I quickly read the paper from Notre Dame and have a question as it relates to X-Wing. Are we only interested with the possible combinations of dice results or the permutations? My gut reaction is combinations. We don't care what order the evades or hits come up only that they do. Am I right? If not I need two more cups of coffee and more paper.

I was actually thinking of combinations rather than permutations myself. That's what I've tended to use. But honestly I'd have to rely on someone with a little more experience than myself.

I quickly read the paper from Notre Dame and have a question as it relates to X-Wing. Are we only interested with the possible combinations of dice results or the permutations? My gut reaction is combinations. We don't care what order the evades or hits come up only that they do. Am I right? If not I need two more cups of coffee and more paper.

I was actually thinking of combinations rather than permutations myself. That's what I've tended to use. But honestly I'd have to rely on someone with a little more experience than myself.

I was thinking about craps dice myself. Don't ask, it's too early in the morning.

I'm terrible at probability and it's cousins, as I can't keep them straight. Never kept it straight in school. Could anyone direct me somewheres to learn them again?

There are a couple of good ones on Binomial Distribution. Wolfram has one: http://mathworld.wolfram.com/BinomialDistribution.html

And here is a PDF from Notre Dame: https://www3.nd.edu/~rwilliam/stats1/x13.pdf

For starters

There's also a site called STAT TREK which I found interesting.

I quickly read the paper from Notre Dame and have a question as it relates to X-Wing. Are we only interested with the possible combinations of dice results or the permutations? My gut reaction is combinations. We don't care what order the evades or hits come up only that they do. Am I right? If not I need two more cups of coffee and more paper.

I was actually thinking of combinations rather than permutations myself. That's what I've tended to use. But honestly I'd have to rely on someone with a little more experience than myself.

I was thinking about craps dice myself. Don't ask, it's too early in the morning.

Just a caution: you'll find a lot out there on dice that assume you're adding the results together. That's interesting to me, and it's terribly relevant to a game like D&D--but it doesn't actually help us very much, except in the very general sense of understanding probability and random variables better.

Our dice are more like weighted coin tosses. For instance, if you're looking at attack dice and your ship has a focus token, the easiest way to treat each die is that it has a 75% chance of coming up as a "success" (and a 25% chance of coming up not a success).

More specifically, a set of dice can meaningfully be modeled as a binomial random variable .

I quickly read the paper from Notre Dame and have a question as it relates to X-Wing. Are we only interested with the possible combinations of dice results or the permutations? My gut reaction is combinations. We don't care what order the evades or hits come up only that they do. Am I right? If not I need two more cups of coffee and more paper.

I was actually thinking of combinations rather than permutations myself. That's what I've tended to use. But honestly I'd have to rely on someone with a little more experience than myself.

I was thinking about craps dice myself. Don't ask, it's too early in the morning.

Just a caution: you'll find a lot out there on dice that assume you're adding the results together. That's interesting to me, and it's terribly relevant to a game like D&D--but it doesn't actually help us very much, except in the very general sense of understanding probability and random variables better.

Our dice are more like weighted coin tosses. For instance, if you're looking at attack dice and your ship has a focus token, the easiest way to treat each die is that it has a 75% chance of coming up as a "success" (and a 25% chance of coming up not a success).

More specifically, a set of dice can meaningfully be modeled as a binomial random variable .

How can you be so coherent this early in the morning? It would've taken me until noon to figure that out!

I quickly read the paper from Notre Dame and have a question as it relates to X-Wing. Are we only interested with the possible combinations of dice results or the permutations? My gut reaction is combinations. We don't care what order the evades or hits come up only that they do. Am I right? If not I need two more cups of coffee and more paper.

I was actually thinking of combinations rather than permutations myself. That's what I've tended to use. But honestly I'd have to rely on someone with a little more experience than myself.

I was thinking about craps dice myself. Don't ask, it's too early in the morning.

