line that looks spectacular across the first hundred playouts and then falls apart once the search sees the reply loses its share of attention to something duller, so the count is a measure of how well a move held up under repeated examination rather than a measure of its best case. A move that wins big in one narrow line but needs your cooperation to get there loses the vote to a move that is merely solid against everything.
The practical consequence is direct: do not play Magnus for a single reply. Setups that depend on the opponent stepping into one particular square, walls that only work if the answer is the obvious one, offers that need a specific greedy response — these are exactly the ideas that this selection rule filters out, because a line requiring one cooperative move is fragile across continuations and never accumulates enough attention to win. The same logic explains why Magnus so often plays a move that looks unambitious. It is not being passive. It has picked the move that is hardest to be punished for.
There is a mirror of this you can apply immediately. When you are choosing between two candidate walls, and one is spectacular against the route your opponent is currently taking while the other is merely good against any route they might take, prefer the second. Wall or Advance gives you the arithmetic for pricing a wall; robustness is the tiebreak the arithmetic does not capture, and it is the tiebreak the bot uses.
One more thing follows from the same rule. In a genuinely balanced position, several moves will end up with nearly equal shares of the search, and the one Magnus plays is close to arbitrary among them. Do not read intent into its quiet moves, and do not imitate them either. It is not building toward anything you are failing to see; it is declining to commit, which is a different and much more annoying thing to play against — and copying a move that was chosen for having no downside will leave you drifting without a plan of your own.
What its budget actually is
Magnus gets a playout ceiling in the low tens of thousands per move — roughly two and a half times the tier below's, and about a third of what the top tier is allowed. The search runs until it either reaches that count or hits a time ceiling of a few seconds, whichever comes first (a fast game clock can stop it sooner still).
What matters about those two numbers is which one binds. On the fixed midgame position the engine is benchmarked against, Magnus spends its whole per-move playout allowance and still finishes in well under half its time ceiling — so in a middlegame of any substance it is the playout count that stops the search, not the clock. That is worth knowing, because it means the tier is defined by how much it thinks rather than by how fast your device is. Whenever it finishes inside that ceiling, the same position gets the same number of playouts on a laptop and on a phone; it just takes longer to arrive on the slower one. Only on hardware slow enough that the time ceiling runs out first does the device start setting the strength.
Where it spends its clock, and where you should spend yours
Magnus does not spend equal effort on every move. Before searching, it scores the position for complexity and uses that score to slide both its think time and its playout target between the tier's floor and its ceiling. Three signals feed that score, with fixed relative weights:
- How many walls are still unspent, both sides counted together. This carries the largest share. Unspent walls are unwritten futures; while they exist, the shape of the board is still undecided.
- How close the race is, measured as the difference between the two shortest-path lengths. It carries the next largest share, and it drops out entirely once one side's lead is wide enough that the outcome is no longer in doubt.
- How many wall slots are still geometrically placeable. The smallest share. An empty board offers well over a hundred; every wall placed removes its own slot and disqualifies its neighbours, so this number falls faster than the wall count does.
Now read that list as advice for a human with a clock, because it is a triage rule and a good one. Think hardest when both players still hold most of their walls, when the two path counts are within a square or two of each other, and when the board is still open — those are the turns where one decision reshapes everything that follows. Move quickly when your lead is already comfortable, when the walls are mostly spent, and when the board is congested enough that only a handful of placements remain legal. Those positions have fewer branches in them, and the time you save there is time you get to spend on the turns that actually decide the game.
Most players do the opposite. They move quickly while the walls are all still in hand, because the position feels obvious, and then agonise over an endgame that is often already arithmetic.
One qualification, because this is a rule about where thinking pays and not a licence to hunt for a wall on every early turn. Wall or Advance says the opposite about the opening proper — the count is dead level, no single wall on an open board clears its threshold, so the answer there is usually just to advance — and the engine sides with that page over this one, since it does not search at all in its first few plies (the opening is a lookup). Both are right about different moments. The turns worth the most thought are the ones where the walls are still in hand and something on the board has already committed, and most of those arrive shortly after the opening rather than during it.
