# Oy Vey - I think I won the "lottery"

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### #1 kryzak

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Posted 30 August 2014 - 10:24 PM

Has this happened to anyone before?  Based on the awesome X-Wing Battle Computer (on Android), the mathwing probability of 5 dice at R1 with TL+F against 3 agility unmodified is almost 0%.  Happened to me today (unfortunately as the 5 dice attacker), just had to share.

Edited by kryzak, 30 August 2014 - 11:46 PM.

### #2 MajorJuggler

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Posted 30 August 2014 - 11:30 PM

Hm, looks like that App uses a Monte Carlo approach rather than getting the exact answer. The exact probability density function should be:

0 hits: 0.2431%

1 hit:  2.2177%

2 hits: 11.6508%

3 hits: 30.4892%

4 hits: 37.7186%

5 hits: 17.6806%

So yeah, that's that's a 1 in 400 chance. How did you get 5 dice attacking you? Jan Ors or Opportunist?

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### #3 kryzak

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Posted 30 August 2014 - 11:45 PM

Yeah, it uses Monte Carlo, you can actually see it happening as it gets closer and closer to the density function. Pretty neat tool for on the fly estimations!

Unfortunately, *I* was the one attacking with 5 dice.  Echo at R1 with TL from FCS and focus from Recon Specialist, attacking a TIE fighter without any mods.

In another round I got shot at by 2 TIEs at R3, unfortunately I didn't have any foci at the time, and in 2 attacks, 3 hits happened, and I rolled 0 evades in 10 dice (and only 4 eyeballs total).  I think each shot had an average of 0.20 hits, so it should have been an average of 0.40 that turned into 3 hits... not as bad as the 1 in 400 above, but still hurts.

### #4 kryzak

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Posted 30 August 2014 - 11:47 PM

Hm, looks like that App uses a Monte Carlo approach rather than getting the exact answer. The exact probability density function should be:

0 hits: 0.2431%

1 hit:  2.2177%

2 hits: 11.6508%

3 hits: 30.4892%

4 hits: 37.7186%

5 hits: 17.6806%

So yeah, that's that's a 1 in 400 chance. How did you get 5 dice attacking you? Jan Ors or Opportunist?

BTW, what program do you use to calculate exact probabilities of everything?  Excel?  That would be pretty neat to have something like that on hand.

### #5 MajorJuggler

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Posted 31 August 2014 - 12:14 AM

Hm, looks like that App uses a Monte Carlo approach rather than getting the exact answer. The exact probability density function should be:

0 hits: 0.2431%

1 hit:  2.2177%

2 hits: 11.6508%

3 hits: 30.4892%

4 hits: 37.7186%

5 hits: 17.6806%

So yeah, that's that's a 1 in 400 chance. How did you get 5 dice attacking you? Jan Ors or Opportunist?

BTW, what program do you use to calculate exact probabilities of everything?  Excel?  That would be pretty neat to have something like that on hand.

MATLAB. I wrote my own scripts. And I guarantee it computes it faster than using a Monte Carlo simulation, and the answer is always exact.

### #6 MajorJuggler

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Posted 31 August 2014 - 12:19 AM

In another round I got shot at by 2 TIEs at R3, unfortunately I didn't have any foci at the time, and in 2 attacks, 3 hits happened, and I rolled 0 evades in 10 dice (and only 4 eyeballs total).  I think each shot had an average of 0.20 hits, so it should have been an average of 0.40 that turned into 3 hits... not as bad as the 1 in 400 above, but still hurts.

Oh, and the PDF for one shot (2 dice + focus vs 4 dice) would be:

[0.6510    0.2632    0.0858]

The average damage is 0.43.

So I guess those were unfocused TIEs attacking? In which case the PDF is:

[0.7940    0.1678    0.0381]  = 0.2441 average damage

And for identical attacks you convolve that with itself to get:

[0.6304    0.2665    0.0888    0.0128    0.0015]

1.42% chance of getting 3+ hits.

### #7 kryzak

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Posted 31 August 2014 - 12:30 AM

BTW, what program do you use to calculate exact probabilities of everything?  Excel?  That would be pretty neat to have something like that on hand.

MATLAB. I wrote my own scripts. And I guarantee it computes it faster than using a Monte Carlo simulation, and the answer is always exact.

Haha, nice.  Used to work in that for many years.  Too bad there's no app for it.

In another round I got shot at by 2 TIEs at R3, unfortunately I didn't have any foci at the time, and in 2 attacks, 3 hits happened, and I rolled 0 evades in 10 dice (and only 4 eyeballs total).  I think each shot had an average of 0.20 hits, so it should have been an average of 0.40 that turned into 3 hits... not as bad as the 1 in 400 above, but still hurts.

Oh, and the PDF for one shot (2 dice + focus vs 4 dice) would be:

[0.6510    0.2632    0.0858]

The average damage is 0.43.

So I guess those were unfocused TIEs attacking? In which case the PDF is:

[0.7940    0.1678    0.0381]  = 0.2441 average damage

And for identical attacks you convolve that with itself to get:

[0.6304    0.2665    0.0888    0.0128    0.0015]

1.42% chance of getting 3+ hits.

They were unfocused TIEs, so the 0.24 is closer.

