Thoughts on countdowns

[herrozerro]

I was actually wondering the math of this as well and I made a simple program in C#. source can be found here.

https://gist.github.com/herrozerro/6ee4f71f437cf201f86c

It should be noted that the Mode could vary wildly, I have had the mode of one die be 1 or as high as 8 in my tests. Here are some of my findings:

1 dice averaged 6.0157 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 45
The median value of rounds are: 4 and the Mode was: { Rounds = 1, Freq = 1681 }

2 dice averaged 8.7963 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 52
The median value of rounds are: 8 and the Mode was: { Rounds = 7, Freq = 754 }

3 dice averaged 10.6625 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 55
The median value of rounds are: 11 and the Mode was: { Rounds = 4, Freq = 631 }

4 dice averaged 11.8739 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 55
The median value of rounds are: 16 and the Mode was: { Rounds = 9, Freq = 739 }

5 dice averaged 12.9392 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 63
The median value of rounds are: 13 and the Mode was: { Rounds = 13, Freq = 599 }

6 dice averaged 13.9056 rounds over 10000 runs.
The shortest set of rounds was: 2 and the most rounds was: 62
The median value of rounds are: 12 and the Mode was: { Rounds = 21, Freq = 238 }

7 dice averaged 14.6642 rounds over 10000 runs.
The shortest set of rounds was: 2 and the most rounds was: 60
The median value of rounds are: 19 and the Mode was: { Rounds = 34, Freq = 26 }

8 dice averaged 15.5141 rounds over 10000 runs.
The shortest set of rounds was: 2 and the most rounds was: 60
The median value of rounds are: 16 and the Mode was: { Rounds = 6, Freq = 207 }

9 dice averaged 16.0385 rounds over 10000 runs.
The shortest set of rounds was: 3 and the most rounds was: 64
The median value of rounds are: 13 and the Mode was: { Rounds = 16, Freq = 559 }

10 dice averaged 16.5726 rounds over 10000 runs.
The shortest set of rounds was: 3 and the most rounds was: 69
The median value of rounds are: 12 and the Mode was: { Rounds = 13, Freq = 679 }

 

[GMMichael]

Interesting...

So a countdown with 1 die gets you, on average, six rounds per die before the bomb blows.
And a countdown with 6 or more dice gets you, essentially, 2 rounds per die before the bomb blows.

On average.

Are any GMs rolling countdowns behind the screen, and using in-game descriptions to convey that a die has been lost?

"Your Petrify spell seems to be wearing off. More stone just broke away from the giant, and now only its legs are coated with rock..."

 

[Morrus]

I assume that's the slow countdown there? It might be interesting to see a similar chart for medium and fast countdowns!

I have "expected countdown lengths" calculated internally. The max and min you have there is additional info, though!

 

[Morrus]

Interesting...

So a countdown with 1 die gets you, on average, six rounds per die before the bomb blows.
And a countdown with 6 or more dice gets you, essentially, 2 rounds per die before the bomb blows.

On average.

Are any GMs rolling countdowns behind the screen, and using in-game descriptions to convey that a die has been lost?

"Your Petrify spell seems to be wearing off. More stone just broke away from the giant, and now only its legs are coated with rock..."

Yes, countdowns are typically expressed with descriptive elements for each stage. An illness might have hairloss at 3 dice, blindness at 2 dice, for example.

 

[herrozerro]

I assume that's the slow countdown there? It might be interesting to see a similar chart for medium and fast countdowns!

I have "expected countdown lengths" calculated internally. The max and min you have there is additional info, though!

Here are the numbers for all rates:

Slow Countdown (6)
1 dice averaged 6.0024 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 54
The median value of rounds are: 10 and the Mode was: { Rounds = 2, Freq = 1401 }
Medium Countdown (5-6)
1 dice averaged 2.9887 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 22
The median value of rounds are: 4 and the Mode was: { Rounds = 1, Freq = 3346 }
Fast Countdown (4-6)
1 dice averaged 1.9948 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 13
The median value of rounds are: 1 and the Mode was: { Rounds = 5, Freq = 305 }

Slow Countdown (6)
2 dice averaged 8.704 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 54
The median value of rounds are: 14 and the Mode was: { Rounds = 19, Freq = 119 }
Medium Countdown (5-6)
2 dice averaged 4.1871 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 24
The median value of rounds are: 2 and the Mode was: { Rounds = 3, Freq = 1928 }
Fast Countdown (4-6)
2 dice averaged 2.6789 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 16
The median value of rounds are: 2 and the Mode was: { Rounds = 1, Freq = 2450 }

