Twin Dice Versus Standard Dice?

by Ryan Keane

I just wanted to go into a little more detail about Twin Dice being roughly equal to a regular die with the same mean and number of sides.

Spoiler: Twin Dice are better than normal. Normal dice are better than 'Sidekicks'.

Definition: "Sidekicks" are coins which show either their face value (heads) or one (tails). For example, a 5-point Sidekick will always show either 5 or 1 in a 50/50 distribution. They haven't been used yet, but they are interesting. This essay also uses modified Triple Dice, such as (2,2,2)-1. These are also theoretical, and a little cumbersome. The (2,2,2)-1 is equal to the sum of three 2-sided dice minus one, and generates the results (2, 3, 3, 3, 4, 4, 4, 5).

Power Attacks

Case 1: Compare (2,2,2)-1 to d6 to a 6-cent sidekick (1 or 6)

I have a (2,2,2)-1 and you have a d6. Who would win? (Y=you, M=me, E=either, depending on who goes first) Table 1: I have a (2,2,2)-1 and you have a d6. Who would win? (Y=you, M=me, E=either, depending on who goes first)

	2	3	3	3	4	4	4	5
1	M	M	M	M	M	M	M	M
2	E	M	M	M	M	M	M	M
3	Y	E	E	E	M	M	M	M
4	Y	Y	Y	Y	E	E	E	M
5	Y	Y	Y	Y	Y	Y	Y	Y
6	Y	Y	Y	Y	Y	Y	Y	Y

Result: 20 M's, 20Y's, 8E's. Table 2: I have a d6 you have a 6-cent Sidekick

	1	2	3	4	5	6
1	E	M	M	M	M	M
6	Y	Y	Y	Y	Y	E

Result: 5M's, 5Y's, and 2E's.
Conclusion: I guess it just doesn't matter.

Case 2: You have a d4, I have either a (2,2,2)-1, d6, or a 6cent Sidekick (either 1 or 6)

Table 3: My (2,2,2)-1 vs. your d4

	2	3	3	3	4	4	4	5
1	M	M	M	M	M	M	M	M
2	E	M	M	M	M	M	M	M
3	Y	E	E	E	M	M	M	M
4	Y	Y	Y	Y	E	E	E	M

Result: 20M's, 5 Y's, 7E's

Table 4: My d6 vs. your d4:

	1	2	3	4	5	6
1	E	M	M	M	M	M
2	Y	E	M	M	M	M
3	Y	Y	E	M	M	M
4	Y	Y	Y	E	M	M

Result: 14 M's, 6 Y's, 4E's

Table 5: My 6-cent sidekick vs. your d4:

	1	6
1	E	M
2	Y	M
3	Y	M
4	Y	M

Result: 4M's, 3 Y's, 1 E

Conclusion: Versus a d4, I'd much rather have the (2,2,2)-1

Case 3: You have a d8, I have either a (2,2,2)-1, d6, or a 6-cent sidekick

(tables omitted)

Results:

(2,2,2)-1: 20 M's, 36 Y's, 8 E's

d6: 15 M's, 27 Y's, 6 E's

Sidekick: 5 M's, 9 Y's, 2 E's

Conclusion: Well THAT was surprising. Considering these three Power Attack results, I'd rather have Twin Dice rather than a single die with the same number of sides and same average roll. Against equal or larger dice there's no real difference. Against smaller dice the Twin Dice do slightly better.

Skill Attacks

That's all fine, but what about comparing the dice for Skill Attacks?

Case 4: You have a d12 left. I have a d10 and a d6

What are the chances that I can make a successful Power Attack? There is a 365/720 chance of at least one of my dice being greater than or equal to yours.

What are the chances that I can make a successful Skill Attack? There is a 50/720 chance of a good Skill Attack. Together that's 415/720 or about 58% chance that I can take your last die this turn.

Case 5: Same as Case 4 but I have a d6 and a dime sidekick (1 or 10)

The chances of a successful Power Attack are still 365/720. However the chances of a successful Skill Attack drop to only 7/720. The total of 372/720 is only about 52%.

In this case, you only have one die so Skill Attacks are out of the question for you. Plus I've looked at the chances of a this-turn kill without worrying about retaliation.