"What is a good Yatzy score?" is a hard question to answer from memory, because most people remember their best game and forget the other forty. So we measured it.
Our Yatzy has a computer opponent that plays properly: before every re-roll it tries all 32 ways of holding the dice, estimates what each is worth, and when it scores it weighs the upper-section bonus and refuses to throw away a box that could be worth much more later. We let that strategy fill in 4,000 score sheets and recorded every one.
These are the Scandinavian Yatzy rules — fifteen boxes including one pair and two pairs, a 50-point bonus for 63 in the upper section, and 50 for a Yatzy. If you play the American version with a 35-point bonus and Yahtzee bonuses, the numbers will run differently.
The scores
| Score | |
|---|---|
| Bottom 10% of sheets | 156 or less |
| Bottom quarter | 178 or less |
| Median | 216 |
| Top quarter | 246 or more |
| Top 10% | 279 or more |
| Best of 4,000 | 338 |
| Worst of 4,000 | 107 |
The average was 215.3, almost exactly the median.
So a rough guide for a thoughtful player:
- Under 180: a bad-luck game, or the upper section got away from you.
- 200–230: a normal game played well.
- Over 250: a good game.
- Over 280: you are in the top one in ten, and some dice went your way.
The bonus is worth more than the Yatzy
This is the finding we would put on the box. We split the 4,000 sheets by whether they got the upper-section bonus, a Yatzy, both, or neither:
| Sheet got… | Sheets | Average score |
|---|---|---|
| Neither | 1,389 | 166.9 |
| A Yatzy, no bonus | 804 | 217.5 |
| The bonus, no Yatzy | 1,085 | 231.5 |
| Both | 722 | 281.9 |
Both are nominally worth 50 points. But the bonus sheets average 14 points more than the Yatzy sheets, because getting the bonus means you also filled the upper boxes well — three or more of a face, again and again — while a Yatzy is one lucky turn.
The bonus was also the more reliable of the two: it landed on 45.2% of sheets, against 38.1% for a Yatzy.
If you play one part of the game deliberately, make it the upper section. Track it against three of each face from the first turn.
The Yatzy rules and strategy page explains the "relative to three" bookkeeping that makes that easy.
The odds of rolling a Yatzy
Separately from the score sheets, we simulated five million turns of pure dice:
- First roll only: 0.078% — about one turn in 1,300. (The exact figure is 6 in 7,776, so the simulation agrees with the arithmetic.)
- Going all out for three rolls, keeping every die that matches your most common face: 4.6% — about one turn in 22.
That is why a Yatzy turns up in only about four games in ten, even though a game has fifteen turns: nobody spends all fifteen chasing it, and nobody should.
Where the points come from
The average contribution of each box across all 4,000 sheets:
| Box | Average | Box | Average |
|---|---|---|---|
| Ones | 1.8 | One pair | 10.3 |
| Twos | 5.2 | Two pairs | 18.2 |
| Threes | 8.7 | Three alike | 15.0 |
| Fours | 12.0 | Four alike | 10.8 |
| Fives | 15.2 | Small straight | 4.7 |
| Sixes | 18.5 | Large straight | 9.3 |
| Full house | 21.4 | ||
| Chance | 22.7 | ||
| Yatzy | 19.1 |
Two things stand out. Of the three fixed-value boxes, the small straight fills least often: worth 15 when it lands, it averaged 4.7, so it scored on only about 31% of sheets — against 38% for Yatzy and 47% for the large straight. If you are going to miss one box, that is the one the dice most often decide for you. And Ones averaged under 2: sacrificing it early costs almost nothing, which is exactly what good players do.
Try to beat the median
Play Yatzy free against the computer, or pass the phone for a two-player game. Our computer plays the strategy measured here, so beating it means beating a 216-point player more often than not.
Other games we have taken apart the same way: is Minesweeper luck? and how many Pyramid Solitaire deals can be won.