Reading a Magnus that starts marching
Sooner or later a Magnus that has been manoeuvring, sidestepping and placing walls will begin walking in a straight line and not stop. It is tempting to read that as the bot conceding. Usually it is not, and knowing which case you are in is worth a move.
The common cause is bookkeeping, not judgement. Once Magnus has spent its own last wall — its supply, not yours — it stops searching altogether and simply steps a shortest path every turn until the game ends (the wall-less shortcut). A Magnus that is comfortably winning marches exactly like a Magnus that is losing, because in both cases the same code path has taken over and no evaluation is involved at all. So the first thing to check when the marching starts is its wall count. If the supply is empty, the march carries no information.
If it still holds walls, one other rule can produce the same picture. After the search finishes, a separate check looks at the answer, and if that answer is a pawn move that does not step onto one of the genuinely shortest routes, it can be discarded and replaced by a plain step toward the goal. Two independent conditions can trigger that replacement, and they are not the same signal. One is positional and early: it applies in the game's opening plies while its pawn is still on the centre column, which is why a straight march in the first few moves means nothing. The other is the one worth reading: the search's own estimate of its winning chances having fallen very low.
Even then it is a hint rather than a verdict, because the rule only ever rewrites a pawn move. A Magnus that thinks it is losing but whose search still prefers to place a wall is left alone and never marches at all. The tell is therefore one-directional: a middlegame march from a Magnus that still holds walls is decent evidence its own numbers have gone bad, while the absence of one is no evidence that they have not. Never let its behaviour substitute for your own count — read the march as confirmation of a lead you had already established for yourself, and convert rather than get clever.
Why the step up from the tier below is smaller than it looks
When the ladder was measured rung by rung in head-to-head play, the rung from the expert tier up to master came out an even split, while the rung below it and the rung above it were both decisive. The recorded explanation is that when the per-tier playout ceilings were re-set, master's dropped further than any other tier's in absolute terms, landing close enough to the expert tier's that its advantage at those positions' complexity did not survive.
That is stated here rather than buried because it should change what you expect. If the expert tier already gives you close games, master will feel similar rather than like a wall. The two tiers run the identical search with the identical playout policy and differ only in how long that search is allowed to run, so what the extra thinking buys is the same ideas chosen more reliably, not different ideas — and at the complexity of those particular games, that turned out to be worth nothing measurable.
Do not generalise the result further than it goes, though. The rung above this one was decisive in the same measurement: the top tier beat master in every game played. More thinking still converts into more strength on this ladder. What the flat rung shows is narrower and more specific — that these two particular ceilings ended up too close together to separate, which is a calibration fact about master, not a ceiling on the method. The genuine step up on the roster is the tier above.
How to beat it
Win on arithmetic, not ambush. The selection rule filters out lines that need a specific reply, so there is no trick on offer against this tier. What is on offer is being ahead in the count, turn after turn, and refusing to spend a wall that does not clear the bar. The grind is the plan, not a fallback from a better one.
Simplify while you are ahead. A wide lead makes the race term in its own complexity score vanish and a filling board removes live placements, so a position you have simplified is one it has fewer resources in — not merely one it thinks about for less time. Spend a wall to delete their best structure rather than to gain one more square, and be willing to accept a slightly worse exchange rate to get there.
Track its wall supply, not just its behaviour. Its wall count tells you which Magnus you are facing: one that is still searching, or one that has already been reduced to a shortest-path machine and cannot surprise you again. That is a fact you can check on every turn, unlike anything you might infer from the moves it chooses.
If a grind is not what you came for, the tier below is one rung down and plays the same game a little more loosely. The current roster with each bot's live rating is on Bots, and unfamiliar terms are in the Glossary. Playing any bot here costs nothing — the paid plans are about coaching and analysis rather than access (Pricing).