Play Threes Online

What Is Threes?

Threes, also called Threes Away and occasionally Tripps, is a five-dice game in which the lowest total wins and every 3 counts as zero. You roll five dice, set aside at least one, roll the rest, set aside at least one more, and so on until all five are set aside, which takes at most five throws. Your score is the total of the dice you kept, with 3s worth nothing.

That inversion changes everything about how a dice game feels. In Yahtzee, Farkle and Going to Boston you hope for big numbers; here a 6 is a disaster and a 1 is merely acceptable. And unlike its luck-only cousins Drop Dead and Stuck in the Mud, Threes gives you a real decision on every throw: which dice to keep and which to gamble on. Keep too much and you lock in a bad score; keep too little and you run out of throws with a 5 and a 6 still on the table. The best play turns out to be precise, a little counterintuitive, and entirely learnable, which is what makes the game worth a page.

A Short History of Threes

Threes belongs to the family of American bar dice games: fast games for a cup and five dice, played for the next round of drinks or a small pot. The rules site dice-play.com describes it as “a popular street game played makeshift in alleyways or living rooms” and gives the betting format in full: everyone antes a unit, the low score takes the pot, ties re-ante and play again, and the winner rolls first next game. Bar-game sites say plainly that it “started as a bar game,” and the alternative name Tripps has the sound of that world.

Beyond that, the trail goes cold. We could not find Threes in R. F. Foster’s Complete Hoyle (1922) or in John Scarne’s Scarne on Dice (1945), the two reference works that document most early-twentieth-century American dice games, and no source names an inventor, a city or a decade. The most honest statement is that Threes is a twentieth-century American folk game of uncertain age that spread through bars, then into family game collections, and then, because its rules fit on an index card and it teaches addition with a twist, into classrooms. Modern parenting sites list it as suitable for “ages 4 to 104” and as “a fun way to practice beginning math skills.” The alternate spelling Threes Away seems to be the family-friendly name and Threes the bar name, but both refer to the same game.

One point on which sources differ is whether a player must keep every 3 rolled. Some family rule sheets say so; the bar rules simply require at least one die to be set aside. Since keeping a 3 is always correct, the distinction never affects the score, and this guide treats it as a matter of etiquette.

Threes Rules

Equipment

• Five six-sided dice
• Pen and paper if you play more than one round
• Two or more players; a dice cup is traditional in the bar version

Object

Finish with the lowest total. On Dice.now you and the computer each take one turn per round for three rounds, and the lower three-round total wins the match. Bar play is usually one turn each for the pot.

How a Turn Works

1. Roll all five dice.
2. Set aside at least one die. You may set aside as many as you like, but never none. Dice set aside are locked for the rest of the turn.
3. Roll the remaining dice and again set aside at least one.
4. Repeat until all five dice are set aside. Because you must keep at least one die per throw, a turn lasts at most five throws.
5. Score. Add up the five dice you kept. Every 3 counts as 0; every other face counts its pips. Lowest score wins.

Scoring Table

Winning

Lowest total wins the round or the pot. In the betting game tied low scorers each add another unit to the pot and play again. In our three-round match, the totals are added and a tied match is a draw.

Worked Examples

Each example shows the throw, the correct keep, and the reasoning. “Expected cost” figures come from the exact analysis in the next section.

