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atgxtg
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 Posted: Thu Jun 30, 2011 3:14 pm Post subject: |
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| crmcneill wrote: | | atgxtg wrote: | | Well, for starter's there is no law of averages, but... |
Maybe not officially, but if you roll a 2D, the roll you are most likely to come up with is a 7 (a 1 in 6 chance) with the odds decreasing for each number value the further away you get from 7, until you only have a 1 in 36 chance of rolling a 2 or a 12. Garhkal, correct me if I'm wrong, but I'm pretty sure what he meant by Law of Averages is that, when rolling multiple dice, the odds are in favor of rolling an "average" number. Therefore, if an NPC has a Command skill of 6D+2, his most likely result on a roll of 6D is 23. That number is reached by dividing his skill up into 2D increments (3 of them). Since the most likely roll on a 2D is 7, multiply 3 x 7, then add the 2 pips for the result. |
That's probability. And technically you are most likely NOT to come up with a 7. (Then is a 5/6 chance of any other value)..
What the "law of averages" is that the outcomes of random events will even out. That is, if someone is rolling poorly for a while they will eventually roll "hot" and it will average out.
That isn't true.The law of independent trails means that previous outcomes have no bearing on future results, IF the results are random.
A good example is with flipping a coin. If you flip a coin 100 times, you wold expect roughly half the results to be "heads". Nowif you got something like 75 head outs of 100, it does not mean that if you keep flipping the coin it will eventually even out. So if you flipped the coin another 100 times you should not expect it to even out to around 100 head out of 200 tosses. If the coin was truely random, ten you should expect about a 50-50 result in the second batch for arond a 125-75 total.
In fact, the original result of 75/25 suggests that the results are not entirely random, but might be biases in some way, and if anything, the trend should continue. |
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CRMcNeill
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| Posted: Thu Jun 30, 2011 3:30 pm Post subject: |
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| atgxtg wrote: | | That's probability. And technically you are most likely NOT to come up with a 7. (Then is a 5/6 chance of any other value).. |
But the odds of rolling any other number are lower than the odds of rolling a 7. The actual odds work out to:
7 = 1 in 6
6 or 8 = 1 in 7.2
5 or 9 = 1/9
4 or 10 = 1/12
3 or 11 = 1/18
2 or 12 = 1/36
You can argue with Garhkal's terminology, but the theory is correct. Even if there is a 5 in 6 chance that a number other than 7 will be rolled on a 2D, it is still the most probable outcome, with the probability against a number being drawn increasing dramatically the further away you get from the median value.
| Quote: | | In fact, the original result of 75/25 suggests that the results are not entirely random, but might be biases in some way, and if anything, the trend should continue. |
That might be true for rolling 1D, but that is the only D value where the number generated has even chance of being a number between 1 and 6. Once multiple dice are introduced, the probability of rolling a number closer to the middle value is the most likely result.
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Bren
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| Posted: Thu Jun 30, 2011 5:10 pm Post subject: |
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| Quote: | | Um, what does RAW mean? I'm reading it a lot around here. |
It's forum jargon. You are neither the first, nor the last that will need to ask. About this time last year I had to ask the same question. Though I suppose we could add a definitions page to make it easier for new comers.
It stands for Rules As Written - in other words what the WEG rules say, unless otherwise specified this is the Star Wars Roleplaying Game Second Edition Revised and Expanded rule book. |
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Bren
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| Posted: Thu Jun 30, 2011 5:43 pm Post subject: |
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| crmcneill wrote: | The actual odds work out to:
7 = 1 in 6
6 or 8 = 1 in 7.2
5 or 9 = 1/9
4 or 10 = 1/12
3 or 11 = 1/18
2 or 12 = 1/36 |
I find it much simpler to maintain the common denominator of 36. It also makes it easier to observe the probability pattern.
