How do you win at dominoes with only two players?

With two players and seven tiles each, 14 of the 28 tiles in a double-six set never come into play, and that changes the game more than having fewer opponents does. You cannot count tiles down to certainty the way you can in a full four-hand deal. In exchange, a pass in a block game is permanent: once your opponent knocks on a number, nothing can ever give them that number again. Most two-player hands are won by the player who builds the line around the numbers the other one is missing.

Which game you are playing matters first, because two-player dominoes is at least three different games depending on the table.

Three ways to deal two players

Block, seven each. Pagat.com, John McLeod's rules site, gives two players seven tiles each; the other 14 stay face down and nobody draws them. A player who cannot play passes. The hand ends when someone plays their last tile or nobody can play.
Draw, seven each. The same deal, but a player who cannot play draws. In pagat's main rules you keep drawing until you play or the boneyard is down to two tiles, which are never drawn. Twelve tiles can come into play.
Full deal, fourteen each. Jamaican Cut-Throat, as pagat records it, deals 14 tiles to each of two players, so there is no boneyard at all. Pagat notes the players may agree to deal seven instead. Some other Caribbean tables play the same full deal.

The scoring also changes by tradition. In pagat's block and draw games the winner scores the loser's pips minus their own, and the game is to 100. Pagat's Puerto Rican draw rules give the winner every pip left in both hands. Cut-Throat scores one point per hand, and you need six wins while the other player still has none. If you lose a hand before reaching six, the score goes back to zero for both. The guide to scoring covers these in full.

What you can count when half the set sleeps

In a four-player partnership deal, every tile you cannot see is in someone's hand. In two-player block it is not. At the start you see your seven tiles, and each of the other 21 has one chance in three of being in your opponent's hand and two in three of sleeping.

That makes holding a number powerful. Each number appears on seven tiles. Say you hold several of them. Here is how likely your opponent is to hold the rest:

Tiles of a number you hold	Unseen	Opponent holds none	Holds exactly one
3	4	16.7%	42.6%
4	3	27.4%	47.9%
5	2	43.3%	46.7%
6	1	66.7%	33.3%

These are exact hypergeometric figures (seven tiles drawn from the 21 you cannot see). With four of a number, your opponent has no answer to it more than a quarter of the time and at most one answer three times in four. Put that number on an end and keep putting it back. Pagat's advice for block and draw games says the same: the better your control of a suit, the more you should try to leave it on the ends.

The other side of the table: your opponent is void in any given number in about one hand in ten (9.8% of seven-tile hands contain no tile of a given number). You will not know which number until they pass.

A pass in two-player block is permanent

When your opponent passes in a block game, they hold no tile of either end number. In a four-player game those tiles are somewhere else at the table and can come back into play. In two-player block they are either in your hand or asleep, and in block nobody draws. Your opponent will never hold those numbers this hand.

Two tile types keep both ends on those numbers, so your opponent stays stuck:

The double of either number. Playing [3-3] on a three leaves a three showing.
The tile that joins them. If the ends are 3 and 1, playing [3-1] on either end leaves 1 and 1 or 3 and 3.

Every other tile you play opens an end your opponent may be able to use.

A worked hand

Two-player block, seven each, pips counted at the end. You hold:

[5-5] [5-3] [5-0] [0-0] [1-0] [4-1] [6-2]

You lead [5-5]. Ends: 5 and 5.
Opponent plays [5-6]. Ends: 5 and 6.
You play [5-0] on a five. Ends: 0 and 6.
Opponent plays [6-4]. Ends: 0 and 4.
You play [4-1]. Ends: 0 and 1.
Opponent passes. They hold no zero and no one.
You play [0-0]. Ends: 0 and 1. Opponent passes again.
You play [1-0] on the one. Ends: 0 and 0. Opponent passes.

You hold [5-3] and [6-2], neither of which fits, so the hand is blocked. The four zeros you never saw, [0-2], [0-3], [0-4] and [0-6], are asleep.

You are left with 16 pips. Your opponent has five tiles, none with a zero or a one, and none of the tiles you have seen. The lightest five such tiles are [2-2], [2-3], [2-4], [3-3] and [2-5], which come to 28 pips. So you have won the block before anyone turns a tile over, and under pagat's scoring you take at least 12 points.

The article on blocked games covers how other tables settle a block. For two players, pagat's rule is simple: the lower count wins, and if the counts are equal nobody scores.

Blocks are the normal ending, not the exception

With 14 tiles asleep, a two-player block hand often ends with both players stuck. We simulated 200,000 hands of two-player block with both sides playing a random legal tile. About 70% ended blocked rather than with someone going out. With both players always playing their heaviest legal tile, the figure was 69%. These are simple strategies, not good ones, but they show the shape of the game. Assume the hand will block, and treat the pips in your hand as the score you are defending.

That has two consequences in pip-scored games:

Heavy tiles are likely to be counted. If most hands block, your [6-5] is likely to end the hand still in front of you. Shed it when a play is otherwise equal.
Do not chase the block blindly. Locking your opponent out only wins if your remaining count is lower. Before you close the game, add up your pips and compare them with the lightest hand your opponent could hold, as in the example.

In Cut-Throat, where a hand is worth one point however many pips are left, pips only decide a blocked hand. Hold your heavy tiles if they keep a number you control.

The same simulation has the leader winning about 57% of hands with random play and 59% with heaviest-first play: an illustration of the first-move edge, not a measured win rate for real players. Pagat's main rules draw for the first lead and then rotate it; some tables give it to the holder of the highest double. Agree on this before the first hand.

Draw games: locks do not hold

In a two-player draw game, a pass means less, because there usually is no pass. A player who cannot play draws, and in pagat's main rules may keep drawing until two tiles remain. Your opponent's missing number is now only missing until they find one in the boneyard.

What carries over from block:

Your count still matters. Every tile your opponent draws adds pips to their hand. Making them draw is the draw game's version of a pass.
Watch what a draw proves. Pagat's main rules let a player draw even when they could play, so a draw proves nothing. In Puerto Rican draw, as pagat records it, drawing while able to play is illegal, so every draw shows the player had nothing for either end. Know which rule your table plays.
Late in the hand, play as if it were block. Once the boneyard is down to its last two tiles, a pass is final again and every lock holds.

The full deal: nothing is hidden

In Cut-Throat with 14 tiles each, the arithmetic turns over. You hold 14 of the 28 tiles, so your opponent holds the other 14. You know their whole hand from the first tile.

That turns the game into a puzzle. Luck still decides the deal, but nothing after it is hidden. A void in a 14-tile hand is rare, about 0.3%, so passes come from numbers running out on the board, not from a missing number in the deal. The skill is working out, several plays ahead, which number your opponent will run out of first, and keeping your own tiles of that number for when it matters. Write both hands down after a few games and replay them. Mistakes are easy to see when everything was visible.

Something to try tonight

Play five hands of two-player block. Every time your opponent passes, say the two numbers aloud and look through your hand for a double of either one, or the tile that joins them. Count how many extra turns that gives you. Then play five hands of the full deal, and before each of your plays, name the tiles your opponent can answer with.

The guide to how much of dominoes is luck explains sleeping tiles in more detail, and the guide to reading a pass covers what a knock tells you at a four-player table.