Just a caution: you'll find a lot out there on dice that assume you're adding the results together. That's interesting to me, and it's terribly relevant to a game like D&D--but it doesn't actually help us very much, except in the very general sense of understanding probability and random variables better.

Our dice are more like weighted coin tosses. For instance, if you're looking at attack dice and your ship has a focus token, the easiest way to treat each die is that it has a 75% chance of coming up as a "success" (and a 25% chance of coming up not a success).

More specifically, a set of dice can meaningfully be modeled as a binomial random variable .

Depending on how accurate we want to be, we could have it trinomial (for crits) or tetranomial (is it just polynomial at that point?) for the focus. But if we ignore crits, a 50-50 native and 25-75 focused makes the math about as easy as it can be while still being useful.

One handy thing for overall probabilities to avoid the "adding chances" problem in the OP, is to do your math on the odds of it not happening. No crits is a 7/8ths chance on each die, so you can roll three dice and have a (7/8)^3 chance of not getting a crit. This can be written as 7^3/8^3, or 343/512. This works out to near as makes no difference 2/3rds. This also lets you ignore the discussion about combinations or permutations!

The next big thing to remember is that this doesn't mean you get a crit every three rolls. These things aren't conditional. It is something called the gambler's fallacy. The previous roll has no bearing on the odds of this roll, so it is still 2/3rds chance to not get a crit every time you roll. However, counterintuitively, this means over enough rolls you should get a crit a third of the time.

How can you be so coherent this early in the morning? It would've taken me until noon to figure that out!

Mainlined caffeine.

Who would have thought that a post about the odds of rolling dice (well essentially that's what it is) on a gaming site could generate 6 pages of discussion about binomial distribution. Makes sense really, but in a casual or passing thought it can seem a bit extreme. I doubt that I could share this post with my co-workers or several of my friends without getting either blank stares or some odd comment about geeks and toys.

Who knew?

I did a bunch of college statistics, and now I am teaching math to sixth graders. It really gives a sense of perspective on math. You can ignore it, you can look at the basics, and you can dig down into the details. The deeper you look the better you understand things, but no one ever has to look.

Trigonometry is not required for a car mechanic, but a car mechanic can use trigonometry to find out if a part will fit without trying a few different ways and maybe giving up.

You can buy a couch set and see if it fits in the living room (and keep the receipt if it doesn't) or you can measure and add and estimate and decide if it is too big for the space.

You can throw your dice and hope for the best, or you can do a bit of probability to know your chances of getting that best, and if it is maybe worth it to be defensive.

[...]

You can throw your dice and hope for the best, or you can do a bit of probability to know your chances of getting that best, and if it is maybe worth it to be defensive.

The thing about 'throwing the dice and hoping for the best' is getting a feel for a Star Warsy game. Getting to know Star Wars, the ships and abilities, actually learning the game as opposed to dissecting it. I could most likely do the math, I've even made up an spread sheet where I enter the dice, and get the odds. I'm no where near as good as many on here. But regardless of that, that isn't what's fun for me.

Of course I like to know that Stealth is better on high agility ships or that an Evade is better than a focus when I'm on defense. But if I need to know the math to have fun then that's just a different game and not a game for everyone.

I'm not saying math or micro efficiency is a bad thing and that is something that certainly drives the tournament thinking. I'm just saying that to "throw the dice and hope for the best", and "do a bit of probability" are not the only options to having fun.

How can you be so coherent this early in the morning? It would've taken me until noon to figure that out!

Mainlined caffeine.

I have three tricks:

1. Very hot showers in the morning.
2. Orange juice instead of coffee.
3. Be woken up by a happy toddler climbing into your bed for a hug and a kiss.

[...]

You can throw your dice and hope for the best, or you can do a bit of probability to know your chances of getting that best, and if it is maybe worth it to be defensive.

