Pub dominoes has a family of scoring games that all work the same way: lay a tile, add up the two open ends, and score if the sum is right. The best known is All Fives, also called Muggins. Fives and Threes adds a second test. This post sets the two systems side by side, total by total.
The two rules
All Fives scores when the ends add up to a multiple of five: 5, 10, 15 or 20. Versions differ on the pay. Some award the whole total, so a 10 scores 10. Others count the fives in it, so a 10 scores 2. This post uses the second convention, because it is the one that compares directly with Fives and Threes: a total of 5 scores 1, 10 scores 2, 15 scores 3 and 20 scores 4.
Fives and Threes scores when the total divides by three, by five, or by both. A multiple of three scores the total divided by three. A multiple of five scores the total divided by five. When both apply, the two scores are added, so a total of 15 scores 5 + 3 = 8.
In both systems here a double at an open end counts both its halves, so a double-four at an end shows 8. Spinners, which open a line in four directions in some pub rules, are left out; every total below comes from the two ends of a single line.
Total by total
With a standard double-six set, the lowest total is 0 and the highest is 22, the double-six at 12 against the double-five at 10. Between 3 and 20 there are nine totals that score in Fives and Threes, covered in full in every scoring end total, 3 to 20. Four of them also score in All Fives.
| Total | Fives and Threes | All Fives |
|---|---|---|
| 3 | 1 | 0 |
| 5 | 1 | 1 |
| 6 | 2 | 0 |
| 9 | 3 | 0 |
| 10 | 2 | 2 |
| 12 | 4 | 0 |
| 15 | 8 | 3 |
| 18 | 6 | 0 |
| 20 | 4 | 4 |
What the table shows
Add the columns and the gap is clear. All Fives, in fives, pays 1 + 2 + 3 + 4 = 10 points across its four totals. Fives and Threes pays 1 + 1 + 2 + 3 + 2 + 4 + 8 + 6 + 4 = 31 across nine. Of the 21 points between them, 16 come from the five totals that All Fives ignores entirely (3, 6, 9, 12 and 18, worth 1 + 2 + 3 + 4 + 6) and 5 come from the 15.
That 15 is the one place where the two games disagree about a total both of them reward. Under All Fives it is three fives and scores 3, a tidy step between 10 and 20. Under Fives and Threes it is five threes and three fives at once, and the two scores stack to 8, which is why 15 is the best total in that game. The totals 5, 10 and 20 are unchanged, because none of them is a multiple of three.
How often a score is available
Points per total is only half the picture; it also matters how many combinations of ends make the total. Counting pairs of end faces, with plain ends of 0 to 6 and doubles of 0 to 12 in steps of two, there are 98 possible pairs, as in the scoring totals post. Multiples of five can be made by 6 + 9 + 2 + 1 = 18 of them (totals 5, 10, 15 and 20). Fives and Threes scores on 48, because the totals 3, 6, 9, 12 and 18 add 4 + 10 + 5 + 8 + 3 = 30 more.
These are counts of combinations, not chances in a game, since they ignore which tiles are still unplayed. They do show the effect: 48 of 98 pairs score in Fives and Threes, against 18 of 98 in All Fives.
Why the extra rule changes the play
In All Fives you build towards four totals, and a player who cannot make a five plays and scores nothing. In Fives and Threes a placement that misses the fives can still land on a three. The choices also get richer: a 12 scores 4 against 2 for a 10, so the larger multiple of five is not always the better total. Run the sum for every tile you hold before you play.
The scoring also changes defence. If a double-six is open, the ends 12 and 3 make 15 in either game, but only in Fives and Threes is the prize 8 points. A player holding the 3 gets 8 instead of 3, so a double left open is a larger gift. The same reasoning is behind blocking in Fives and Threes.
Which game is in the app
The Play listing for Fives and Threes Dominoes describes Fives and Threes only: if the ends total divides by three, score the total divided by three; if it divides by five, score the total divided by five; when both apply, add the two. It does not list All Fives as a mode, so this post compares the two systems on paper and makes no claim that the app can play both.
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. The table shows the open-end totals and the points scored after each move. You play solo against a computer opponent on Casual or Competitive, to a target of 61, 121, 181 or 241 points. There are no adverts or in-app purchases, and optional match points are in-game only with no cash value.