odds & probability
Knowing the math behind the dice helps you make smarter decisions. Here are the real probabilities for every combination.
single roll odds (all 5 dice)
Your chances of rolling each combination on a single throw of all 5 dice:
| Combination | Odds |
|---|---|
| Jatzee (5 of a kind) | 0.08% |
| Large Straight | 3.09% |
| Small Straight | 12.35% |
| Full House | 3.86% |
| Four of a Kind | 1.93% |
| Three of a Kind | 15.43% |
chasing jatzee
What are your odds of getting Jatzee based on what you're holding?
| Starting With | 2 Rolls Left |
|---|---|
| Four of a kind | 19.44% |
| Three of a kind | 4.63% |
| Two of a kind | 1.08% |
| Nothing (all different) | 0.13% |
With 4 of a kind and just 1 roll left, you have a 16.67% (1 in 6) chance of hitting Jatzee. Those are decent odds!
straight probabilities
Odds of completing a straight based on what you're holding:
| Holding | Large Straight |
|---|---|
| 4 in sequence (e.g., 2-3-4-5) | 33.33% |
| 3 in sequence, need 2 dice | 11.11% |
| 3 in sequence (inside, e.g., need 3 in 1-2-4-5) | 16.67% |
full house math
Completing a full house from different starting points:
| Holding | Odds (1 Roll) |
|---|---|
| Three of a kind + pair | 100% (done!) |
| Three of a kind, rolling 2 dice | 16.67% |
| Two pair, rolling 1 die | 33.33% |
expected values
Average points per category if you play optimally:
| Category | Average |
|---|---|
| Ones | 2.5 |
| Twos | 5.0 |
| Threes | 7.5 |
| Fours | 10.0 |
| Fives | 12.5 |
| Sixes | 15.0 |
| Chance | 23.5 |
This is why Chance is so valuable late game - the expected value of 5 random dice is about 17.5 points, but you can often do better by being selective about when you use it.