• Throw 1: 3-1-4-3-6. Keep both 3s (0 points). Do not keep the 1: with three dice still to roll, a 1 costs 1 point now, while an extra die re-rolled is expected to cost only 0.85 points. Roll three dice. Throw 2: 2-4-6. No 3. Keep the lowest die, the 2. Roll two. Throw 3: 3-5. Keep the 3, roll the 5. Throw 4: 1. Keep it, turn over. Score 0 + 0 + 2 + 0 + 1 = 3. A good turn.
• Throw 1: 1-1-4-5-6. No 3. You must keep something; keep one 1 (expected final score 6.83). Keeping both 1s is slightly worse (7.23), because the second 1 costs a full point while an extra die is worth only 0.6. Roll four.
• Throw 1: 1-1-1-1-3. Keep everything, score 4. Re-rolling any of the 1s can only make the total worse or equal: rolling one die costs 3 points on average against the 1 you would give up. This is the “cheap hand” exception to the usual rule of re-rolling 1s early.
• Throw 1: 4-5-6-6-6. Ugly. Keep the 4 (you must keep one, and it is the cheapest) and roll four dice. Expected final score about 9.8. Under the shooting-the-moon rule five 6s would have won outright; this hand is one 4 short of glory.
• Two dice left: 2-6. Keep the 2, roll the 6. Keeping both scores 8; keeping the 2 and rolling one die costs 2 + 3 = 5 on average.
• Two dice left: 1-4. Keep the 1. With one die still to roll, the last die is expected to cost 3, so 1 + 3 = 4 beats 5.
• Three dice left: 1-2-2. Keep all three for 5. Re-rolling one 2 would cost 1 + 2 + 3 = 6 on average; re-rolling both 2s would cost 1 + 4.39 = 5.39. Keeping everything is best by a small margin.
• Three dice left: 2-2-5. Keep one 2 only (expected 6.39). Keeping both 2s scores 4 + 3 = 7 on average.

The Odds

Finding a 3

The chance of at least one 3 among n dice is 1 − (5/6)ⁿ:

Five 3s on a single throw is 1 in 7,776 (0.013 percent); so is five 6s.

The value of a die still to roll

The key to Threes is to know what a die that has not yet been set aside is worth, in expected points, if you play the rest of the turn perfectly. We computed this exactly by enumerating every possible throw for one to five dice and, for each, choosing the number of lowest dice to keep that minimizes the total. Call the result V(n), the expected final score of n dice still in play:

Two things follow immediately:

• A turn played perfectly averages 6.25 points, and three rounds average about 18.8.
• The marginal cost of leaving one more die unkept falls as you have more dice. With five dice, an extra die in the cup will add only 0.42 points on average; the last lone die adds 3.00. That is why you should re-roll a 1 early (it costs 1, more than 0.42 or 0.60) but keep it late (when the alternative costs 1.39 or 3.00).

How much strategy is worth

Simulating 400,000 turns for each policy:

The simple threshold rule gets within 0.13 points of perfect play, and the only thing it misses is the cheap-hand exception described below. Note that “keep 3s only” produces more perfect zeros than optimal play: it re-rolls more dice, which raises variance, and in a one-turn pot game against several opponents that can be exactly what you want.

Threes Strategy

1. Always keep every 3

A 3 costs nothing now and can never be improved by re-rolling. There is no exception. The computer keeps all its 3s and the rule of etiquette in many families is that you must.

2. Early in the turn, keep nothing but 3s

With four or five dice still to roll, an unkept die will add only 0.42 to 0.60 points on average. A 1 costs a full point, so re-roll it. If a throw has no 3 at all, set aside your single lowest die because you must keep something, and re-roll everything else.

3. Start keeping 1s when two dice remain

With two dice in the cup, an extra die costs 1.39 on average, so a 1 (cost 1) is now a bargain. With one die left, the last die costs 3.00, so keep a 1 or a 2 rather than roll it.

4. Keep a 2 only as the last die, or in a cheap hand

Two points is more than the 1.39 an extra die costs with two dice left, so a 2 is re-rolled until only one die remains. The exception is when the dice you would re-roll are collectively cheap: 1-2-2 with three dice left is kept whole (5 points) because re-rolling either 2 is expected to cost more than 2.

5. Watch for the cheap-hand exception

The threshold rules above compare one die at a time. Occasionally a whole hand is worth keeping even though no single die passes the test: 1-1-1-1-3 scores 4 if kept, while keeping the 3 and re-rolling four dice is expected to score 5.83. Ask yourself, “if I stop now, what do I score, and is that below the expected result of rolling on?” If your kept dice plus the V value of the rest is higher than the total of what is on the table, keep it all.

6. Play the situation in the last round

Expected value is the right guide when a round is one of several. In the final round of a match, play to the score you need. If you trail by 8 and the computer has finished, a “safe” 6 loses just as surely as a 12; re-roll more aggressively than the tables suggest, chasing 3s, because only a very low score helps. If you lead comfortably, keep 1s and 2s earlier than usual to avoid a blow-up.

