Super Yahtzee
My 5-year-old son invented new rules for Yahtzee. That was fun, but then I wanted to know if the scoring is fair(-ish) and what a good strategy would be. Further down is an analysis of the probabilities in his scoring system. It has a surprising insight!
If you want to play it, you can download the score sheet below.
Rules
Super Yahtzee uses standard Yahtzee rules (5 dice, 3 rolls per turn) with these additions:
New categories:
| Category | Dice | Points |
|---|---|---|
| Super Yahtzee | 1-1-1-1-4 | 100 |
| Super Street | 1-1-2-3-5 | 70 |
| Super Full House | 2-2-2-6-6 | 60 |
Modified categories:
- 3 of a Kind: sum all dice, +10 bonus if a 6 is present
- 4 of a Kind: sum all dice, +20 bonus if a 6 is present
Upper section:
- You can combine dice to create extra matches. Rolling 6-6-4-1-1 counts as three sixes because 4+1+1=6. Multiple combinations are allowed.
Probabilities
I calculated exact probabilities for a single roll and ran Monte Carlo simulations (100,000 trials) for three rolls with optimal strategy.
Single roll (out of 7,776 possible outcomes):
| Category | Ways | Probability | Odds |
|---|---|---|---|
| Super Yahtzee | 5 | 0.064% | 1 in 1,555 |
| Super Street | 60 | 0.77% | 1 in 130 |
| Super Full House | 10 | 0.13% | 1 in 778 |
| Yahtzee (any 5 of a kind) | 6 | 0.077% | 1 in 1,296 |
| Four of a Kind | 156 | 2.0% | 1 in 50 |
| Full House | 300 | 3.9% | 1 in 26 |
| Large Straight | 240 | 3.1% | 1 in 32 |
| Small Straight | 1,200 | 15.4% | 1 in 6 |
With three rolls:
| Category | Probability | Odds |
|---|---|---|
| Super Yahtzee | 3.6% | 1 in 28 |
| Super Street | 14.7% | 1 in 7 |
| Super Full House | 6.1% | 1 in 16 |
| Yahtzee (any 5 of a kind) | 4.6% | 1 in 22 |
On a single roll, Super Yahtzee (1 in 1,555) is harder than regular Yahtzee (1 in 1,296). With three rolls and optimal strategy, Super Yahtzee becomes easier (3.6% vs 4.6%) because targeting a specific four-of-a-kind plus one die is more achievable than any five-of-a-kind.
In a 13-turn game, expect to hit Super Yahtzee about once every 2 games, Super Full House once every 1-2 games, and Super Street almost twice per game.
The scoring is generous. Super Yahtzee pays double regular Yahtzee despite being only slightly harder with three rolls. It’s fun!