Dice Probabilities and Strategy
What are the real odds of rolling a Five of a Kind? Should you aim for the upper section bonus? Here are the exact probabilities, and the strategy that follows from them.
Probability on a single roll of 5 dice
Rolling all 5 dice once, with no keeps or rerolls, here's the exact probability of each combination, calculated across all 7,776 possible outcomes (6⁵):
| Combination | Probability | Detail |
|---|---|---|
| Three of a Kind (3+ matching dice) | 21.3% | 1656 / 7776 |
| Small Straight (4 consecutive values) | 15.4% | 1200 / 7776 |
| Full House (3 + 2) | 3.9% | 300 / 7776 |
| Large Straight (5 consecutive values) | 3.1% | 240 / 7776 |
| Four of a Kind (4+ matching dice) | 2.0% | 156 / 7776 |
| Five of a Kind (all 5 matching) | 0.077% | 6 / 7776 |
These figures apply to a single roll. In practice, you get 3 rolls and can keep useful dice, so your real in-game odds are much better — especially for Three of a Kind, Four of a Kind, and straights.
The 63-point bonus
63 points on the upper section is the average of 3 dice per category (3 Ones, 3 Twos, 3 Threes... up to 3 Sixes). It's the benchmark to aim for: whenever a roll gives you a natural three-of-a-kind on a high value (Fours, Fives, or Sixes), it's almost always worth committing it to the upper section rather than elsewhere if you're behind on the bonus.
General strategy
- Always keep dice that form a pair or better on the first roll: it's the foundation of almost every profitable category.
- Only chase Five of a Kind if you already have three or more matching dice on the first roll; trying from zero matching dice is statistically a losing move.
- Late in the game, use the Chance category for a bad roll rather than zeroing out a category that's still reachable.
- If the 63-point bonus is out of reach, prefer zeroing out an upper section box rather than Five of a Kind or a straight, which are rarer and worth keeping open.