The double cross in Dots and Boxes, revealed

The effect: two free boxes that lose the game

Every good trick begins with something that looks like a mistake. Your opponent is collecting a chain of four, closes two boxes, and then, instead of finishing, draws a line at the far end. Two boxes are sitting there for you. You take them with a single line and feel rather pleased with yourself.

Then you notice it's still your turn, and every line left on the board opens a chain. You hand over the next one, and the one after that. Those two free boxes were the price of your whole endgame.

The method: the all-but-two move, step by step

Here's what was really going on. Your opponent ran out of safe lines and had to open a long chain of four at one end.

Red closes the first box, then the second. Each box earns another line, so the turn stays with red. With two boxes left, red doesn't close the third. Red draws the end line on the far side instead. Now the last two boxes share a single missing line, and whoever draws it collects both.

Blue takes the pair and, having scored, has to draw again, straight into the next chain. The setup move red made has a name of its own: double-dealing. The line blue draws to collect the pair is the double cross itself, a term made popular by Elwyn Berlekamp's book on the game.

Try the double cross against the computer

Reading about a trick only gets you so far. Here's a board to practice on: two rows of three boxes with every top and bottom line drawn. The computer moves first, has no safe line left, and must open one of the rows for you.

Take all three boxes of the first row and you'll have to open the second row yourself, so the game ends 3 to 3. Take one, leave the last two as a pair, and the computer is forced to open the second row for you. Final score: 4 to 2, your way.

The loop version: all but four

Loops are the harder variation. A loop has no open end, so when your opponent opens one you can't leave a single pair behind. Take everything except the final four boxes, then draw the line that splits those four into two pairs. Your opponent collects both pairs and still has to open the next chain.

That version costs four boxes instead of two, so it's only worth doing when the chains still to come are big enough to pay it back.

When the double cross isn't worth it

1. On the last chain of the game. There's nothing left to control, so sweep every box.
2. When only short chains remain. Giving up two boxes to win back one or two is a losing trade.
3. When the loop price is too steep. Four boxes for a single chain of three or four rarely adds up.

Before you turn boxes down, count what's still on the board. If the chains to come are worth more than what you're handing over, go ahead. If not, cash in everything now.

How to stop someone using it on you

The best defense is to make the trick impossible. When you're forced to give away two boxes, draw the line between them rather than an end line. That splits them into two single boxes, and there's no pair left to hand back. Strong players call this the hard-hearted handout. The end-line version, which lets your opponent turn the boxes down, is the half-hearted one.

Your other defense is the chain count. Win that fight in the middle of the game and your opponent never gets the chance to set the trick up. The Expert computer here knows all of this, and since it runs entirely in your browser, you can lose to it as often as you like in complete privacy.