2 = 1/36
3 = 2/36
4 = 3/36
5 = 4/36
6 = 5/36
7 = 6/36
8 = 5/36
9 = 4/36
10 = 3/36
11 = 2/36
12 = 1/36
So the odds of rolling 7 or better on 2D is (6+5+4+3+2+1)/36 = 21/36 ~ 58% and the odds of rolling less than 7 are (5+4+3+2+1)/36 = 15/36 ~ 42%.
So I would argue that it is only a bit better than 50-50 that the 2D skill rolls a seven. And in fact as the number of dice increase the probability of rolling the average or expected value or above will approach a probability of 50%. Garhkal seems to be assuming that a chain of 3 NPCs all make a roll that is equal to or greater than 15 just because the expected or average value for their command skill is greater than 15. But that is actually a pretty big assumption. To make the probabilities easier I will change the skills to even dice, but that won't really change the result. I will reference the February D6 Magazine that had a nice table of probabilities for succeeding (and failing) different difficulties for different numbers of D6.
Captain Command 6D Probability of success = 88%
Gunnery Officer Command 5D Probability of success = 73%
Gun Pit Officer Command 5D Probability of success = 73%
Gun Crew Officer Command 4D Probability of success = 46%
So the odds that all the officers above the Gun Crew Officer make their rolls are 88% x 73% x 73% = 47%. So the odds are 53% that at least one of the officers above the crew chief in the chain of command fails his command roll.
Note that the odds that all four officers make their command rolls is about 22% or less than 1 in 4.
| Quote: | | You can argue with Garhkal's terminology, but the theory is correct. |
If someone can tell me what the theory is, I'd have a pretty good idea of how to prove it true (or false) given the typical assumptions for simple probabilities. |
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garhkal
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| Posted: Thu Jun 30, 2011 5:56 pm Post subject: |
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| vanir wrote: |
Um, what does RAW mean? I'm reading it a lot around here.
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Rules As Written.
WHAT it says in the book.
| atgxtg wrote: |
As far as the rest goes, the big problem is that the command bonuses don't stack. When you do a combined action, the guy who gets the bonus must be one of the guys being commanded. So the Captain can't give a bonus to the gunnery soldier who ends up taking the shot.
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I have yet to see anything saying they can't.
| crmcneill wrote: | | atgxtg wrote: | | Well, for starter's there is no law of averages, but... |
Maybe not officially, but if you roll a 2D, the roll you are most likely to come up with is a 7 (a 1 in 6 chance) with the odds decreasing for each number value the further away you get from 7, until you only have a 1 in 36 chance of rolling a 2 or a 12. Garhkal, correct me if I'm wrong, but I'm pretty sure what he meant by Law of Averages is that, when rolling multiple dice, the odds are in favor of rolling an "average" number. Therefore, if an NPC has a Command skill of 6D+2, his most likely result on a roll of 6D is 23. That number is reached by dividing his skill up into 2D increments (3 of them). Since the most likely roll on a 2D is 7, multiply 3 x 7, then add the 2 pips for the result. |
Yup. Just like if i roll 4d4, my average would be (2.5 per d4 or 5 per 2).. so 4d4 averages to 10.
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CRMcNeill
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| Posted: Thu Jun 30, 2011 6:22 pm Post subject: |
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One could always take a page from WOTC's book. Instead of "Taking a 10", you could "Take an Average" (or whatever word you want to use), so that rather than rolling for every little thing, if your "average" is good enough to clear the difficulty number, you pass automatically...
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Bren
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| Posted: Fri Jul 01, 2011 10:27 am Post subject: |
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| crmcneill wrote: | | One could always take a page from WOTC's book. Instead of "Taking a 10", you could "Take an Average" (or whatever word you want to use), so that rather than rolling for every little thing, if your "average" is good enough to clear the difficulty number, you pass automatically... |
In that case you should use a lower number than 3.5 for each die, say a 2 or 3 per die. Otherwise players would only roll when they thought they needed a lucky roll higher than the average. |
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CRMcNeill
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| Posted: Fri Jul 01, 2011 11:41 am Post subject: |
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| Bren wrote: | | In that case you should use a lower number than 3.5 for each die, say a 2 or 3 per die. Otherwise players would only roll when they thought they needed a lucky roll higher than the average. |
I was just throwing out a random suggestion, but if I did use this rule, I would probably stick to the 7 for every 2D, or use the 3 value at the lowest. After all, w/ WOTC, they are assuming a result of 10 on a single D20, which has a probability of 1 in 20, as opposed to the 1 in 6 possibility of a 7 on a 2D.
