Board 8 > A probability question

(+) Yeah! (+)

Hello all, I'm trying to find out the probabilities of certain outcomes in this X-wing Miniatures game I play, so I'm hoping someone who's good at calculating this sort of thing can figure out the following for me:

The parameters:
There are 2 types of dice, attack and defense. Both are D8's, with the following sides:
Attack: 3 hit symbols, 1 crit symbol, 2 focus symbols, 2 blank symbols
Defense: 3 evade symbols, 2 focus symbols, 3 blank symbols
Hits and crits are 1 damage each, evade symbols cancel 1 hit each. Any hits/crits left uncanceled are 1 damage per dice. Blanks do nothing. Focuses are variable (explained below). For the purposes of these scenarios, crits are basically just hits.

Scenario 1:
If I roll 3 attack dice, and my opponent rolls 2 defense dice, what are the odds of dealing at least 1 damage? Please count "focus" symbols as "blank" symbols.

Scenario 2: The above, but 4 attack dice vs 3 defense dice.

Scenario 3: 3 attack dice vs 2 defense dice. Please count "focus" symbols as "hits" for attack and "evades" for defense.

Scenario 4: The above, but 4 attack dice vs 3 defense dice.

Or if you don't want to actually do the math, if you can tell me what the formulas would be here I can also follow those instructions and calculate it myself. Thank you!
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Oh

Ummm

Bump?
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let me see if I can work through this for scenario 1 at least

0 DEF: 25/64 (5/8 x 5/8)
1 DEF: 30/64 (3/8 x 5/8) + (5/8 x 3/8)
2 DEF: 9/64 (3/8 x 3/8)

0 ATT: 1/8 (1/2 x 1/2 x 1/2)
1 ATT: 3/8 (Hit Miss Miss, Miss Hit Miss, and Miss Miss Hit, all at 1/8 each)
2 ATT: 3/8 (HHM, HMH, MHH, 1/8 each)
3 ATT: 1/8 (1/2 x 1/2 x 1/2)

25/64 x 7/8 = 175/512 is the % of getting and beating 0 def
30/64 x 4/8 = 120/512 for 1 def
9/64 x 1/8 = 9/512 for 2 def

Add that up and it's 304/512 if I'm not confused, or 59.375% of at least 1 hit
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think you've missed critical hits on offense, tom
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Tom got the number I got for 3v2 as well.
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I have 59.38%, 61.67%, 83.94%, and 87.17%. Excel is very helpful for this by the way.
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I counted them as hits (right?)
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my bad - assumed they were worth 2 damage instead of 1
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Sceptilesolar posted...

I have 59.38%, 61.67%, 83.94%, and 87.17%. Excel is very helpful for this by the way.

Your numbers for 2, 3 and 4 are much higher than mine.
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Are crits canceled by evades?
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Awesome you guys, thank you.

Assuming Sceptile is on the money with the other 3 scenarios, I'm surprised it's that much of a jump when adding in the focus symbols. I know it bumps up a single attack dice's chance to hit to 75%, while a single defense dice's chance to evade only goes to 62.5%, but a 20%+ bump is significant. Also glad to know that my hunch about simply adding a dice to both sides has minimal effect (which I guess is common sense but hey, if I were sure about this stuff I'd have done it myself right?) Thank you guys so much.

Edit: Ah, I see there is some discrepancy on tera's side. I will wait for further data, but still thanks everyone for all the effort.
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JeffreyRaze posted...

Are crits canceled by evades?

It's not really relevant for the purpose of this calculation, but in the game you have to cancel all hits before you can cancel crits. IE if you roll 2 hits and a crit, and your opponent rolls 2 evades, they have to cancel the hits and take the crit. But if you only roll 1 hit and a crit, and they roll 2 evades, then yes the crit gets canceled.
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Emeraldegg posted...

Awesome you guys, thank you.

Assuming Sceptile is on the money with the other 3 scenarios, I'm surprised it's that much of a jump when adding in the focus symbols. I know it bumps up a single attack dice's chance to hit to 75%, while a single defense dice's chance to evade only goes to 62.5%, but a 20%+ bump is significant. Also glad to know that my hunch about simply adding a dice to both sides has minimal effect (which I guess is common sense but hey, if I were sure about this stuff I'd have done it myself right?) Thank you guys so much.

Wait, you wanted to count the focuses for defense too? I didn't do that. Easy to change if so.

Looking at it again, I see where I was misreading. Now it's 69.87% and 70.45% for the second set.
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For reference, I got:

#3: 69.87%
#4: 70.45%

Sooo....
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Sceptilesolar posted...

Emeraldegg posted...

Awesome you guys, thank you.

Assuming Sceptile is on the money with the other 3 scenarios, I'm surprised it's that much of a jump when adding in the focus symbols. I know it bumps up a single attack dice's chance to hit to 75%, while a single defense dice's chance to evade only goes to 62.5%, but a 20%+ bump is significant. Also glad to know that my hunch about simply adding a dice to both sides has minimal effect (which I guess is common sense but hey, if I were sure about this stuff I'd have done it myself right?) Thank you guys so much.

Wait, you wanted to count the focuses for defense too? I didn't do that. Easy to change if so.

Aha, and there's the discrepancy. Yes, focuses on defense dice count as evades for the scenarios that call for it.
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yeah, i finally grinded through it, and i have 59.38%, 61.67%, 69.87%, and 70.45%
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And every time I do #2 I get 50%.

So I don't know what's up with that.
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Awesome. Thanks again guys.
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btw, intuitively, this should make sense to you (that increasing the attacking dice's probability improves their chances of succeeding overall)

if you take this to the logical limit and say that your X+1 offensive dice have 4 HIT and 4 FOCUS and your X defensive dice have 3 EVADE and 4 FOCUS, you should expect to get X+1 hits every time - which of course is impossible to evade completely, so you'd succeed at 100%
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tera, for #2 i have:

0 hits: 1/64
1 hit: 9/64
2 hits: 27/64
3 hits: 27/64

0 evade: 9/64
1 evade: 30/64
2 evade: 25/64
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SeabassDebeste posted...

tera, for #2 i have:

0 hits: 1/64
1 hit: 9/64
2 hits: 27/64
3 hits: 27/64

0 evade: 9/64
1 evade: 30/64
2 evade: 25/64

...there are 4 attack dice and 3 defence dice in #2.

<_<
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fuck, that's #3 that i just pasted lol

offense
0: 0.0625
1: 0.25
2: 0.375
3: 0.25
4: 0.0625

defense
0: 0.244140625
1: 0.439453125
2: 0.263671875
3: 0.052734375
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Yeah, I see my screwup there, copied the wrong numbers. It looked wrong at a perfect 50 lol.

So yeah:

#1: 59.38%
#2: 61.67%
#3: 69.87%
#4: 70.45%
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