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More Sicherman Dice

The last post about Sicherman Dice was basically just a definition. Now for the application.

In Action! and other games, success is measured by rolling higher than Skill Score + Ability Score + Dice Roll. The official rules use 3 regular dice (3d6). An alternate rule uses a 20 sided dice (1d20). After doing some calculations, it is also possible to use Sicherman Dice. As a shorthand, I will refer to rolling two Sicherman dice as 2dS. 2dS means rolling the Sicherman dice and using one as a ten digit and the other as a ones digit. Thus if you rolled an 8 on one die and 2 on the other, the result would be 28 or 82.

At first, I thought of having the die with the larger numbers be a tens digit and the smaller one as the ones digit. Then I realized that most people would make the largest roll the tens digits no matter what. After checking the odds, it doesn't affect odds to succeed very much. So, the way to read a 2dS roll is to make the largest two-digit number possible.

For example, if I roll a 3 and 4 respectively, the result is 43. If I roll a 6 and 1, the result is 61.

Odds: Four Test Cases

Before talking about odds, I have to say that it is difficult to post a table that looks the same as the matrix in the Action! rules. As a result, I'm going to take four characters and discuss them specifically as a cross-section of all possibilities. I'll give a skill score and an attribute score to each one. Then I'll discuss the odds of each character achieving success.

The first character is the Realistic level character. The realistic character has a skill score of 3 and an attribute score of 3. This means, of course, that the Realistic character will need dice roll + 6 to determine success.

The second character is the Cinematic level character. The Cinematic character has a skill score of 6 and an attribute score of 6. This means that he or she will need dice roll + 12 to determine success.

The third character is the Extreme level character. The Extreme character has a skill score of 8 and an attribute score of 8. This means that success is determined by dice roll + 16.

The fourth character is the Paragon character. This character is the pinnacle of human achievement with a skill score of 10 and an attribute score of 10. Success is dice roll + 20 for success.

Odds: Target Numbers

After playing with the numbers, I think I've come up with the best possible set of target numbers. For reference, here are the difficulties and target numbers from Action!

Difficulty Levels & Target Numbers

Description ----- TN
Average/Easy....12
Tricky...............15
Challenging......18
Difficult.............21
Demanding.......24
Extreme...........27
Legendary........30

Now under the new 2dS system, the numbers look like this:

Description ----- TN
Average/Easy....24
Tricky...............36
Challenging......48
Difficult.............60
Demanding.......72
Extreme...........84
Legendary........96

To give some reference to these numbers, I look at them as percentile ability. A person in the 96 percentile of their task should be able to pull off some legendary things if they are lucky.

Odds: The Numbers

In the Action! System, the matrix shows a table with needed rolls of 3d6 to succeed. Since I am looking at odds, and not actual rolls needed, I need to first provide odds based on the Action! System for success. (This is for 3d6)

The Realistic person has to roll a six or better to perform an Average/Easy task. The odds of rolling a six or better are 95.37%. To perform a Tricky task, a roll of nine or better is needed. Odds of that are 74.07%. For the rest, I'll just list the roll needed and the odds for rolling that number or better. Challenging - 12 or better - 37.50%. Difficult - 15 or better - 9.26%. Demanding - 18 or better - 0.46%. Extreme and Legendary are technically possible by rule, but the character must roll an 18. The chances of rolling an 18 are 1 in 216 or 0.46%.

The Cinematic person can automatically perform an Average/Easy task. Odds are 100%. To perform a Tricky task, a roll of three or better is needed. Odds of that are 100%. For the rest: Challenging - 6 or better - 95.37%. Difficult - 9 or better - 74.07%. Demanding - 12 or better - 37.50%. Extreme - 15 or better - 9.26% and Legendary - 18 or better - 0.46%

The Extreme person can automatically perform Average/Easy, Tricky, and Challenging tasks. Odds are 100% for all three. For the rest: Difficult - 5 or better - 98.14%. Demanding - 8 or better - 83.79%. Extreme - 11 or better - 50.00% and Legendary - 14 or better - 16.20%

Finally, our Paragaon can automatically perform Average/Easy, Tricky, Challenging, and Difficult tasks. Odds are 100% for all four. For the rest: Demanding - 4 or better - 99.53%. Extreme - 7 or better - 90.74% and Legendary - 10 or better - 62.50%

It seems that once you hit the Paragon, very little is beyond your capability. This bodes ill for superhuman characters, but that's a subject of a different post. Without delay, here are the odds for the same four characters under the 2dS system. I'll warn you, the odds are lower.

The Realistic person has to roll a 18 or better to perform an Average/Easy task. The odds of rolling a six or better are 97.22%. To perform a Tricky task, a roll of 30 or better is needed. Odds of that are 91.66%. For the rest, I'll just list the roll needed and the odds for rolling that number or better. Challenging - 42 or better - 66.66%. Difficult - 54 or better - 36.11%. Demanding - 66 or better - 16.66%. Extreme - 78 or better - 16.66% Legendary tasks are technically possible by rule, but the character must roll an 84, the highest roll possible on Sicherman dice. The chances of rolling an 84 are 2.77%.

The Cinematic person can automatically perform an Average/Easy task. Odds are 100%. To perform a Tricky task, a roll of 24 or better is needed. Odds of that are 91.66%. For the rest: Challenging - 36 or better - 72.22%. Difficult - 48 or better - 50.00%. Demanding - 60 or better - 33.33%. Extreme - 72 or better - 16.66% and Legendary tasks - 84 - 2.77%

The Extreme person can automatically perform an Average/Easy task. Odds are 100%. To perform a Tricky task, a roll of 20 or better is needed. Odds of that are 97.22%. For the rest: Challenging - 32 or better - 83.33%. Difficult - 44 or better - 52.77%. Demanding - 56 or better - 33.33%. Extreme - 68 or better - 16.66% and Legendary tasks - 80 or better - 16.66%

Finally, our Paragaon can automatically perform an Average/Easy task. Odds are 100%. To perform a Tricky task, a roll of 16 or better is needed. Odds of that are 97.22%. For the rest: Challenging - 28 or better - 91.66%. Difficult - 40 or better - 72.22%. For the rest: Demanding - 52 or better - 47.22%. Extreme - 64 or better - 19.44% and Legendary - 76 or better - 16.66%

What a Difference

It seems like more able characters are penalized, but only because the scale changed. It's true that almost everyone has a 1 in 6 chance of performing an Extreme task. The Realistic and Cinematic person have much better chances, while the other two have much worse chances. What this does is allow superhuman characters chances to do things beyond the standard difficulty levels and have some challenge. Otherwise, you have to target numbers in triple digits for a challenge while everyone has at least a 2.77% chance to perform superhuman feats.

One other note - bonuses and penalties are now factors of five. What used to be a +1 bonus is now a +5 bonus. A -3 penalty is -15 points, now.

Conclusion

This was more of an exercise than anything. Still, I think that a mechanic based on Sicherman Dice is viable. As far as Action!, I believe it would require more rules changes. It would also require a sliding scale of what is "Legendary" depending on the level of the game. What might be Legendary in a Realistic game, might only be Demanding in an Extreme game. It's something to think about.

The main issue of using Sicherman Dice as percentile dice is that it is impossible to roll a number between 64 and 81. That's a huge gap that wreaks havoc with probabilities for success. Even if I made an easy task a TN of 12 and Legendary a TN of 84, the differences are not that large. For the record, there are 21 possible rolls for 2dS as I describe them here. The rolls are: 11, 21, 31, 32, 33, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, 81, 82, 83, 84.

Still in search of different mechanics for fun. Let me know what you think of the effect of Sicherman Dice.