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. This creates memorable moments when you hit the jackpot.