The thing about 'throwing the dice and hoping for the best' is getting a feel for a Star Warsy game. Getting to know Star Wars, the ships and abilities, actually learning the game as opposed to dissecting it. I could most likely do the math, I've even made up an spread sheet where I enter the dice, and get the odds. I'm no where near as good as many on here. But regardless of that, that isn't what's fun for me.

Of course I like to know that Stealth is better on high agility ships or that an Evade is better than a focus when I'm on defense. But if I need to know the math to have fun then that's just a different game and not a game for everyone.

I'm not saying math or micro efficiency is a bad thing and that is something that certainly drives the tournament thinking. I'm just saying that to "throw the dice and hope for the best", and "do a bit of probability" are not the only options to having fun.

I like math, and I spend a lot of time doing math, so it's natural to me to do it that way. You don't need to know all the math to play the game, or even to be good at the game.

That is, math is absolutely the right way to look at the game. It's just not the only right way.

That is, math is absolutely the right way to look at the game. It's just not the only right way.

Do the math, but don't look like you're doing the math...

How can you be so coherent this early in the morning? It would've taken me until noon to figure that out!

Mainlined caffeine.

I have three tricks:

• Very hot showers in the morning.
• Orange juice instead of coffee.
• Be woken up by a happy toddler climbing into your bed for a hug and a kiss.

[...]

You can throw your dice and hope for the best, or you can do a bit of probability to know your chances of getting that best, and if it is maybe worth it to be defensive.

The thing about 'throwing the dice and hoping for the best' is getting a feel for a Star Warsy game. Getting to know Star Wars, the ships and abilities, actually learning the game as opposed to dissecting it. I could most likely do the math, I've even made up an spread sheet where I enter the dice, and get the odds. I'm no where near as good as many on here. But regardless of that, that isn't what's fun for me.

Of course I like to know that Stealth is better on high agility ships or that an Evade is better than a focus when I'm on defense. But if I need to know the math to have fun then that's just a different game and not a game for everyone.

I'm not saying math or micro efficiency is a bad thing and that is something that certainly drives the tournament thinking. I'm just saying that to "throw the dice and hope for the best", and "do a bit of probability" are not the only options to having fun.

I like math, and I spend a lot of time doing math, so it's natural to me to do it that way. You don't need to know all the math to play the game, or even to be good at the game.

That is, math is absolutely the right way to look at the game. It's just not the only right way.

Hot showers after breakfast.

OJ upsets my stomach hence the coffee.

No kids, fortunately for them.

[...]

You can throw your dice and hope for the best, or you can do a bit of probability to know your chances of getting that best, and if it is maybe worth it to be defensive.

The thing about 'throwing the dice and hoping for the best' is getting a feel for a Star Warsy game. Getting to know Star Wars, the ships and abilities, actually learning the game as opposed to dissecting it. I could most likely do the math, I've even made up an spread sheet where I enter the dice, and get the odds. I'm no where near as good as many on here. But regardless of that, that isn't what's fun for me.

Of course I like to know that Stealth is better on high agility ships or that an Evade is better than a focus when I'm on defense. But if I need to know the math to have fun then that's just a different game and not a game for everyone.

I'm not saying math or micro efficiency is a bad thing and that is something that certainly drives the tournament thinking. I'm just saying that to "throw the dice and hope for the best", and "do a bit of probability" are not the only options to having fun.

Yeah! Making pew pew noises and actually barrel rolling my ships when I barrel roll is the best part. But eventually I don't have fun if I never win. Knowing the math can give me an edge. It doesn't make it more fun, but it can give me a little bit of an advantage.

There is a cool application of statistics called Bayesian Probabilities. It makes you weight things based on prior knowledge. In practice this pretty much means going with your gut, but making sure you think through everything that can have an effect first. We are really good at instinctively doing math. No one does physics to catch a ball, but physics is happening. No one does math to drive around a corner fast, but math is happening. No one needs to do math to roll dice, but math can help you guess what the roll will tend to be.