Slow Countdown (6)
3 dice averaged 10.5471 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 62
The median value of rounds are: 22 and the Mode was: { Rounds = 14, Freq = 398 }
Medium Countdown (5-6)
3 dice averaged 5.0434 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 37
The median value of rounds are: 6 and the Mode was: { Rounds = 4, Freq = 1622 }
Fast Countdown (4-6)
3 dice averaged 3.1232 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 13
The median value of rounds are: 2 and the Mode was: { Rounds = 4, Freq = 1521 }

Slow Countdown (6)
4 dice averaged 11.9473 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 80
The median value of rounds are: 10 and the Mode was: { Rounds = 12, Freq = 610 }
Medium Countdown (5-6)
4 dice averaged 5.6517 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 24
The median value of rounds are: 9 and the Mode was: { Rounds = 3, Freq = 1513 }
Fast Countdown (4-6)
4 dice averaged 3.511 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 16
The median value of rounds are: 2 and the Mode was: { Rounds = 1, Freq = 640 }

Slow Countdown (6)
5 dice averaged 12.9635 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 58
The median value of rounds are: 8 and the Mode was: { Rounds = 14, Freq = 546 }
Medium Countdown (5-6)
5 dice averaged 6.1778 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 26
The median value of rounds are: 3 and the Mode was: { Rounds = 5, Freq = 1611 }
Fast Countdown (4-6)
5 dice averaged 3.8284 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 18
The median value of rounds are: 7 and the Mode was: { Rounds = 6, Freq = 758 }

Slow Countdown (6)
6 dice averaged 13.8806 rounds over 10000 runs.
The shortest set of rounds was: 2 and the most rounds was: 73
The median value of rounds are: 12 and the Mode was: { Rounds = 6, Freq = 411 }
Medium Countdown (5-6)
6 dice averaged 6.5371 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 25
The median value of rounds are: 6 and the Mode was: { Rounds = 7, Freq = 1215 }
Fast Countdown (4-6)
6 dice averaged 4.0386 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 16
The median value of rounds are: 5 and the Mode was: { Rounds = 6, Freq = 794 }

Slow Countdown (6)
7 dice averaged 14.7514 rounds over 10000 runs.
The shortest set of rounds was: 2 and the most rounds was: 56
The median value of rounds are: 12 and the Mode was: { Rounds = 21, Freq = 274 }
Medium Countdown (5-6)
7 dice averaged 6.8823 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 29
The median value of rounds are: 8 and the Mode was: { Rounds = 5, Freq = 1549 }
Fast Countdown (4-6)
7 dice averaged 4.2296 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 19
The median value of rounds are: 4 and the Mode was: { Rounds = 5, Freq = 1637 }

Slow Countdown (6)
8 dice averaged 15.3569 rounds over 10000 runs.
The shortest set of rounds was: 3 and the most rounds was: 55
The median value of rounds are: 16 and the Mode was: { Rounds = 7, Freq = 401 }
Medium Countdown (5-6)
8 dice averaged 7.2099 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 28
The median value of rounds are: 7 and the Mode was: { Rounds = 6, Freq = 1548 }
Fast Countdown (4-6)
8 dice averaged 4.4274 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 19
The median value of rounds are: 6 and the Mode was: { Rounds = 3, Freq = 2450 }
Slow Countdown (6)

9 dice averaged 16.1287 rounds over 10000 runs.
The shortest set of rounds was: 3 and the most rounds was: 63
The median value of rounds are: 20 and the Mode was: { Rounds = 30, Freq = 69 }
Medium Countdown (5-6)
9 dice averaged 7.4771 rounds over 10000 runs.
The shortest set of rounds was: 2 and the most rounds was: 28
The median value of rounds are: 6 and the Mode was: { Rounds = 5, Freq = 1461 }
Fast Countdown (4-6)
9 dice averaged 4.5905 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 21
The median value of rounds are: 5 and the Mode was: { Rounds = 5, Freq = 1870 }

Slow Countdown (6)
10 dice averaged 16.5551 rounds over 10000 runs.
The shortest set of rounds was: 3 and the most rounds was: 71
The median value of rounds are: 10 and the Mode was: { Rounds = 27, Freq = 132 }
Medium Countdown (5-6)
10 dice averaged 7.7478 rounds over 10000 runs.
The shortest set of rounds was: 2 and the most rounds was: 29
The median value of rounds are: 10 and the Mode was: { Rounds = 9, Freq = 976 }
Fast Countdown (4-6)
10 dice averaged 4.731 rounds over 10000 runs.
The shortest set of rounds was: 1 and the most rounds was: 20
The median value of rounds are: 3 and the Mode was: { Rounds = 4, Freq = 2700 }