Score four of a kind in the upper box of its number first (four 5s go in Fives), then in 4 of a kind, then in 3 of a kind. That simple order is almost perfect: with every other decision made perfectly, it costs only 0.14 points a game against an exact solver. By contrast, always putting four of a kind in the 4 of a kind box costs 5.42 points a game, and using 3 of a kind for them costs 11.53. The only time to break the order is when the upper bonus is nearly decided.
The same idea covers three of a kind: it's par for the upper section, so it usually belongs in the upper box too. Yahtzee is a Hasbro trademark; Poozee isn't affiliated with Hasbro, and our version of the game is called Yacht Dice.
How we measured
Every number here comes from the exact solver behind our Yahtzee strategy guide. It knows the best play from every scorecard situation under the standard American rules, and averages 254.59 points a game. We followed the exact probability of every roll, hold and scorecard through all 13 turns, and for every turn that ends on four of a kind, three of a kind or a full house, we recorded which box perfect play picks and what the upper box, 3 of a kind, 4 of a kind, Full house and Chance would each have been worth. "Four of a kind" here means exactly four; five of a kind has its own rules.
To price a habit, we gave a perfect player one fixed rule for where the dice go and kept everything else perfect, including which dice it holds. The drop in its exact average score is what the habit costs.
Perfect play ends 2.37 turns a game on exactly four of a kind, 18.2% of all turns, so this choice comes up about twice a game. It ends a turn on exactly three of a kind (with two different odd dice) 3.35 times a game, and a full house 1.43 times. As a check, we also played 2,000 games of perfect play with seeded dice through the game's own rules: 4,650 turns ended on exactly four of a kind, 2.33 a game.
Where perfect play scores four of a kind
Here's where perfect play puts each four of a kind. "Per 100 games" is how many turns end on it in 100 games, and "Other" covers Chance and every other box.
| Four of a kind | Per 100 games | Upper box | 4 of a kind | 3 of a kind | Other |
|---|---|---|---|---|---|
| 1s | 19.1 | 67% | 23% | 1% | 9% |
| 2s | 29.8 | 71% | 21% | 2% | 6% |
| 3s | 35.6 | 69% | 23% | 3% | 5% |
| 4s | 43.1 | 65% | 26% | 5% | 5% |
| 5s | 50.6 | 60% | 29% | 6% | 5% |
| 6s | 58.4 | 58% | 30% | 7% | 5% |
The 4 of a kind column is mostly four of a kinds that arrive after their upper box is already filled. When the matching upper box is open, perfect play puts four of a kind there 97.2% of the time, for 1s as much as for 6s, and the upper box is still open for 66% of the four of a kinds perfect play rolls.
The rule, step by step
- The upper box of its number. Four of a kind is one better than par, three of each number, so it puts you ahead in the race for the 35-point upper bonus. When both are open, 4 of a kind instead of the upper box costs 6.66 points on average.
- Then 4 of a kind. Once the upper box is filled, perfect play uses 4 of a kind 99.9% of the time it's open. 3 of a kind would score exactly the same today, but it's far easier to fill later: any three of a kind will do. Leave 4 of a kind open instead and it often ends the game as a zero. With the upper box filled, 3 of a kind instead of 4 of a kind costs 9.32 points on average.
- Then 3 of a kind. With 4 of a kind filled too, 3 of a kind gets them 95% of the time.
- Then Chance, or a dump. With all three boxes filled, perfect play uses Chance 73% of the time it's open.
Pro tip: Before you score four of a kind, look at the upper box first, not the lower section. Four 3s in Threes (12 points) usually beats the same dice in 4 of a kind, even though 4 of a kind pays more today.
What the wrong habits cost
Here's each habit's exact average with perfect play everywhere else:
| Where four of a kind goes | Average score | Points lost per game |
|---|---|---|
| Perfect play | 254.59 | - |
| Upper box, then 4 of a kind, then 3 of a kind | 254.45 | 0.14 |
| 4 of a kind first for 4s, 5s and 6s | 250.12 | 4.47 |
| 4 of a kind first | 249.17 | 5.42 |
| 3 of a kind first | 243.05 | 11.53 |
The rule costs only 0.14 points a game. Grabbing the bigger number does real damage: always putting four of a kind in the 4 of a kind box costs 5.42 points a game. Playing low four of a kinds perfectly but sending 4s, 5s and 6s to 4 of a kind first still costs 4.47 points a game, because high four of a kinds are exactly what the upper bonus runs on. And using 3 of a kind for them costs 11.53, more than twice as much, since it wastes the easy box and leaves the hard one open.
Early or late, ahead or behind
The choice that matters most is the first one: upper box or 4 of a kind, when both are open. Here's how often perfect play faces that choice in 100 games, how often it takes the upper box, and what 4 of a kind would cost instead, on average:
| Turn | Per 100 games | Upper box | Points lost by 4 of a kind instead |
|---|---|---|---|
| Turns 1‑4 | 74.1 | 99.8% | 6.24 |
| Turns 5‑9 | 48.5 | 94.4% | 7.08 |
| Turns 10‑13 | 7.1 | 79.8% | 8.21 |
Late in the game, perfect play takes 4 of a kind more often, but the upper box still wins four times in five, and the average cost of getting it wrong only grows.
