This isn't even really like a game.

[OCBG]

It's basically just pure luck to if you get an automated scoring roll.
Seems like multiple times, I pushed my luck taking several rolls to get 500-750 points, only to have my opponent get 1000-1500 points doing absolutely nothing. It doesn't appear to be evenly distributed either, but the same players receiving these high scoring rolls.

[Jellby]

A dice game that's random? You're kidding.

[OCBG]

The odds of rolling all six dice as a scoring combination in Farkle are quite low, specifically about 0.0129% or 1 in 7776. This means it's very rare to achieve this outcome on the first roll.

Yet on BGA happens quite often. It shouldn't be occurring multiple times per game?

[JohnnyCyclops]

The odds of rolling all six dice as a scoring combination in Farkle are quite low, specifically about 0.0129% or 1 in 7776. This means it's very rare to achieve this outcome on the first roll.

Yet on BGA happens quite often. It shouldn't be occurring multiple times per game?

1 in 7776 appears to be the odds of rolling any six of a kind, so six 1s, or six 2s, etc.

There are other ways to score.

On your most recent game your opponent rolled a six-dice straight, 1,2,3,4,5,6. That’s about 1.5% likelihood. 720 in 46656. My maths may be off! (Roll any dice, so 6 chances, then the second dice must be one of the five other options, then the third dice one of the four remaining options, and so on. So 6*5*4*3*2*1=720 against all possible combination 6*6*6*6*6*6=46656).

That same turn they rolled five of a kind. I make that 1 in 1296, so around 0.07%.

So, they did ok with the first roll (will happen once every 65 rolls, assuming dice order does not matter). But then struck gold with the rarer five of a kind.

Where are you seeing multiple six of a kind rolls? Please share the table number. I’m curious.

[OCBG]

On average a set of Hot Dice should occur 9 times per game of 20,000 points no piggybacking.
Guess that does sound like a decent amount of times. I'll try to see next time how often it occurs. Anyways here is some more breakdown analysis.

What are the odds of scoring on all 6 dice in the first roll of Farkle?

To score on all 6 dice, every die must contribute points. That includes:

A straight (1–2–3–4–5–6)

Three pairs (e.g., 2x2s, 2x4s, 2x6s)

Two triplets (e.g., 3x2s + 3x5s)

Six-of-a-kind

Four-of-a-kind + a pair

All 1s or 5s

Other full scoring combos

There are 46,656 total combinations when rolling 6 dice (6^6).

Some combinations that score with all 6 dice:

Straight (1–2–3–4–5–6)

6! = 720 permutations

720 outcomes

Three pairs (e.g., 2x2s, 2x4s, 2x6s)

Choose 3 numbers: C(6,3) = 20

Permutations per combo = 6! / (2! * 2! * 2!) = 720

20 × 720 = 14,400 outcomes

Two triplets (e.g., 3x2s and 3x5s)

Choose 2 numbers: C(6,2) = 15

Permutations = 6! / (3! * 3!) = 20

15 × 20 = 300 outcomes

Minimum confirmed scoring combinations:
720 + 14,400 + 300 = 15,420

Estimated probability:
15,420 / 46,656 ≈ 33.05%

When including other rare scoring combos (e.g., 4x1s + 2x5s), the real-world estimate rises to:

~37% chance of scoring on all 6 dice in your first roll.

Step-by-step Breakdown
1. Chance of scoring on all 6 dice in one roll
From earlier:

~37% chance per full 6-dice roll.

2. How often do you roll 6 dice in a game to 20,000?
This depends on how many turns it typically takes to reach 20,000 points.

Let’s make some fair assumptions for standard play:

Average turn score (with no piggybacking): ~750–1,000 points

Let's use 850 points per turn as a working average

20,000 ÷ 850 ≈ 23.5 turns per game → roughly 24 turns

In each turn, you start with 6 dice. If you score on all 6, you "hot dice" and roll all 6 again within the same turn.

But we’re only counting initial 6-dice rolls, one per turn.

3. Multiply the odds by the number of 6-dice rolls
24 turns × 37% = 8.88

On average, a player will score on all 6 dice in about 9 turns per game

Final Answer
On average, you will score on all 6 dice in about 9 turns during a standard Farkle game to 20,000 points (with no piggybacking).

This assumes:

~24 turns per game

~37% chance of scoring on all 6 dice per roll

This number can vary slightly depending on your scoring aggressiveness and luck, but 9 is a solid average under normal play conditions.

[Meeplelowda]

The odds of rolling all six dice as a scoring combination in Farkle are quite low, specifically about 0.0129% or 1 in 7776. This means it's very rare to achieve this outcome on the first roll.

Yet on BGA happens quite often. It shouldn't be occurring multiple times per game?

Where are you seeing multiple six of a kind rolls? Please share the table number. I’m curious.

It should be easy to find examples if it's happening multiple times per game.