The people that like math will do the math anyway, and then it helps us program a computer to do what we can do by instinct and practice. Knowing the math can help, but not knowing the math and going with your gut will often get the similar results. But understanding the math makes your gut better!

You don't need to know all the math to play the game, or even to be good at the game.

Speaking as someone who is not a math guy... I love that people have done the math for me.

Even though I can't calculate the odds of getting 3 <hit> results, it's handy to know what they are. Because if you know the odds, that will improve your game. It really comes down to how much information you have when you make your decision.

The more information you have and can act upon, the better your decisions are likely to be. Sure sometimes you'll have your Fell one shot at range 3 behind a rock. but knowing how unlikely that is to happen is going to pay off far more often than not.

Likewise, knowing that my chance to get at least 1 hit with Wedge at range 1 on a uncloaked Phantom with 1 damage card, is really pretty good, is going to impact my decision on how to move him and what to do with him.

You don't need to know all the math to play the game, or even to be good at the game.

Speaking as someone who is not a math guy... I love that people have done the math for me.

Even though I can't calculate the odds of getting 3 <hit> results, it's handy to know what they are. Because if you know the odds, that will improve your game. It really comes down to how much information you have when you make your decision.

The more information you have and can act upon, the better your decisions are likely to be. Sure sometimes you'll have your Fell one shot at range 3 behind a rock. but knowing how unlikely that is to happen is going to pay off far more often than not.

Likewise, knowing that my chance to get at least 1 hit with Wedge at range 1 on a uncloaked Phantom with 1 damage card, is really pretty good, is going to impact my decision on how to move him and what to do with him.

I like this above. I can do the math. I don't want to. I'm doing it all the time. I'd rather someone who loves math make these pretty tables I can down load that shows attack; attack + focus; attack + target lock; against 1 die; 2 dice; 2 dice plus evade or focus or... and so on. You get the point.

I enjoy math and yep, occasionally do problems just for fun. You see my favorite one in an earlier post. But I like just playing sometimes too. I play so I can escape reality.

Whoo Hoo, Pew, Pew, don't get cocky kid

Happy May the fourth.

I'm terrible at probability and it's cousins, as I can't keep them straight. Never kept it straight in school. Could anyone direct me somewheres to learn them again?

There are a couple of good ones on Binomial Distribution. Wolfram has one: http://mathworld.wolfram.com/BinomialDistribution.html

I was most disturbed by another link on this website which said "Recreational Mathematics".

Psst, I've got some £10 bags of illegal equations, guaranteed to blow your mind.

Cheers

Baaa

Three of them are already spoken for, right?

Not too many people got the joke. :-(

I am a professional poker player. I see the same things in poker that I see in X-Wing.

Human beings see patterns where none truly exist, and rarely do they understand what "the long run" really means. It just appears to them that they have taken a "horrible beat", when in reality, it is often a probable event that truly occurs.

That's funny you said this. I play and deal Poker. It cracks me up when someone complains about the dice when you just lost a $1000 pot to a gut shot.

I did the maths; I know the exact odds of getting an X amount of evades or hits depending on whether I have a target lock, focus, evade or autothrusters on hand. Simply knowing part of the odds has influenced my piloting decisions in order to take maximum advantage of most tactical situations...

At the same time, I somehow believe that my dice require... no... demand their fill of ritual ionisation of targets so that they can be captured, preferably those of high PS. Only then can I turn in the bounties and then... my dice will be satisfied and continue rewarding me with magnificent predator rerolls. Math meets irrational belief and somehow coexist.

Oh well, sanity is relative to the people around you, so in my meta, I'm still good

I'd like to know how you came up with the numbers using both TL an focus. Remember us poor non-science people. The hardest math I had to do in the last 18 years was using Hardy Cross and the Hazen-Williams formula.

you use the binomial distribution with a probability of 0.5 for natural hits/crits, but with TL and focus you do the binom. distribution with a probability of 0.94.

why 0.94? because the chance of rolling a blank is 0.25, so the chance of rolling anything but a blank is 0.75.

so if you can reroll the die, you get a chance of either a success on the first try, 0.75, or a blank on the first try 0.25, times a success on the reroll, 0.75

so it's 0.75+0.25*0.75=0.94

you add chances that are x OR y and multiply chances that are x AND y

Ok, now I'm really lost. If the first two numbers in the equation represent the OR part and the third number represents the AND doesn't that come out to 0.75? (1*0.75) Please excuse this Math Challenged Fool.

