How to Win Yahtzee — the data
Yahtzee is a solved game. We computed the exact expected-value-optimal strategy with dynamic programming — and optimal play averages about 254 points (exactly 254.50 in our solve). Here's what the optimal policy actually does: which dice to keep, which categories to chase, and how to bank the upper-section bonus.
Expected points per category (optimal play)
Under the optimal policy, here's how many points each of the 13 categories contributes on average — measured by playing the exact optimal strategy. Upper section in teal, lower section in amber:
Takeaway: the lower section carries the score — Large Straight leads at about 34.7 points on average — but the upper section is where the +35 bonus is won. Optimal play banks that bonus roughly 68% of games.
The upper-section bonus: aim for three of each
The 35-point bonus triggers at 63 points in the upper section. That number isn't arbitrary — it's exactly three of every face (three 1s + three 2s + … + three 6s = 63). So "three of each on average" is the bonus pace to keep:
| Number | Three-of-a-kind value | Optimal avg |
|---|---|---|
| Ones | 3 | 4.2 |
| Twos | 6 | 9.5 |
| Threes | 9 | 14.2 |
| Fours | 12 | 17.8 |
| Fives | 15 | 21.0 |
| Sixes | 18 | 24.6 |
"Three-of-a-kind value" = points from exactly three of that face; the six of them sum to the 63-point bonus threshold. "Optimal avg" = average points the optimal policy actually banks in that box.
If you're ahead of the three-of-each pace early, the bonus is on track; if a number falls well behind (e.g. you can only muster one 6), the solver often cuts its losses there and protects the categories it can still hit. Optimal play earns the bonus about 68% of the time.
Best opening keeps
The single most important decision each turn is what to keep after the first roll. These are the exact EV-optimal keeps from our solver for several common opening rolls (with two rerolls still to come):
| Opening roll | Optimal keep | # kept |
|---|---|---|
| 1 2 3 4 6 | 1, 2, 3, 4 | 4 |
| 1 2 3 4 5 | 1, 2, 3, 4, 5 | 5 |
| 2 3 5 5 5 | 5, 5, 5 | 3 |
| 1 2 3 6 6 | 6, 6 | 2 |
| 1 1 1 1 4 | 1, 1, 1, 1 | 4 |
| 2 2 5 5 6 | 5, 5 | 2 |
| 6 6 6 6 6 | 6, 6, 6, 6, 6 | 5 |
| 1 2 2 4 5 | 2, 2 | 2 |
Keep what's already working, reroll the rest. The optimal policy holds pairs, trips and four-in-a-row sequences and throws back the dead dice — it almost never rerolls a strong made combination chasing something bigger.
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How we got these numbers
An EXACT optimal-strategy solver, not a heuristic or a sampled estimate of the strategy. We compute the value of every reachable game state — which of the 13 categories are still open, the upper-section progress toward the 63-point bonus (capped at 63), and whether the Yahtzee box has already scored 50 (making further Yahtzees worth a +100 bonus) — by backward induction. For each state we solve the three-roll turn exactly: from the final hand we pick the category that maximises immediate score plus the value of the resulting state, then roll the optimal keep/reroll decisions backwards through the second and first rerolls over the 252 dice multisets (with their multinomial weights, never the 7,776 ordered rolls). The empty-board value is the optimal expected final total, which comes out to ~254.6 — the well-known solved value, confirming the model. Reported bonus and Yahtzee frequencies come from forward-playing this exact optimal policy. Standard American scoring with the Yahtzee bonus and Joker rule. A guide to optimal expected value — not a guarantee on any single game, which still swings widely with the dice.
Validation: the exact optimal expected total computes to 254.50,
matching the well-known solved value of ≈ 254.6 (we accept 253-256). Reported
bonus/Yahtzee frequencies come from forward-playing the exact optimal policy for
60,000 games. Source code lives in our sims/ folder
(yahtzee_sim.py). See also the full Yahtzee entry.
Common questions
What is the best possible average score in Yahtzee?
With perfect, expected-value-optimal play the average final score is about 254 points (our solver computes 254.50, the famous solved value for standard American rules). That is the theoretical ceiling for long-run expected value — a single game still swings widely with the dice. The optimal strategy scores the 35-point upper-section bonus about 68% of the time and rolls at least one 50-point Yahtzee about 33% of the time.
Are the extra Yahtzee bonuses worth chasing?
They're huge when they come — each additional Yahtzee after the first is worth +100 points under the joker rule — but you can't plan around them. Optimal play rolls a second-or-later Yahtzee in only about 8% of games. The right approach is the one the solver takes: play for expected value every turn, and bank the +100 windfall on the rare occasions a second Yahtzee shows up rather than forcing it.
Should you always go for the upper-section bonus in Yahtzee?
Mostly yes. The bonus needs 63 points in the upper section, which is exactly three of each number (3×1 + 3×2 + … + 3×6 = 63). Optimal play earns the bonus around 68% of the time, so it is a central goal — but the solver will sacrifice it when a turn's dice make a big lower-section score (a Yahtzee, large straight, or full house) the higher-EV play.
What should you keep on your first Yahtzee roll?
It depends on the roll, and our solver gives the exact-EV keep for each. As a rule the optimal policy keeps toward your strongest developing combination — high pairs/trips for the bonus and four-of-a-kind/Yahtzee, or four-in-a-row for a straight — and rerolls low, unconnected dice. The table on this page lists the optimal keep for several common opening rolls.