What really changes the answer is the upper bonus. Par is three of each number in the upper boxes you've filled, so with 24 in Sixes and 15 in Fives, par is 33 and you're 6 ahead. A dash means perfect play reaches that spot in fewer than 1 game in 1,000.
| Upper section | Per 100 games | 1s, 2s, 3s in the upper box | 4s, 5s, 6s in the upper box |
|---|---|---|---|
| Within 6 points of par | 119.8 | 99% | 99% |
| 7 or more ahead of par | 7.5 | 93% | 59% |
| 7 or more behind par | 1.3 | 73% | 21% |
| Bonus already earned | 0.8 | 65% | - |
| Bonus out of reach | 0.3 | 32% | 0% |
92% of these decisions come within 6 points of par, and there the upper box wins for low and high numbers alike. Only when the bonus is nearly decided, either nearly safe or nearly gone, do high four of a kinds start going to 4 of a kind for the points. Low ones mostly stay up top unless the bonus is out of reach, since four 1s or 2s score so little in 4 of a kind.
The Yahtzee box barely matters: perfect play takes the upper box 97.3% while the Yahtzee box is open and 93.9% once it's filled.
Three worked positions
In each table, "points lost" is how much the box lowers your expected final score compared with the best box, with perfect play afterward either way.
First turn: 2‑2‑2‑2‑6
The tempting play is 4 of a kind for 14 points instead of 8 in Twos.
| Box | Points lost |
|---|---|
| Twos: 8 | Best |
| 4 of a kind: 14 | 3.73 |
| 3 of a kind: 14 | 13.31 |
| Chance: 14 | 19.31 |
Twos wins with an expected final score of 253.27. Four 2s put you 2 points ahead of par in a box that averages under par, and 4 of a kind stays open for a bigger four of a kind later.
Turn 5, Sixes already filled: 6‑6‑6‑6‑5
Fives holds 15 and Sixes 18, exactly par, and Small straight and Full house are filled. Every lower box that takes these dice pays the same 29 points.
| Box | Points lost |
|---|---|
| 4 of a kind: 29 | Best |
| 3 of a kind: 29 | 10.12 |
| Chance: 29 | 14.68 |
Same points today, very different futures. 3 of a kind and Chance are easy to fill well later; 4 of a kind isn't.
Turn 6, 11 points ahead of par
Fives holds 20 and Sixes 24: 44 points against a par of 33. Small straight, Large straight and Full house are filled. Here's the break from the rule:
| Final roll | Perfect play | Other box | Points lost |
|---|---|---|---|
| 4‑4‑4‑4‑6 | 4 of a kind: 22 | Fours: 16 | 1.84 |
| 3‑3‑3‑3‑6 | Threes: 12 | 4 of a kind: 18 | 0.52 |
You need only 19 more points from Ones to Fours, where par is 30, so four 4s are worth more as 22 points in 4 of a kind. Four 3s still go up top. Both are close calls, which is why the plain rule loses so little over a whole game.
Three of a kind and full houses
Three of a kind is exactly par, so it belongs in the upper box too. Here's where perfect play scores exactly three of a kind (with two different odd dice) when the upper box and 3 of a kind are both open:
| Three of a kind | Per 100 games | Upper box | 3 of a kind |
|---|---|---|---|
| 1s | 8.3 | 100% | 0% |
| 2s | 18.6 | 100% | 0% |
| 3s | 23.6 | 100% | 0% |
| 4s | 31.0 | 99% | 1% |
| 5s | 36.9 | 90% | 10% |
| 6s | 43.0 | 69% | 31% |
The exception is a big total of 6s (and, less often, of 5s). With three 6s totaling 25 or more in the first four turns, perfect play takes 3 of a kind 80% of the time: 6‑6‑6‑5‑4 on the first turn is worth 2.43 points more in 3 of a kind (27 points) than in Sixes (18). Here's what each habit for three of a kind costs:
| Habit for three of a kind | Points lost per game |
|---|---|
| 3 of a kind first | 3.88 |
| Upper box first | 0.31 |
| Upper box first, but 3 of a kind for 25 or more in turns 1‑4 | 0.21 |
Full houses are simpler: perfect play scores a full house in the Full house box 98.0% of the time that box is open, and always scoring it there costs 0.05 points a game. When both are open, 3 of a kind instead of Full house costs 11.18 points on average. The only full house perfect play ever moves to 3 of a kind is 6‑6‑6‑5‑5, the biggest one: 28 points there against 25 in Full house.
Practice with the hint
In Yacht Dice, press Hint after your last roll and the game highlights the box the perfect solver would use, so you can test the rule on your own four of a kinds. For the full picture of chasing par, see our upper bonus guide, and for how boxes like 4 of a kind score, our Yahtzee rules guide.
Keep playing
- Play Yacht Dice and put the upper-box-first rule to work
- How to get the Yahtzee bonus: par, your odds and when to give up
- Yahtzee strategy: which dice to hold and where to dump a bad roll
- What is a good Yahtzee score? Exact percentiles from perfect play
Frequently asked questions
Where should I score four of a kind in Yahtzee?
In the upper box of its number if that box is open (four 5s in Fives), then in 4 of a kind, then in 3 of a kind. That order costs only 0.14 points a game compared with perfect play.
Should I score four of a kind as 3 of a kind?
Not while the 4 of a kind box is open. With the upper box filled, putting four of a kind in 3 of a kind instead of 4 of a kind costs 9.32 points on average, because 3 of a kind is far easier to fill later.
Is it a waste to put four 1s or four 2s in the upper section?
No. On the first turn, 2‑2‑2‑2‑6 is worth 3.73 points more in Twos (8 points) than in 4 of a kind (14 points). Four 2s put you ahead of par for the upper bonus and keep 4 of a kind open for bigger dice.
When should you use 4 of a kind instead of the upper box?
Only when the upper bonus is nearly decided. Within 6 points of par, perfect play uses the upper box 99% of the time; 7 or more points ahead, it puts four 4s, 5s or 6s in the upper box only 59% of the time.