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The tree of variations

Intermediate · 12 min

A calculation branches at every reply: list them all, then go through each branch once.

Play it without an account

The tree of variations: List every reply to your move, then answer each branch once.

The idea

List every reply to your move, then answer each branch once.

  1. Re1+ is the trunk: White can answer Rxe1, Qxe1 or Qf1.
  2. Each branch needs its own mate: Qh1 after Rxe1, Qg2 after Qxe1.
  3. Once the rook leaves e4, the bishop guards h1 and g2.

In a game: Before you play a check or a capture, count your opponent’s replies and answer each one.

How the lesson begins

A line is one path of moves: you play this, your opponent plays that. But at every turn your opponent has a choice, so a calculation is really a tree. Your candidate move is the trunk, and each reply your opponent could make is a branch. You need an answer to every branch, not only to the reply you expect.

This is Hans Fahrni against Aaron Nimzovich, Karlsbad 1911. Black to move. Black has a strong candidate: the check Re1+.

The tree of variations, step 1: Black to move
Black to move

A question

Black has played Re1+. Before you calculate any further, list White’s replies. How many legal moves does White have?

The tree of variations, step 2: White to move
White to move
  • Three: Rxe1, Qxe1 and Qf1
  • One: Rxe1, the natural recapture
  • Two: the captures Rxe1 and Qxe1
Show the answer

Three: Rxe1, Qxe1 and Qf1.

Right. The king has no square: the queen on h3 covers g2, h2 and h1, and the rook covers f1. So White must take the rook, with the rook or the queen, or block on f1. That is three branches.

In numbers

Blunders in real games

Blunders in every hundred moves, by rating, in a sample of rated Lichess games from 2026 that Lichess analysed.
RatingValue
Under 8006.6
800 to 11994.2
1200 to 15992.8
1600 to 19992
2000 and up1.3

Play it on the board

In GreyChess the lesson is played on a live board: your answers are judged as you move, and the positions to remember become flashcards.

Continue the lesson free