1 hour ago, Daeglan said:As a big fan of probability and statistics, let me see if I can help explain the most common forum position on this issue from a more math-based perspective. Although first, I would be remis if I didn't correct an apparent misunderstanding of the rules-as-written:
--If a Dark-side Force user wants to use the white pips they rolled on a Force power check, they must flip a Destiny Point in order to do so, and then additionally suffer 1 strain per white pip they use as a Force Point. They also suffer 1 conflict for black pip they use as a Force Point.
--If a Light-side Force user wants to use the white pips they rolled on a Force power check, they must flip a Destiny Point in order to do so, and then additionally suffer 1 strain per white pip they use as a Force Point. They also suffer 1 conflict for black pip they use as a Force Point.Both sides suffer strain equally for making use of the other alignment's pips. The only difference is conflict; a Dark-sider is unlikely to care overmuch about taking conflict, while it is probably a concern for a Light-sider. So if your concern stems from Dark-siders needing to suffer strain and Light-siders not having to suffer strain, that's not an issue.
Also, keep in mind that, while the distribution per side is not perfectly even, the Force die has exactly 8 white pips and 8 black pips on it, so with perfectly average rolls, two characters of opposite alignment will, over the course of twelve Force power checks, generate the same number of useable pips. Obviously perfectly average rolling is ridiculously unlikely, so that's why we use odds
Thank you for trying to elaborate on the matter and making a detailed post. However I have to correct you already, because as far as I know, dark siders don't gain conflict when using dark side points, they only suffer the strain, which is on pg. 281 in FaD, and to be sure I just re-read the paragraph for dark siders. However, it's possible that you're assuming that whats detailed on pg. 281 in FaD, is addional to whats on pg. 280, the part that says he suffers conflict equal to the amount dark side points used. However, the reason I don't think thats intended as being additional, is then the dark sider would be suffering strain every time the user would be using the force.
Also, you're writing that a light-side force user wants to use light side points, they must flip a destiny point in order to so, and then suffer additionally suffer 1 strain per light side point they use, and that they also suffer 1 conflict for each dark side point they use - I'm sure you meant for every dark side point spent they gain strain and conflict.
I don't believe that you can use the perfect average to determine that something with an assymetrical spread is balanced because it has the exact same amount points spread out. I think this very similar to the regression toward the mean. I assume you know, that even though it's said in theory that it takes the same amount of rolls as there are sides to reach the perfect average, that doesn't work that way in practice, and it's more likely that it will take a lot more rolls to achieve the perfect average, which for most part probably will more rolls than will happen in a game session. Furthermore, you can't accurately calculate how many rolls it's going to take to achieve the perfect average, means you can't use it to determine if it's balanced on or not. Fact is that it attempts to achieve balance around the average, but when results are not within the average, but out closer to the extremes (min and max), then it's not very balanced and it won't feel balanced, and for some it will make for a good experience (those who get the good rolls), and for others it will make for a bad experience (those who get the bad rolls.)
There is assymetrical and symmetrical balance, where balancing symmetrically on a fundamental level will make it easier to achieve a better cohesive and congruent balance. But when trying to balance assymetrically on a fundamental level, will be very difficult and more often than not, will have certain areas or certain times that won't be and won't feel balanced. So it's generally better to balance symmetrically on a fundamental level than trying to balance assymetrically on a fundamental level and try to balance various incidentals and make everything fit around the imbalance on the fundamental level. Clearly, the force dice on the fundamental level based around asymmetrical balance, they trying to balance the incidentals around various mechanics and resource management.
I think it makes for better balance to have the force dice symmetrically balanced and have the other mechanics to support the lore, like have the light and dark side points have different qualities to them, have them able to affect in different ways, have both side take sided conflict when using the opposite force side.
2 hours ago, Absol197 said:Now, the best way to look at this problem, from a numbers perspective, is not to look at mixed results. Calculating the odds of 2 black pips and 2 white pips is complex, and it (usually) doesn't matter. Both characters will look at that and see 2 pips they can use. It's easier to look SOLELY at, "What are the odds of me rolling so many pips of my color?"
