In pubs, Fives and Threes is commonly played by four people in two partnerships. Partners sit opposite each other, the two partners' scores are added together, and the first partnership to reach the target wins. The scoring of each play is unchanged: when the two open ends total a multiple of three or five, you score the total divided by three, by five, or both. What changes is who holds the tiles and what you can work out from the way others play. House rules vary, so treat this as the usual pattern rather than the only one.
This post describes the table game. The Play listing for Fives and Threes Dominoes describes solo play against a computer opponent, so nothing below is a description of an app feature.
The deal and the table
Each of the four players takes 7 tiles from a double-six set. That is 4 × 7 = 28, and a double-six set has exactly 28 tiles, so every tile is dealt and there is no boneyard. A player who cannot match an end cannot draw; they pass. Compare the two-player game, where the same 7-tile hands leave 14 tiles in the boneyard (see drawing from the boneyard).
The number of ways to deal 28 distinct tiles into four hands of 7 is 28! ÷ (7!)4, which is 472,518,347,558,400. You see 7 tiles; the other 21 are split evenly among three players.
Turns in a hand
Because the partnerships alternate, you play, then an opponent, then your partner, then the other opponent. If every tile is played, each player makes 7 plays and the hand lasts 28 plays, 14 by each partnership. A hand that ends with someone going out, or with a block, is shorter. A block happens when no one can play to either end; with no boneyard, that can happen while tiles remain in hands.
The shared target makes the arithmetic different from the solo game. To reach 61 in a single 28-play hand a partnership would need 61 ÷ 14 ≈ 4.4 points on each of its 14 plays, which is far above what most plays score, so a match takes several hands. The origin of the 61 target is covered in playing to 61.
What you know about your partner
The 21 tiles you cannot see are shared equally, 7 each, among your partner and the two opponents. The count of a number is fixed: every number from blank to six is printed on 7 tiles. If you hold k of them, 7 − k are out there, and your partner holds on average one third of those, which is (7 − k) ÷ 3 tiles. With four of a number in your hand, the remaining three are split on average one each.
The chance that your partner holds none of the remaining tiles of a number is C(21 − (7−k), 7) ÷ C(21, 7). With k = 4, so 3 tiles outside, that is 27.4%; with k = 3 it is 16.7%; with k = 5 it is 43.3%. The same figures apply to either opponent individually. Together the two opponents hold 14 of the 21 tiles, so with 3 outside (k = 4) at least one opponent holds one in 97.4% of deals.
Setting up your partner
The only legal communication is the play itself, and talking about hands is not allowed in the usual pub game. That makes each play a small piece of information, and a few habits follow.
- A pass tells everyone something. A player who passes holds no tile of either end's number. With no boneyard to draw from, a pass is exact information and the whole table sees it. If your partner passes on a 4, you know none of the other tiles of 4 are in their hand, so they sit with the opponents or with you.
- Leave a total your partner can score on. The opponent on your left plays between you and your partner, so you change one end and cannot control what they do before your partner answers. Leaving an end on a number the opponents have just passed on keeps their answers away, the same idea as in blocking.
- Return your partner's number. If your partner keeps playing to one number, it may be their long suit (see long suits). Leaving that number on an end gives them a play, though it also gives the opponents the chance that they hold it too.
- Think about the score, not just your own. A 15 total made by your partner's play and a 15 made by yours are worth the same to the shared score, so give up a small score if it leaves your partner a larger one, and do not leave an opponent a total they can turn into 8 points.
Blocking for the partnership
The block matters more than in the solo game. When the table is blocked the hand ends, and the usual pub practice is to count the tiles left in hands. The details of that count vary from pub to pub, so agree it before the first hand. What does not vary is the principle: if your partnership is ahead on the board, ending a hand sooner favours you, and the reverse if you are behind.
A number is dead when all 7 tiles of it are on the table and visible, and counting spots is how you see that coming; counting tiles sets out the method. In a four-player hand the count is a shared job: your partner is counting the same numbers, so a play that closes off a number for the opponents closes it for your side only if you still have a tile elsewhere.
The scoring rules themselves are the same as in the two-player game, which scoring explained walks through with worked totals.
Fives and Threes Dominoes is played solo against a computer opponent on Casual or Competitive, to a target of 61, 121, 181 or 241 points, with 6, 7, 8 or 9 tiles per player. The scoring and the counting in this post carry over to that game. There are no adverts or in-app purchases, and optional match points are in-game only with no cash value.