The best first guess in Liesofpdle, calculated

Why the opener deserves a plan

Your first guess is the only one you play blind. Every later guess can react to the colors and arrows you have already seen, but the opener is chosen before you know anything. That makes it the one guess you can prepare in advance.

A good opener does not need to be right. Its job is to split the 29 possible answers into small groups, so that the feedback tells you which group to search next. Picture two extremes. A guess that produced the same row of colors whatever the answer would teach you nothing. A guess that produced a different row for every answer would hand you the solution on the second try. Real openers sit between the two, and this page measures exactly where.

The method

For each boss, we simulated a first guess against each of the 29 possible answers, with the comparison function the game itself uses. Each simulation yields a pattern: green or gray for Type, Weakness, Region and DLC; green, up arrow or down arrow for Chapter and HP. Answers that produce the same pattern cannot be told apart after that guess, so we group them together.

Three numbers then describe an opener:

• Candidates left (average): how many answers remain possible after the guess, on average. If a group holds n of the N answers, the hidden boss lands in it with probability n/N and leaves you n candidates. Adding n/N × n over all the groups gives the sum of the squared group sizes, divided by N.
• Information: the same idea expressed in bits, as in the well-known Wordle analyses. Each bit halves the field on average; picking one boss out of 29 takes a little under 5 bits.
• Worst case: the size of the largest group, in other words what you are left with if luck turns against you.

The Boss mode ranking

The best opener, Arlecchino, the Blood Artist, leaves 3.5 candidates on average out of 29, which is worth 3.3 bits of information. In the worst case, 6 candidates remain. Romeo, King of Puppets and Lumacchio, Leader of the Bastards follow closely. At the bottom of the table, Parade Master leaves 8.3 candidates on average, more than twice as many.

Why the middle of the range wins

Chapter and HP are the two columns that answer with an arrow, and arrows reward middle values. If your guess sits in the middle of the range, the arrow cuts the remaining bosses roughly in half, whichever way it points. If it sits at one end, almost every answer produces the same arrow and the cell tells you next to nothing.

The bottom of the ranking proves the point. Parade Master has the lowest HP total of the whole roster, 4,400, so its HP cell shows an up arrow for every other boss. It is also fought in chapter 1, which means its Chapter cell points up for nearly every answer as well. Two of its six clues are close to useless before the game even starts. The other weak openers share the same flaw: Mad Donkey has the second-lowest HP total, Simon Manus, Awakened God carries the highest chapter number, and Two-faced Overseer has the second-highest HP total.

Arlecchino, the Blood Artist, at the top of the ranking, shows the other side of the coin. Its HP total is among the highest, so that arrow is not much use. Its chapter number, however, sits right in the middle of the list: 14 bosses come before chapter 5, 13 come after it, and one shares it. Its three other main clues each match a small group: 6 other Puppets, 7 other bosses weak to Acid and 7 other DLC bosses. Every cell asks a different question, and together they spread the answers across many small groups.

A full game with the best opener

Here is a complete game opened with Arlecchino, the Blood Artist, where the hidden boss is Mad Donkey. After the opener, each guess is the remaining candidate that splits the others best.

The first row is almost entirely gray, and that is useful. The answer is not a Puppet, is not weak to Acid and comes from the main game. Both arrows point down: it is fought in an earlier chapter and has fewer HP. Only four bosses fit: three Stalkers and one Carcass.

The second guess is not the most likely answer but the most useful question. Survivor is fought in chapter 3, between Mad Donkey's chapter 2 and the chapter 4 of the other two candidates, and its HP total sits between those of The Atoned and Fallen Archbishop Andreus. Its Type and Weakness cells, meanwhile, set the lone Carcass apart from the Stalkers. Each remaining boss therefore gets its own combination of colors and arrows, and the third guess is a sure thing. Guessing Mad Donkey second would have been a gamble: had it been wrong, Survivor and The Atoned would still have produced exactly the same row.

Across all 29 possible answers, this simple method finds the boss in 2.6 guesses on average with the data of version 1.12.0.0, and never needs more than four. Opening with Romeo, King of Puppets does slightly better over a whole game, at 2.5 guesses on average and never more than three, even though it leaves slightly more candidates after the first guess. Opening with Parade Master costs about 2.9 guesses on average, and seven answers then take four tries.

Legion Arms: a much smaller puzzle

Legiondle only has 10 possible answers, so the stakes are lower, but the same logic applies.

The best opening guess is a 4-way tie between Aegis, Falcon Eyes, Icarus, and Left Arm of Steel. Each of them leaves 1.2 candidates on average and never more than 2; the table simply lists them in alphabetical order. Followed up with the same method, any of them finds the answer in two guesses on average and never needs a fourth.

The worst opener, Puppet String, still leaves only 2.0 candidates on average, but it illustrates the principle neatly. It is the only Utility arm and the only one with the Grapple mechanic, so those two cells come back gray for every other answer. Its ATK of 60 is beaten by seven arms out of nine, so its arrow nearly always points up. Aegis, one of the joint leaders, is just as unique on Type and Mechanic, but its ATK of 100 sits in the middle of the range, and its Balanced scaling is shared with three other arms. One well-placed numeric value makes the difference.

Weapons, amulets and quotes: no opener to optimize

In Weapondle and Amuldle, a guess is only right or wrong. Every wrong guess removes exactly one item, so there is no clever opener: the only strategy is to recognize the icon. Study shapes and colors in the weapons codex and the amulets codex rather than guessing at random.

Quotedle is a matter of reading. The line is the only clue, and each guess is right or wrong. The game draws the character first and only then one of their lines, so each of the 16 possible speakers is equally likely: a character with many lines is no more likely to be the answer than one with few. Use what the line tells you, its tone, its vocabulary, the person it addresses, and check the characters codex when a voice escapes you.

Practical takeaways

• Open Boss mode with Arlecchino, the Blood Artist or Romeo, King of Puppets. Less than one candidate separates them.
• In Legiondle, any of Aegis, Falcon Eyes, Icarus, and Left Arm of Steel makes an equally good opener.
• After the first row, prefer a candidate whose chapter and HP fall in the middle of what remains. A guess at the edge of the range wastes its arrow.
• Read Type and Weakness together: the two columns are tightly linked, as the boss weaknesses guide shows.
• When only two or three candidates remain, play one of them, since it can win on the spot.
• Test the method in Practice mode first; how to play explains how.