So, to start, let's look at the two characters, one Light-sider and one Dark-sider, and use the following suppositions: They have Force rating 1, they refuse or are unable to use the opposite color pip, they attempt twelve checks, and they roll statistically average rolls. Here's their results, both in percentage and number of rolls:
Pips | Light | Dark
00 | 58.33% (7 rolls) | 41.67% (5 rolls)
01 | 16.57% (2 rolls) | 50.00% (6 rolls)
02 | 25.00% (3 rolls) | 0 8.33% (1 roll)So in this test, the Light-sider failed to do anything with the Force 7 times, and the Dark-sider failed 5 times, for a total advantage in success rate of 16.67% to the Dark-sider. The Light-sider got to activate an upgrade 3 times, and the Dark-sider got to activate an upgrade 1 time, for a total advantage in upgrade rate of 16.67% to the Light-sider. It's up to you if the risk of failing completely is worth the chance of getting that single upgrade, but assuming they are roughly equal, both sides are equal, but with different "areas of expertise," as it were. Both characters suffered 0 strain.
Now, we have them do the same thing, but say they are always willing and able to spend a Destiny Point and suffer strain to use the other alignment's pips. The chart is now:
Pips | Light | Dark
00 | 00 .00% (0 rolls) | 00 .00% (0 rolls)
01 | 66.67% (8 rolls) | 66.67% (8 rolls)
02 | 33.33% (4 rolls) | 33.33% (4 rolls)This time, they have failed an equal number of times (0), and been able to activate upgrades an equal number of times (4). Both characters have also suffered 8 strain. The difference here is how many destiny points they spent. The Light-sider has spent 7 Destiny Points, while the Dark-sider has spent 5 Destiny Points. A 16.67% advantage is Destiny Point expenditure to the Dark-sider. The Light-sider has also gained 8 conflict; the weight of this is entirely subjective and depends on the character, so we'll treat this as a general "negative point" for the Light-sider. Final results is that the Light-sider had to spend more Destiny Points and suffered unwanted conflict for the exact same result as a Dark-sider.
Okay, that's Force rating 1, let's do the same for Force rating 2.
First Test (aligned pips only):
Pips | Light | Dark
00 | 34.03% (49 rolls) | 17.36% (25 rolls)
01 | 19.44% (28 rolls) | 41.67% (60 rolls)
02 | 31.94% (46 rolls) | 31.94% (46 rolls)
03 | 0 8.33% (12 rolls) | 0 8.33% (12 rolls)
04 | 0 6.25% ( 0 9 rolls) | 00 .69% ( 0 1 roll)Here, the Light-sider failed 49 times and the Dark-sider failed 25 times (16.67% advantage to Dark). Light activated 97 upgrades, while Dark activated 73 upgrades (14.12% advantage Light). Notably, both characters rolled 2 useable pips and 3 useable pips the exact same amount of times. The difference came in the rarer 4 useable pips; the cost for the Dark side's ease of use is that it occasionally falls short of the results achievable by those who follow the disciplined path. Again, both characters suffered 0 strain.
So now for the test where the characters spend Destiny Points. I'll dispense with the charts here (what? Me? Dispense with charts? I must have been replaced with a body-snatcher! * ), as they'll obviously be exactly equal at all pip-levels. We're also going to be more discerning: the characters will only spend a Destiny Point and suffer strain if they roll fewer than 2 pips. They need that basic power and upgrade, but they want to conserve as much as possible, so they'll make do with that minimum level.
With that in mind, the Light-sider has spent a total of 77 Destiny Points and suffered 126 strain. The Dark-sider has spent 85 Destiny Points and suffered 110 strain. So Light has an advantage in spending fewer Destiny Points (4.94% advantage), but suffered more strain (6.78% advantage to Dark).
As we get higher in Force rating, the higher number of dice coupled with the even number of pips on each die starts to sharply pull both sides into obtaining an average roll result ( 2 / 3 * FR). The Light-sider will always fail a bit more than the Dark-sider, but also reach above the average a bit easier as well.
