Block Dominoes Guide: Playing Well Against the Computer, and Against People

Seven tiles arrive, and before anyone plays you can tell most of what the hand will ask of you. Check three things, in order: which doubles you hold, which number you hold most of, and how heavy the hand is.

Start with the doubles. 6-6 is the highest double in the set, so if you hold it you open, and you must open with it. That is good news: you are not waiting on anyone, and the line begins with a 6 at each end. Your other double, 1-1, is the kind that gets stranded. It fits only a 1, and your only other 1 is on 3-1. Play 1-1 the first time a 1 shows rather than saving it.

Next, count each number. Threes are on three of your tiles (6-3, 4-3 and 3-1); sixes, ones and twos on two each; fours, fives and blanks on one each. Threes are the number you want on the ends, because you can answer them longest. So: open with 6-6, and on your next turn, if a 6 is still showing, play 6-3 to turn one end to a 3.

Finally, weight. The pips add to 43, close to the 42 an average seven-tile hand carries (168 pips across 28 tiles is 6 per tile, times 7). A blocked hand is decided on pips, so 43 is neither cushion nor burden. After 6-6 the heavy tiles are 6-3, 4-3 and 5-2. The 5-2 is the awkward one, your only 5 and one of two 2s; shed it the first time a 5 shows.

What to do with a bad hand

A bad hand has no double higher than somebody else's, no number on more than two tiles, and a pip total in the fifties. You cannot exchange tiles and nobody draws, so it is played as dealt. Stop trying to win it and try to lose it cheaply: the winner scores the pips left in your hand, so every heavy tile shed is points not given away, and when two plays are otherwise even, play the heavier. Over a session the deals even out, and the player who paid least for the bad hands is usually the one ahead.

The opponents are chosen below the table. Each level is a fixed procedure, not a personality, and the procedure tells you where it is weak.

Easy

Easy plays the first legal tile in its hand, in hand order. It does not prefer doubles or heavy tiles, and does not look at what its remaining tiles will still match.

Easy never protects itself, so you do not need to attack it; play the normal game. Easy holds a double until a matching number happens to show, and is often still sitting on 5-5 or 6-6 when a hand blocks, so a block against Easy is usually worth having. If you are losing to Easy, the fault is almost always hoarding: you kept a big tile for later, and later never came.

Medium

Medium scores every legal move and plays the highest. A double is worth +12. Each pip on the tile is worth +1.5, so 6-4 scores 15 for weight alone. Every tile still in hand that matches an open end after the move is worth +2, which rewards flexibility. That is the whole procedure; it never looks at earlier turns.

So Medium never uses your passes. Against Hard, or a person paying attention, a pass is a permanent admission that you hold neither end number, and it is used against you for the rest of the hand. Against Medium a pass costs only the turn, so do not contort your hand to avoid one. Medium is also predictable. Because a double starts at +12, 2-2 (12 + 6 = 18) outranks 6-5 (16.5) unless the flexibility bonus tips it, so with a double available Medium nearly always plays it, and of two heavy plays it takes the heavier.

Hard

Hard runs Medium's scoring and adds three bonuses: +14 if the move leaves both ends showing the same number, so it likes to close the line; a bonus that rises as fewer unseen tiles carry the number it leaves on an end, so it prefers numbers that are running out; and +15 for every open end showing a number an opponent has passed on. The last one changes how you should play, because a pass proves you held neither end number at that moment, and since nobody draws, it stays true until you go out.

Against Hard, avoid passing early. A pass in the first few turns hands it a number it can steer the ends towards for the rest of the hand, and at +15 per end that outweighs everything else in its scoring, so it will. Prefer plays that leave both ends showing numbers you can still answer, even at the cost of holding a heavier tile a turn longer. When Hard closes the line, it spent a tile of that number to do it; count how many of that number are still unseen before deciding whether to answer or let the end sit. To keep pace, keep the same pass table Hard keeps; the article on reading opponents from their passes shows how.

Each level is measurably stronger than the one below. Over 6,000 simulated hands per matchup, Medium beat Easy 59.6% of the time, Hard beat Easy 63.2%, and Hard beat Medium 54.6% (each about plus or minus 0.6%). The steps are real, so move up deliberately. But they are not huge: Hard still loses more than a third of its hands to Easy, so a single hand says little. Judge yourself over twenty or thirty.

On Easy, count one number. Sixes are the usual choice. Seven tiles carry a six, and by mid-hand you should be able to say how many have been played, how many you hold, and so how many are still out. Move up when you can do that without losing track of your own hand and are winning more hands than any single opponent.

On Medium, count two numbers, the two on the open ends, and before every play say what both ends will show afterwards. Notice your own passes too: Medium does not punish them, so this is the safe place to learn how often you pass and why. Move up when you can hold both counts through a hand and are ahead on the running score after ten hands.

On Hard, keep a pass table: for each opponent, the two numbers showing when it passed. Before leaving a number on an end, ask who has passed on it and how many tiles of it are unseen. When that is routine you are doing everything Hard does with the same information, and the remaining difference is the deal.

The counting arithmetic is worked through in the mathematics of Block Dominoes, and the last-few-tiles decisions in the endgame article. Neither is repeated here.

The scoring is built for a session. The winner of each hand scores the pips left in every other hand, and totals accumulate through “Next hand” until you press New Game. There is no built-in target, so set one before you start, say 100, and play until someone crosses it.

Because the winner takes everyone's leftover pips, the size of a win depends on how heavy the losers are. Going out against three players holding 20 pips each is worth 60; the same win against three players holding 1-0 each is worth 3. The running score should change what you play for.

When you are behind, you need large hands, and large hands come from blocks: a blocked hand ends with everyone still holding tiles, so a block you win on pips pays from three full hands at once. Close the line when you can, keep your own hand light so you win the count, and accept the risk that someone goes out first. That risk is the price of a swing big enough to matter.

When you are ahead, the arithmetic reverses. The gap closes only through a hand you lose while heavy, so end hands quickly and cheaply: go out as soon as you can rather than waiting for a closing play, and shed the heavier tile whenever two plays are otherwise equal, so that a lost hand costs four points instead of twenty. A player 40 ahead who loses the next three hands at 5 points each is still 25 ahead.

A worked case. You trail 55 to 85, target 100. A quick win against light hands of 3, 4 and 2 pips scores 9 and leaves you at 64, still 21 behind, with the leader needing 15. A blocked hand won against hands of 11, 8 and 8 scores 27 and puts you at 82 against 85. The second is worth waiting for only if you are confident of winning the count.

The rules here are one variant, and other tables play others, so settle these before the first tile is turned: the target score; what happens when a blocked hand ties on pips (split the points, replay, or award it to the player who did not make the last play); whether the highest double opens every hand or the opener rotates; how many tiles each player takes (seven here, whatever the seat count, with the rest set aside); and who shuffles. The rules page gives this site's answer to each and is a reasonable default to hand round.

With people, a pass is still proof and still stays true, but people also play out of habit or hurry. Do not read too much into that: the only choices in this game are which tile and which end, so there is no bluff to see through, only the pass table and the count. Partnership variants exist elsewhere, and in any of them signalling to a partner by timing, gesture or remark is cheating. Nothing on this site teaches it.

One honest note. The computer is not a tournament-strength opponent. Every level weighs each move with a fixed list of bonuses and plays the best-scoring one for this turn only; none looks ahead, none works out which exact tiles you must still hold, and only Hard uses passes at all. A person who counts two numbers, keeps a pass table and thinks a turn ahead is already doing more than Hard does. Beating Hard consistently means you have the habits, not that you will beat a good table.