Wow, convolution, haven't heard that term in a long time.  Nice!

So another near 1% chance thing happening today.  I'm glad it's just a double fluke, because I went into the match with Echo+FCS+Recon+VI vs 5 AP TIE fighters pretty confident, and then next thing I know, I haven't damaged ANY of them after 4-5 rounds of shooting and I have 1 hull left.  I was like, "what just happened?"

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### #8 force kin

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Posted 31 August 2014 - 02:01 AM

...go on...

### #9 Krankenstein

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Posted 31 August 2014 - 03:21 AM

I was always curious if someone has ever tried playing a game without using dice? Instead always using the statistically most probable result in resolving attacks and evades. There is always the rounding up/down, but I would assume that it would be decided upon so that it is the same throughout the game.

Without going into a debate whether or not the game should be played this way, I'm more interested in what happened in such game. Was it faster? Balanced? How did it change your tactical thinking knowing exactly what would happen? Were you more cautious or reckless? Did it change your list building thinking, and how?

The reason I won't try it myself is that I suck at math IF you do try this, let me know how it went.

Edited by Krankenstein, 31 August 2014 - 03:22 AM.

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### #10 kryzak

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Posted 31 August 2014 - 03:36 AM

that might be a cool idea to try.  Using that Monte Carlo app, you can probably simulate a game like that pretty easily.  I do like some randomness in the game, since I don't want it to be too much like chess, but sometimes the variance is a little too great for my liking (probably because of the low amount of dice thrown, compared to a game like 40K), and once in a blue moon, something like today happens.

Granted, if everything is based on the average amount (rounded up or down), the game would still be more interesting than chess because you're still guessing what the other player is doing and you have many of the movement actions you can do.

### #11 MajorJuggler

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Posted 31 August 2014 - 09:01 AM

Ha ha, no there is definitely not an App for MATLAB. But there is a \$100 student license instead of paying \$3000 ;-)

Although, actually, you can make executables out of it, but that also costs licence \$\$\$ and it doesn't come with the student version.

### #12 TasteTheRainbow

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Posted 31 August 2014 - 09:21 AM

More importantly...

How did the game end?
Truth Matters. Math matters.
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### #13 hackshot

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Posted 31 August 2014 - 09:50 AM

Nothing can save you if you've offended the Dice Gods.

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### #14 Hobojebus

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Posted 31 August 2014 - 10:40 AM

Your numbers mean nothing, offer sacrifice to the dice gods listen not to these number wizards they will lead you astray my children.
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### #15 kryzak

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Posted 31 August 2014 - 10:48 AM

Ha ha, no there is definitely not an App for MATLAB. But there is a \$100 student license instead of paying \$3000 ;-)
Although, actually, you can make executables out of it, but that also costs licence \$\$\$ and it doesn't come with the student version.

Yeah, I remember when I got to use the free company version. It was pretty sweet.

More importantly...
How did the game end?

Not too well for me. We had to end the game because it went way over time with you neither of us being able to kill each other. I had 1 hull left and no there fluke agility dice result, but my attack dice results remained terrible. So the guy won based on points.

Looks like dice do matter.

Of course it matters, but most of the time you can mitigate and minimize issues. But when I offend the dice gods like I did here, no amount of skill or list building will save me. I'm just glad this doesn't happen often.

### #16 StevenO

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Posted 31 August 2014 - 01:53 PM

People win the lottery don't they?

Long odds can happen even if the nice figure happens to round to zero.  In an RPG what are the odds of rolling three straight 20s?  1/8000 or 0.0125%  Have you ever seen it happen?  Maybe.

### #17 kryzak

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Posted 01 September 2014 - 12:46 AM

People win the lottery don't they?

Long odds can happen even if the nice figure happens to round to zero.  In an RPG what are the odds of rolling three straight 20s?  1/8000 or 0.0125%  Have you ever seen it happen?  Maybe.

Of course, if it's a non-zero probability, it can happen.  Just partially venting and partially seeing if others have similar battle stories.

And no, I'm not lucky enough to roll or see someone roll 3 natural 20s.  I wish I did sometimes. ;-)

### #18 StevenO

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Posted 01 September 2014 - 12:42 PM

I was going to mention ability score arrays with d6s but it seems people don't like hearing about how insanely well the seem to beat the odds on a regular basis.

### #19 kryzak

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Posted 01 September 2014 - 12:56 PM

I was going to mention ability score arrays with d6s but it seems people don't like hearing about how insanely well the seem to beat the odds on a regular basis.

That makes me want to play some D&D... oh wait, I'm doing that tonight.

### #20 StevenO

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Posted 01 September 2014 - 01:16 PM

I was going to mention ability score arrays with d6s but it seems people don't like hearing about how insanely well the seem to beat the odds on a regular basis.

That makes me want to play some D&D... oh wait, I'm doing that tonight.

I still dabble in the previous editions of DnD but for me my favorite RPG by far is StarWars SAGA Edition.  In either place I see far too many people asking for "help me optimize my character" when they come it with stat arrays that a 1 percenter would find hard to swallow.  One of the last ones came in and while they were using a pretty crazy rolling method they had 18x3,17,15x2 all of which of course were better than average with the rolling method.

Edited by StevenO, 01 September 2014 - 01:18 PM.

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