Hopefully this has been helpful. As we can see, both alignments suffer strain roughly equally, and while they have different areas they excel at, both Light-siders and Dark-siders are fairly equal. Not to toot my own horn, but I've done most of this math already in my Force Points thread, which @Daeglan has helpfully linked above. If you have further statistics questions, I'm happy to answer them! The important piece that I think gets lost is that both sides have the same numbers of pips on the Force die , which means over an arbitrary amount of time, they will be rolling the same number of useable Force Points. The only thing that changes is the distribution: Light-siders tend to get their points bunched up, and Dark-siders get them spread out. Making the Dark side easier to use consistently, but the Light-side able to make up for the inconsistency with bursts of inspiration.
* WE HAVE TAKEN THE TOGRUTA! SOON YOUR PUNY HU-MAN BODIES SHALL BE OURS! LONG SHALL THE SQUELZAAN ASCENDANCY RULE!
It is certain help to get more data and view points on the matter. However, my approach is different, as I'm looking at the probability of an exact outcome where both sides are involved in the outcome in a single roll, which I think should be obvious from my recent calculation, where yours only reflect the outcome for specific side respectively on a single roll, a single dicepool that is. Basically your results are for individual sides on individual rolls, where my results for an individual result that constains both.
To give an example, you have a result that says something specifically about the probability for getting 2 dark side points respectively when making rolls with a force rating of 2, then you have a result that says something specifically about the probability for getting 2 light side points respectively when making rolls with a force rating of 2.
My results says something specifically about the probability for a specific outcome where a certain amount dark side and light side points generated with a certain force rating.
Do you see the difference, and do you see why I would choose this method over the one that you used? Like wise what it can show what yours doesn't?
2 hours ago, Absol197 said:EDIT: Ah, after reading your most recent post (the one right above this one), I think I see the problem(s). There are three main points of yours that I'll try to address:
1) Light-side has a higher probability to get more pips.
This is entirely true. However, if they do not want to pay a cost, they also have a higher probability to get absolutely nothing they can use. Meaning they have to make the choice between A) Do nothing; or B) Pay a DP, suffer strain, and take conflict more often than a Dark-sider has to make the same choice.2) My previous charts are for the odds across an arbitrarily high number of rolls, not a single roll.
This one is more about statistics in general, but the odds of a result across a perfectly even statistical spread and the probability of that result on a single roll are exactly the same. So while I tend to express things as an average of all possible rolls, the numbers are just as valid being used as the probability of getting the result you're looking for on a single roll.3) My previous charts separate results for Dark and Light side, and do not provide combined results.
This was done for multiple reasons, the two primary ones being ease of readability and because most players only really care about the odds on rolling pips their character can use with no cost. There is a third set of charts for "grey" pips further down the thread, which gives the probability of the total number rolled regardless of color. I'll grant you that this does lack perfect granularity, as depending on which side of the Force you are on, the strain cost you'd be paying to access all those pips will vary. Once again, this was done to make the chart easier to read, and because I assumed that if you're spending a Destiny Point to get access to opposite-alignment pips you were planning on spending as much strain as possible anyway. However, I can confirm that the expected strain cost will average out over a character's life time. Dark-side results cling strongly to the average, so using them as a baseline, Light-siders will spend less for high-pip results, and spend more during the more frequent times they fail, balancing the scales.
1) Exactly, and that is a consequence of the assymetrical point spread and in my opinion is what fundamentally imbalances it - the assymmetrical point spread.
2) Just be sure that we're not misunderstanding each other here because of differences in the terminology we use, when I say "a single roll" I'm litterally talking about rolling whatever is in the dice pool, even if that is a single dice. You say that the previous charts are for the odds across an arbitrary high number of rolls, not a single roll, are you here talking about an arbitrary amount for sampling or do you treat rolling each dice pool as a single roll?
How so can they be just as valid if they're expressed as a statistical average rather than a probability? Also, the numbers I have been looking for includes both types and amount of points in the result, which yours does not include.
3) Yes, but that chart doesn't specify what outcome it specifically was, my reasons for doing these calculations aren't to find numbers to aid my play, but to figure out where the balance is weighted towards more specifically, because I can tell that because of the assymmetry it's around the averages. But also to see if was actually reasonably balanced. But, I don't think basing balance around averages makes for good balance, especially because when you hit the extremes and you keep hitting the extremes, that is where it potentially can be a bad experience for the player(s).