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.