There are four "successes" (hits and crits) on the red dice, and two focus results we can convert into successes with a focus token. The probability of getting a success is 4/8 + 2/8 = 3/4 or 0.75. The probability of a blank result is 2/8 or 0.25.

If you get a blank result, you reroll it. (It's a new, independent roll.) So in order to get a success, you get one without needing a reroll, or you get one by rolling a blank and then rolling a success.

That makes the probability 0.75 + (0.25 x 0.75).

So? If one die has a 93.75% chance using a Focus and Target Lock (0.75 + (0.25 x 0.75)).

Does three dice have a:

• 82.40% of all three scoring a hit
• 16.48% of two of three scoring a hit
• 1.10% of only one scoring a hit
• 0.02% of scoring no hits at all or 1 out of 4096

I'd like to know how you came up with the numbers using both TL an focus. Remember us poor non-science people. The hardest math I had to do in the last 18 years was using Hardy Cross and the Hazen-Williams formula.

you use the binomial distribution with a probability of 0.5 for natural hits/crits, but with TL and focus you do the binom. distribution with a probability of 0.94.

why 0.94? because the chance of rolling a blank is 0.25, so the chance of rolling anything but a blank is 0.75.

so if you can reroll the die, you get a chance of either a success on the first try, 0.75, or a blank on the first try 0.25, times a success on the reroll, 0.75

so it's 0.75+0.25*0.75=0.94

you add chances that are x OR y and multiply chances that are x AND y

Ok, now I'm really lost. If the first two numbers in the equation represent the OR part and the third number represents the AND doesn't that come out to 0.75? (1*0.75) Please excuse this Math Challenged Fool.

There are four "successes" (hits and crits) on the red dice, and two focus results we can convert into successes with a focus token. The probability of getting a success is 4/8 + 2/8 = 3/4 or 0.75. The probability of a blank result is 2/8 or 0.25.

If you get a blank result, you reroll it. (It's a new, independent roll.) So in order to get a success, you get one without needing a reroll, or you get one by rolling a blank and then rolling a success.

That makes the probability 0.75 + (0.25 x 0.75).

So? If one die has a 93.75% chance using a Focus and Target Lock (0.75 + (0.25 x 0.75)).

Does three dice have a:

• 82.40% of all three scoring a hit
• 16.48% of two of three scoring a hit
• 1.10% of only one scoring a hit
• 0.02% of scoring no hits at all or 1 out of 4096

All the dice hitting is going to be (.9375)^(number of dice) for those of you keeping score at home. All misses is going to be (1-.9375)^(number of dice). Looks like those numbers are right to me!

Yeah for me

Okay I can do the distribution well enough, even to include focus and Target Lock.

I can do the distribution on Green Dice, even with focus too.

But

A) How do I calculate the odds of both.

X Red Dice to X Green Dice = x%

B) How do I add the Evade?

Cheers

Baaa

Okay I can do the distribution well enough, even to include focus and Target Lock.

I can do the distribution on Green Dice, even with focus too.

But

A) How do I calculate the odds of both.

X Red Dice to X Green Dice = x%

B) How do I add the Evade?

A) You change the sign on the distribution of successes on the green dice, and take the convolution sum of the two distributions (with negative results set to 0).

B) It depends. If you're interested in just the outcome of a single attack, just add 1 to all the possible results (instead of a minimum of 0 evades, you have a minimum of 1 evade). If you're interested in the value of the evade token across several attacks, it's best to build a computer simulation.