Reading Opponents in Block Dominoes: What a Pass Tells You

Block Dominoes hands you one piece of certain information about an opponent’s tiles, over and over: the pass. This article is about how to record passes, what they rule out, and how to set the open ends so that a seat which has already passed keeps passing.

What a pass proves

A player passes only when no tile in their hand matches either open end. So a pass proves exactly two facts: at that moment the player holds no tile carrying the left-end number, and none carrying the right-end number. It says nothing about the other five numbers.

The fact keeps its value because Block Dominoes has no drawing. A hand only ever shrinks. A player who holds no 5 now cannot hold one later, since there is nowhere for a new 5 to come from. In Draw Dominoes, a different game, the same pass would expire the moment the player picked up a tile from the boneyard. In Block it lasts until the hand ends.

Two limits are worth stating. A pass records what the player holds now, not what they held earlier: a seat that played a 4 on turn 5 can pass on 4 on turn 25, once its last 4 has gone. And in a two- or three-player deal a pass tells you nothing about the tiles set aside; those are unseen, but they are in nobody’s hand.

Keeping a pass table

You need one line per seat and, against each, the numbers that seat has passed on. The information is announced: when a computer seat cannot play, the game shows a notice saying the seat passed, and the two open ends are still on the felt to be read off. The game does not keep the list for you, so keep it yourself.

Here is the log from a four-player hand. The seats in turn order are North, West, you and East. North held 6-6 and opened with it, as the holder of 6-6 always does when four players use all 28 tiles. The diagram shows the line after ten turns; the hand ran to 26 turns and contained four passes.

Turn 8 is the row that matters for the play that follows. East had played 4-6 on turn 4, then found the ends showing 2 and 5 and passed. Turn 12 is the same seat passing at the same two numbers, which adds nothing. Turn 25 shows a number joining North’s list twenty turns after North played it: the 2-4 is there in the diagram, second from the left.

Steering an end to a passed number

It is turn 11, the ends show 2 and 4, and East plays after you. Three of your tiles are legal. 1-2 fits the 2 end and would leave 1 and 4 open. 3-4 fits the 4 end and would leave 2 and 3. 4-5 fits the 4 end and would leave 2 and 5.

The pass table decides it. East holds no 2 and no 5, so after 4-5 both ends show numbers East cannot answer, and East must pass again. After 3-4 the 3 end is open to East, and you know nothing about East’s 3s; as it happens East held 1-3. After 1-2 the 1 and the 4 are open, and East’s 4-6 on turn 4 proved only that East was dealt at least one 4, not that none remain.

4-5 is also your heaviest tile, at 9 pips. Play it on the right. East passes on turn 12, the second row of the table, and the turn moves on to North with East one tile further from going out than everyone else.

Be clear about what this achieves. Forcing a pass from East does nothing to North and West, who both play before the turn comes back to you, and either may change an end. Steering works on the seat that plays immediately after you. Setting both ends to the same number, which shuts out every seat lacking that number, is a related and more expensive idea covered in the article on controlling both ends.

Combining two passes

One pass rules out two numbers. Two passes at different ends can rule out three or four, and late in a hand that is enough to name the tiles an opponent can hold. The two-player game, which is what the site deals on a phone-sized screen, gives the sharpest version, because there is only one opponent to read.

Your opponent opened with 4-4. With two players, 14 tiles are set aside, and the opener must be the highest double held at the table. You hold neither 5-5 nor 6-6, and your opponent cannot, or would have opened with it. Both are among the set-aside tiles for the whole hand.

The opponent passed on turn 7 with the ends at 0 and 5, and again on turn 9 with the ends at 0 and 3. Combined: no 0, no 3, no 5. Now list the 18 unseen tiles, the way the endgame article does for the last few turns, and strike out every tile that carries a 0, a 3 or a 5. Six survive: 1-1, 1-2, 2-2, 2-6, 4-6 and 6-6. You already know 6-6 is set aside. Your opponent’s four tiles are therefore four of these five: 1-1, 1-2, 2-2, 2-6 and 4-6.

Whichever tile is the missing one, the opponent holds at least one of 2-6 and 4-6, so certainly holds a 6. The lightest four of the five are 1-1, 1-2, 2-2 and 2-6, which add up to 2 + 3 + 4 + 8 = 17, so the opponent holds at least 17 pips.

Now your play. 3-6 fits the 3 end and would leave 0 and 6 open, and you have just established that the opponent holds a 6: that play hands over a turn and a chance to shed. 0-3 fits either end. Played on the 0 end it leaves 3 and 3; played on the 3 end it leaves 0 and 0. Both force a pass, but only the second lets you keep going. After 0 and 0 you follow with 0-5, leaving 0 and 5, another certain pass. Then you hold only 3-6, which fits neither end, so you pass too, and the hand is blocked.

Blocked in your favour. You are left with 9 pips; the opponent has at least 17. The winner of a blocked hand scores the pips left in the other hands, exactly as if they had gone out, so this line is worth as much as going out would be. In the actual hand the opponent held 1-1, 2-2, 2-6 and 4-6, which is 2 + 4 + 8 + 10 = 24 points to you. Had you opened the 6 instead, and the opponent answered with 2-6 and later 2-2, the hand would still have blocked in your favour, but with 8 + 4 = 12 pips gone from the opponent’s hand, for 12 points rather than 24.

What a play tells you

A play is weaker evidence than a pass, but it is not nothing. It proves the player held that tile, which removes it from the unseen count for both numbers on it. It does not prove they hold another of either number: a seat that has played its only 4 is in the same position on 4s as a seat that never had one, and only a later pass will tell you which.

The opening play is the exception, because it is forced. Whoever opens must hold the highest double at the table. With four players all 28 tiles are dealt, so 6-6 always opens and the opening tells you nothing. With two or three players, any opening double below 6-6 tells you which doubles are set aside: a 4-4 opening means 5-5 and 6-6 are out of the hand, as in the example above, and neither you nor your opponent can ever play them.

Which end a player chooses is not evidence. A tile that fits both ends can go on either, and no rule compels the choice, so nothing can be proved from it.

Why there is no bluffing

Reading opponents in card games usually means detecting deception. In Block Dominoes there is nothing to detect. A player who holds a legal tile must play one. The game’s Pass button appears only when you have no legal move, and the computer seats are bound by the same rule. So a pass can never be a bluff, and a play can never be a false signal about the numbers it shows. The whole space of decisions is which legal tile to play and which end to put it on. Everything you learn from the table is true, and the only skill in reading opponents is keeping track of it. You cannot bluff either.

The Hard opponent keeps the same table

The site’s Hard level plays the method in this article. Each time any seat passes, the game records the two open-end numbers against that seat. When Hard chooses a move, it scores every legal option and adds 15 points for each open end the move would leave showing a number one of its opponents has passed on. The same score rewards a move that leaves both ends the same, and a move that leaves a number few unseen tiles still carry. Medium does none of this; it looks only at its own hand. Over 6,000 simulated hands, Hard beat Medium 54.6% of the time, with an uncertainty of about 0.6% either way.

You can test it. Choose Hard below the table, play until you have to pass, and note the two numbers showing. Then watch how often the computer seats bring the ends back to those numbers. Hard has one weakness you can use against it: it pools every opponent’s passes into a single list and does not check which seat plays next, so it will sometimes steer an end to a number you passed on when the seat that actually plays next holds plenty of them. A table kept per seat, as above, is finer than the one the computer keeps.