Most dominoes games pay something to the player who goes out first, and most of them work it out from the spots still in the loser's hand. That makes a high-spot tile a liability you carry until you play it. This post counts the heavy tiles in a double-six set, shows what a stuck hand can cost under one common convention, and sets that against what the same tiles can score on the line.
Which tiles are heavy
A double-six set has 28 tiles and 168 spots, an average of 6 per tile, as the double-six set post counts. Call a tile heavy if it carries 9 or more spots. There are exactly six: the 6-6 (12), the 5-6 (11), the 4-6 and 5-5 (10 each), and the 3-6 and 4-5 (9 each). Together they hold 12 + 11 + 10 + 10 + 9 + 9 = 61 spots, which is 36.3% of the set's 168 on 21.4% of its tiles.
Lower the bar to 8 and three more tiles join (the 2-6, 3-5 and 4-4), giving nine tiles and 85 spots, just over half of all the spots in the set. The weight of a hand therefore depends mostly on whether it holds a few of these tiles, not on how many tiles it has.
How many you will be dealt
Dealing n tiles from 28 means the expected number of heavy tiles is 6n ÷ 28. For 7 tiles that is 1.5, and for 9 tiles it is 1.9. The chance of a 7-tile hand holding none of the six is 14.4%, so 85.6% of hands start with at least one. At 9 tiles the chance of none is 7.2%. Hand size is covered in what hand size changes; the point here is that a heavy tile in your first hand is the normal case, not bad luck.
What a stuck hand costs
Rules vary from table to table, so this is one convention, not the only one. In a common pub version, when a player goes out, they score the spots left in the opponent's hand. Some tables round that total to the nearest five, and some count only a share of it. The Play listing for the app says only that you can switch the going-out bonus on or off. It does not say how the bonus is counted, so nothing below describes the app.
Under the plain-sum convention, take two stranded hands of three tiles. A hand of 6-6, 5-6 and 4-6 leaves 12 + 11 + 10 = 33 spots behind. A hand of 0-0, 0-1 and 0-2 leaves 0 + 1 + 2 = 3. Rounded to the nearest five, those become 35 and 5. The gap between them is 30 spots, and it comes entirely from which three tiles were left. By comparison, a normal play in Fives and Threes scores the end total divided by three or five, so a 30-spot gap is large next to most single plays.
What heavy tiles are worth on the line
Heavy tiles are not only a burden, because big end totals are where the large scores sit. A double at an open end counts both its halves, so a 6-6 laid on a 6 shows 12 at that end. Against a plain end of 0 the total is 12, which scores 12 ÷ 3 = 4. Against a 3 it is 15, which scores 5 + 3 = 8. Against a 6 it is 18, which scores 6. The post on 15 shows why that middle result is the best total in the game.
The catch is flexibility. A tile with two different numbers fits two kinds of end, and a double fits only one. The 6-6 can be played only on a 6, while the 5-6 can go on a 5 or a 6. A heavy double that is hard to place is the tile most likely to be stuck in your hand at the end.
A rule of thumb
These are guidelines drawn from the counts above, not proven strategy.
- Equal scores, play the heavier tile. If two plays score the same, the heavier tile is the one you least want left over. Playing it costs nothing and cuts what you could lose.
- Hard-to-place heavy doubles go early. The 6-6 and 5-5 each fit only one number. If a matching end is open and the play scores, take it before the end moves.
- Hold a heavy tile when it sets up a big total. If the 5-6 would turn a 4 into 15 next turn, waiting for it can be worth more than an immediate small score. The risk is that your opponent changes the end first.
- Hold less as the hand shrinks. Early on the boneyard gives you a way out, and the risk of being caught is small. When the boneyard is empty and tiles are few, the tiles you still hold are the ones you pay for. See drawing from the boneyard for how that stage works.
A higher target softens the penalty, because one hand matters less when the match is long, while a short target makes a single big going-out score decisive. The app offers targets of 61, 121, 181 and 241 points, so the same tile can be right to hold in one match and wrong to hold in another. You can try that choice yourself in Fives and Threes Dominoes.
Counting what is left
The heavy tiles also give you information. Six tiles hold 61 spots, so if you have seen four of them played or in your own hand, the opponent can hold at most two. Tracking the six is far easier than tracking all 28, and it tells you roughly how much weight the other hand could be carrying. That is the same method as in counting tiles, applied to the part of the set that matters most for the going-out score.
Fives and Threes Dominoes scores by threes and fives, adds both when both apply, and counts a double at an open end by both its spots. You play solo against a computer opponent on Casual or Competitive, with 6, 7, 8 or 9 tiles each and a target of 61, 121, 181 or 241 points, and you can switch the going-out bonus on or off. There are no adverts or in-app purchases, and optional match points are in-game only with no cash value.