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garhkal
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| Posted: Fri Jul 01, 2011 1:08 pm Post subject: |
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I could see 3 being the 'take 3' route..
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CRMcNeill
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| Posted: Fri Jul 01, 2011 1:12 pm Post subject: |
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| garhkal wrote: | | I could see 3 being the 'take 3' route.. |
Works for me
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"No set of rules can cover every situation. It's expected that you will make up new rules to suit the needs of your game." - The Star Wars Roleplaying Game, 2R&E, pg. 69, WEG, 1996.
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Bren
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| Posted: Fri Jul 01, 2011 2:53 pm Post subject: |
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| crmcneill wrote: | | Bren wrote: | | In that case you should use a lower number than 3.5 for each die, say a 2 or 3 per die. Otherwise players would only roll when they thought they needed a lucky roll higher than the average. |
I was just throwing out a random suggestion, but if I did use this rule, I would probably stick to the 7 for every 2D, or use the 3 value at the lowest. After all, w/ WOTC, they are assuming a result of 10 on a single D20, which has a probability of 1 in 20, as opposed to the 1 in 6 possibility of a 7 on a 2D. |
Is that a 10 before or after modifications?
The 1/6 vs 1/20 probability of the number isn't really relevant. The expected value on a D20 is 10.5, so taking 10 is rounding down from 10.5. That would be similar to assuming 3 per D6 rather than 3.5 per D6. |
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CRMcNeill
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Location: Redding System, California Sector, on the I-5 Hyperspace Route.
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| Posted: Fri Jul 01, 2011 3:36 pm Post subject: |
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| Bren wrote: | | Is that a 10 before or after modifications? |
Before. The modifiers are usually pretty constant (at least for skill levels)
| Quote: | | The 1/6 vs 1/20 probability of the number isn't really relevant. The expected value on a D20 is 10.5, so taking 10 is rounding down from 10.5. That would be similar to assuming 3 per D6 rather than 3.5 per D6. |
Fair enough. Garhkal suggested using the 3, and that seems as good a number as any.
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"No set of rules can cover every situation. It's expected that you will make up new rules to suit the needs of your game." - The Star Wars Roleplaying Game, 2R&E, pg. 69, WEG, 1996.
The CRMcNeill Stat/Rule Index
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Bren
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| Posted: Fri Jul 01, 2011 3:51 pm Post subject: |
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| crmcneill wrote: | | Fair enough. Garhkal suggested using the 3, and that seems as good a number as any. |
In general that seems too easy to me in general since it turns what may be only a 50% chance into an automatic success.
I guess if I want to advance the plot without taking the time to roll things out or risking failure or complications, letting the PCs take a 3 on every dice is a pretty good way to do that. |
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CRMcNeill
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| Posted: Fri Jul 01, 2011 4:06 pm Post subject: |
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| Bren wrote: | | I guess if I want to advance the plot without taking the time to roll things out or risking failure or complications, letting the PCs take a 3 on every dice is a pretty good way to do that. |
I think there are restrictions in the WOTC, like that it can't be used in combat and the action takes twice as long as normal. And that doesn't mean the GM can't throw in complications at dramatically important moments
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The CRMcNeill Stat/Rule Index
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Fallon Kell
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| Posted: Fri Jul 01, 2011 4:17 pm Post subject: |
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I'm not sure this is my cup o' tea, but even if it were, I would make them roll the chance die normally.
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