7. In a pot with many players, raise your variance

Against five opponents the winning score is usually 3 or lower, so an average 6 is worthless. Re-roll 1s longer, keep only 3s, and accept more bad turns in exchange for more perfect ones. The “keep 3s only” policy scores worse on average but produces twice as many zeros.

8. Use the game to teach the value of waiting

Threes is a clean way to show children (or adults) why a small certain cost is sometimes worse than an uncertain one. A 1 in hand looks safe; the table shows that with four dice to roll it is worth giving up. Have players guess, then check against the V table.

Common Mistakes

• Keeping 1s on the first throw. The most common error. A 1 costs 1; an extra die in the cup costs 0.42. Re-roll it.
• Re-rolling a 3. Never. It is worth zero and cannot get better.
• Keeping too many low dice “to be safe.” Safety in Threes means locking in points. With five dice, the safe play scores about 15; the correct play scores about 6.
• Forgetting the keep-one rule. You cannot re-roll all your dice. Keep the lowest one if nothing else appeals.
• Counting 3s as 3. Easy to do when adding quickly. Our game writes each kept 3 as “3→0” in the running total.
• Keeping a 2 with three or four dice left. It costs 2; the alternative costs under 0.85. Roll it.
• Treating the last die as a free roll. A lone die is expected to cost 3 points. If you already hold a 1 or a 2 in your hand, keep it.

Variants and House Rules

• Shooting the moon. Five 6s, the worst possible throw, wins the pot outright. Rare (1 in 7,776 on the first throw) but beloved in bar play. We do not use it.
• Mandatory 3s. Every 3 rolled must be set aside. It changes nothing about correct play but removes the temptation to bluff in a betting game.
• Threes Away High. The same turn structure, but the highest total wins; 3s still count zero and must still be kept, which makes them a penalty rather than a prize. Correct play flips: keep 6s and 5s early, and re-roll low dice.
• Pot play. Everyone antes a unit; low score takes the pot; tied low scorers re-ante and play again; the winner rolls first next game.
• Fixed number of rounds. Family play usually agrees three, five or ten rounds, or a time limit, and adds the totals.
• Fours or Ones. The same game with a different zero face. Making 1 the zero face is much gentler (the lowest face is already free); making 6 the zero face is much swingier.
• Chicago-style rounds. Some groups play Threes as a running series in which each round’s loser pays the winner the difference in points.

If you like choosing what to keep against a clock of throws, Yahtzee and Ship Captain Crew offer the same three-throw rhythm with high scores as the goal; Pig reduces the decision to a single question; and Drop Dead removes the decision entirely so you can see how much of Threes was luck.

Glossary

• Set aside / keep: Lock a die for the rest of the turn. At least one per throw is compulsory.
• Threes away: The game’s family-friendly name; also the cry when a player keeps a 3.
• Zero face: The face that counts nothing, a 3 in the standard game.
• Perfect turn: Five 3s, scoring 0.
• Shooting the moon: House rule making five 6s an instant win.
• Cheap hand: A throw whose total, if kept whole, is below the expected result of rolling on.
• V(n): The expected points that n dice still to be rolled will add under best play (3.00, 4.39, 5.23, 5.83, 6.25).
• Marginal cost: The expected extra points from leaving one more die unkept, from 0.42 (five dice) to 3.00 (one die).
• Pot: The pool of antes taken by the low scorer in the betting game.

Play Threes Online on Dice.now

The game at the top of this page is Threes against the computer over three rounds, lowest total wins. Press Roll to throw five dice, then tap the dice you want to set aside; the button changes to show what you are about to do (“Keep 2, roll 3” or “Keep 1 and finish”), and it stays disabled until you have chosen at least one die, so the keep-one rule enforces itself. Dice you have set aside turn green and are locked; the running total beneath the dice writes out every kept die with 3s shown as “3→0,” and the cards above the dice show your total and how many throws you have used out of five. Keep all ends the turn with everything on the table when you are happy with a cheap hand.

The computer plays in full view with the exact optimal policy from the tables above: it always keeps 3s, keeps 1s when two or fewer dice remain, keeps a 2 only as its last die, and recognizes cheap hands. Its choices are written to the log throw by throw, so you can compare them with your own. After three rounds the lower total wins, the result appears with your lowest single round and your win-loss record (stored on your device only), and you can play again. Roll the dice.