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In Star Wars, you can spend resources to upgrade green dice to yellow.

Green dice have eight sides, five success symbols, and five advantage symbols. The average success rate is 0.6255 and the average advantage rate is 0.625.

Yellow dice have twelve sides, nine success symbols, eight advantage symbols, and one triumph symbol. The average success rate is 0.83 (counting the triumph as a success) and the average advantage rate is 0.66. There's also a 1/12 chance of narrative benefit from a triumph, of course.

My teammates seem to really like spending resources for dice upgrades, but to me it looks like the math doesn't work out. Isn't it a lot better to use those light side destiny tokens for narrative benefits?

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  • \$\begingroup\$ Is one Proficiency die better than two Ability dice? related. Possible dupe? \$\endgroup\$ – Tritium21 Aug 21 '16 at 2:17
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    \$\begingroup\$ I really don't think that question is a duplicate of this one. Is there any way to remove that template? \$\endgroup\$ – Dan B Aug 21 '16 at 6:01
  • \$\begingroup\$ Its a manually typed comment. If its not, its not, and the close vote will time out. \$\endgroup\$ – Tritium21 Aug 21 '16 at 6:03
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Star Wars dice are extremely difficult to analyse statistically and I speak as someone who has taught statistics at a Master's degree level. My congratulations to the people who designed them for that.

You cannot treat success and advantage as though they were independent outcomes because they aren't; both dice have faces with one of each. You also can't add up all the symbols and divide by the number of sides as say that is the chance because this treats .7 successes as a meaningful result which is only reasonable in dice pools with dozens of dice: this never happens. Alternatively, .7 represents the long run average over all possible dice rolls, however, in the long run all humans are dead, what matters is if we avoid death now!

So, what does happen? (All results are /24)

Result    Green    Yellow
   -         3        2
   S         6        6 (inc. T)
  2S         3        4
  AS         3        6
   A         6        2
  2A         3        4

Upgrading gives a 5/24 chance of significant improvement. Reducing you chance of nothing by 1/24, giving 2 success instead. It upgrades single advantage 4/24 times, adding a success 3/24 and another advantage 1/24. In addition it carries that magical triumph symbol, which can change the path of the adventure.

Now additional advantages (and triumphs) are always advantageous (heh) but additional successes are more situational.

In combat each extra success do another wound (yay!); outside of combat you generally need one more success than failure and any left over are wasted, a bit like carrying water through the desert - you have to have enough but too much is just dead weight. To work this out you need to consider the whole dice pool - how many failures will you need to overcome? If it's a lot, a 4/24 chance of an extra one from an upgrade is not to be sneezed at. If success is a cake walk, sneeze away!

As to if light side points are better used for narrative benefits, that is situational on your style of play as well as the dice pool situation. A well prepared group who likes to cover all bases in planning is likely to need them less than a group that takes things on the run.

How valuable a light side point is also depends on their velocity in your particular group. This is largely dictated by the GM's attitude but players have their impact too. A group where points pass back and forth rapidly will value them less "easy come, easy go"; hoarders on both sides of the screen drive the value up. Interestingly, both play styles will tend to have one when they really, really need one: the laissez-faire because they usually have one, the misers because they usually save one.

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  • \$\begingroup\$ If you are highly likely to succeed or fail on green, then yellow won't help much. If you are 'close' on green, then yellow probably will be the difference between success and failure. \$\endgroup\$ – MikeP Aug 21 '16 at 2:18
  • \$\begingroup\$ If it is critically important that you succeed, then go yellow. \$\endgroup\$ – MikeP Aug 21 '16 at 2:18
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You got the math wrong:

Green Die

  • 1/8 (12.5%) per side:
    • 1 Blank
    • 2 Successes
    • 2 Advantages
    • 1 2x Success
    • 1 2x Advantage
    • 1 Advantage & Success

This is: 1/8 nothing ; 5/8 (62.5%) for 1+ Success, 5/8 for 1+ Advantage; 1/8 (12.5%) for 2 Successes, 1/8 for 2 Advantages

Yellow Die

  • 1/12 (8.3%) per side:
    • 1 Blank
    • 1 Advantage
    • 2 Success
    • 3 Advantage & Success
    • 2 2x Success
    • 2 2x Advantage
    • 1 Triumph (which is "both a Success and can do even better things over the Advantage", so I count it on both)

Sums up for: 8.3% Blank, 8/12 (66.6%) 1+ Success, 7/12 (58.3%) 1+ Advantage, 2/12 (16.6%) for 2 Succeses, 2/12 for 2 Advantages, 1/12 (8.3%) Triumph

Conclusion

  • The chance of gaining no positive result drops from 12.5% to 8.3%, which is significant, likewise the chance for any positive result raises from 87,5 to 91,7%.
  • The chance for 1 or 2 Successes raises slightly from 62.5% to 66.3%
  • The chance for 1 or 2 Advantages lowers slightly from 62.5 to 58.3%
  • The chance for 2 Successes XOR Advantages raises from 12.5% to 16.6%
  • The chance for 1 Triumph raises from 0% to 8.3%

So, the yellow die is in fact better than the green one.

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  • \$\begingroup\$ Looks like you're right. Good catch, thanks. \$\endgroup\$ – Dan B Aug 21 '16 at 5:57
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Analysing Star Wars dice is different to most other RPGs, because there are negative dice as well.

Analysing only the improvement to a single dice is a poor way of looking at it.

To take something with simpler maths, lets imagine I had a DnD weapon that did 1d8 damage. I can improve that to 1d10, which is an increase from 4.5 to 5.5 - 22%. Sounds alright I suppose.

But lets imagine I had some 'difficulty dice', and my actual damage was 1d8 minus 1d6. Upgrading that to 1d10-1d6 is an increase from 1 to 2 - 100%. For each 1 benefit to our positive dice, we got 5 benefit to our net result.

In Star Wars, a small increase in your sum of beneficial dice can provide a massive increase in your odds of a positive result, and your average successes/advantages.

The extent to which this occurs is dependent on your current dice pool.

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