Yahtzee Strategy: What Perfect Play Does, With the Odds

The best Yahtzee strategy is to play for the 35-point upper bonus, don't jump at every straight draw early in a turn (with 3‑4‑5‑6‑6 on your first roll, hold the 6s), and dump bad rolls into a low upper box instead of Chance. A computer playing perfectly averages 254.59 points a game; a player who grabs the most points every turn averages 217.4. Playing for the upper bonus alone closes 15 points of that gap.

Every number below comes from an exact solver we built for Poozee's Yacht Dice, which plays by the same American scorecard rules. Here's how it works, what it does, and the odds of each scorecard pattern.

How we measured

A Yahtzee game is small enough to solve completely. At the start of any turn, all that matters is which boxes are filled, your upper-section total so far, and whether your Yahtzee box holds 50. That's 536,320 possible situations. Working backward from the last turn, the solver computes the best expected final score from each one, trying every way to hold dice on every roll. The strategy it finds is the best possible: no other way of playing averages more.

Under the official rules (including the forced joker rule, below), perfect play averages 254.59 points. Tom Verhoeff's Optimal Solitaire Yahtzee Player, a well-known reference, reports 254.5896 for a slightly looser joker rule that lets an extra Yahtzee go in any open box. Switched to that rule, our solver gives the same 254.5896.

Averages for other strategies are exact too: instead of simulating games, we followed the probability of every roll and every scorecard through all 13 turns.

"Stay on pace" means valuing the bonus while three of each remaining number would still reach 63. That one idea is worth 15 points a game. The last 22 points come from many smaller decisions, and the rest of this guide shows some of the biggest.

1. Play for the upper bonus

The bonus is 35 points for 63 or more in Ones through Sixes. 63 is exactly three of each number, so think of every upper box as "three of a kind, please." Four 6s or four 5s put you ahead of pace; two 6s put you behind.

Perfect play gets the bonus in 68.1% of games. Greedy play, which takes the most points each turn with no thought for later, gets it in only 3.2%.

Pro tip: Track your pace, not your total. After Sixes, Fives and Fours with three each, you have 45 and need only 18 from Ones, Twos and Threes.

2. Early in a turn, a high pair can beat a straight draw

These examples are the first roll of a game, with two rolls left. "Points lost" is how much the tempting hold lowers your average final score, assuming perfect play afterward either way.

The pattern in these rolls: a straight draw open at both ends (2‑3‑4‑5 becomes a large straight with a 1 or a 6) is worth holding. A draw that only one number completes (1‑2‑3‑4, or 3‑4‑5‑6 when you already have the small straight) is worth less than a pair of 4s or 6s headed for the upper section.

Two pairs? Keep only the higher pair: 6‑6 beats 5‑5‑6‑6 by almost 3 points, even though 5‑5‑6‑6 makes a full house 5 times in 9. And on the first turn, perfect play even breaks up a full house of 2s and 3s to go after the 3s.

With one roll left, the straight comes back

Fewer rolls change the math. Same first turn, but now after the second roll, with one roll to go:

With one roll left, a pair has only one chance to grow, while a small straight in hand is 30 points you keep either way. The two-pair decision is nearly a tie by then.

3. Dump bad rolls in a low upper box, not Chance

Sometimes the dice don't fit anything. On the first turn, here's where perfect play puts two junk rolls:

Taking 1 point instead of 17 looks backward, but Chance is your safety net for a bad turn later, and it averages 22.0 points under perfect play. Ones averages just 1.9, so giving it up early costs little.

4. Five of a kind: chase it, but don't count on it

Perfect play scores 50 in the Yahtzee box in 33.7% of games and scratches it (a zero) in the rest. It earns an extra 100-point bonus 0.096 times per game on average, about once every 10 games.

The boxes perfect play most often zeroes are the Yahtzee box (66.3% of games), 4 of a kind (36.4%) and the large straight (18.2%). The upper boxes are almost never zeroed, apart from Ones (10.8%).

Yahtzee odds

Odds for one roll count all 7,776 ways five dice can land. Odds for three rolls assume you hold the dice that give you the best chance of that pattern.

The five-of-a-kind chance, 4.60%, comes from holding your most common number each time. That's about once every 22 turns, so in a 13-turn game you should expect to chase it rather than plan on it.

The rules these numbers use

The standard American scorecard: 35 points for 63 or more in the upper section; 25 for a full house, 30 for a small straight, 40 for a large straight, 50 for five of a kind; three of a kind, four of a kind and Chance score the total of the dice. An extra five of a kind earns 100 points if the Yahtzee box holds 50, and it's a joker: it must go in the matching upper box if that's empty, otherwise in any empty lower box (where full house and straights score in full), otherwise as a zero in an upper box.

Practice with a perfect coach

Yacht Dice uses these rules. Its Hint button shows what the solver would hold or score, and the Hard computer plays the perfect strategy, so you can see the moves above in real games. Medium plays the "stay on pace" strategy from the table, and Easy takes the most points each turn. Yahtzee is a Hasbro trademark; Poozee isn't affiliated with Hasbro.

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