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Old May 3rd, 2008, 01:57 PM
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Zetacron vs. Q9: A basic statistical analysis

One thought I had for Zetacron was as a Q9 counter. Sure, the points aren't even close, but I thought it might be worth seeing if Zetacron could at least do some damage before becoming queglix-fodder.

Here's the setup: Zetacron moves within range of Q9 and gets the first shot in. What is likely to happen?

If Zetacron has two attack dice and Q9 has 7 defense dice: (no boosts from height, etc)

Q9 will receive somewhere between 0 and 4 wounds with the following probabilities:

4 wounds: 1.46%
3 wounds: 5.12%
2 wounds: 10.61%
1 wound : 16.64%
0 wounds: 66.16%

So, that's only a 33.84% chance of getting at least one wound on Q9.
At 180 points for 4 life, I figure that 1 wound on Q9 is worth 45 points.

The 'expected' number of wounds is .59. (".59 wounds?" "Yeah, I know; shut up.") I figure that .59 wounds on Q9 is worth 26.55 points. So Zet would need nearly 3 shots on Q9 to earn his points. I don't think he's going to get much more than one shot before Q9 mows him down.

On average, it would take 6.8 shots to give Q9 all 4 wounds. I don't think Q9 is going to let Zetacron get that many shots in.

("Hey, how do you take .8th of a shot?" Sigh.)

Okay. but what if Zetacron has three attack dice and Q9 has 7 defense dice?: (Zetacron has height or whatever)

Now Q9 will receive somewhere between 0 and 6 wounds with the following probabilities:

6 wounds: 0.73%
5 wounds: 2.56%
4 wounds: 6.04%
3 wounds: 10.88%
2 wounds: 15.32%
1 wound : 17.76%
0 wounds: 46.71%

So, now that's a 53.29% chance of getting at least one wound on Q9.

The 'expected' number of wounds is now 1.22. Using the same calculation as above, that 1.22 wounds is worth 54.9 points, almost enough for Zet to earn his points.

On average, it would take 3.2 shots to give Q9 his 4 wounds. Again, Zeta probably won't get more than one shot, but things are a lot better. And instead of a measly 1.46% chance of killing Q9 in one shot, now he's got a 9.33% chance of doing so.

--------------

Clearly, Zetacron doesn't own Q9, or even come close. But he does have a reasonable chance of getting his points back if he can make the first move. Of course, Deadly Shot is highly variable, so sometimes Zetacron is going to do squat, and sometimes he's going to do some real damage.

Thoughts? I think it's worth a shot. (And one shot is all he's going to get!)
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  #2  
Old May 3rd, 2008, 02:01 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

Thats a pretty good bit of writing. Good job. Except for one minor detail. He can't give 3 wounds (example) because thats an odd number. He'll always give an odd number.

EDIT: Ignore that. I just realized I was talking of skulls and not damage. My bad!
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Old May 3rd, 2008, 02:18 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

Very nice! I figured that he really couldn't take Q9, but is worth his points. Nice job!
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Old May 3rd, 2008, 03:28 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

I'm not a math guy like some of you here, but wouldn't Zeta's 4 defense help out against a 3 attack? Especially in the second case where Zeta has the height advantage over Q9? I mean, that's 5 defense right there. Certainly he would live long enough to at least get a second, and possibly, a third shot, right?

"Chewie should move 6, lumbering or not. He's got long-ass legs"-
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Old May 3rd, 2008, 03:56 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

Quote:
Originally Posted by rym View Post
I'm not a math guy like some of you here, but wouldn't Zeta's 4 defense help out against a 3 attack? Especially in the second case where Zeta has the height advantage over Q9? I mean, that's 5 defense right there. Certainly he would live long enough to at least get a second, and possibly, a third shot, right?
Well Q9 has a normal attack of 4 in a range of 8, not 3. If he's within a 6 (I believe) range however, he can do 3 attacks of 3 or any amount involving 1, 2, or 3 attack until he reaches 9 dice. And, when you're rolling for attack, you have a better chance of rolling a skull, than you do with rolling a shield (50% chance of rolling 1 skull when rolling 1 attack dice, and 33.3% chance of rolling 1 shield when rolling 1 defense dice). If Q9's attack was 3, Zetacron would have a better chance than before, but still would not have a better chance of blocking all, than Q9 would on taking life away. I'd say that they'd both have about an equal chance of wining the roll, but Zetacron doesn't have a better chance, like you're saying (according to the fact that there's 3/6 faces are skulls, and only 2/6 faces are shields on the dice, 50% are skulls, 33.3% are shields, and a 16.6% are blank(s)). But since Q9's attack is 4, he has a better chance of inflicting a wound, than Zetacron has of blocking all skulls. I too am not a math guy, but I know the percent/fractions of the dice.

Last edited by Cleon; May 3rd, 2008 at 04:02 PM.
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Old May 3rd, 2008, 03:56 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

Mathguy's awesome match-up calculator is a great tool for shedding light on questions such as this.

It will tell you that without height Zetacron kills Q9 4.11% of the time, and inflicts 0.5 wounds in the process of being killed the rest of the time. This gives an expected value of 29.0pts damage done.

With height, Zetacron kills Q9 21.94% of the time, and inflicts 0.9 wounds in the process of being killed the rest of the time. This gives an expected value of 71.1pts.

These numbers are under the assumption that Q9 is using his Queglix in 3/3/3 mode, and that the fight starts at the start of a round with an initiative roll (and all order markers are on these figures indefinitely).

So what do we conclude?

1. Zetacron is not worth his points against Q9, assuming no other factors are in play.

2. Zetacron benefits hugely from height.

Probably not a great surprise to anyone.
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Old May 3rd, 2008, 04:10 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

Yeah, I think that Zetacron would get at least two shots in... even with mathematical probability figuring against his survival.

I've seen (more often than not) only two skulls rolled out of three and two or three shields rolled out of five... and with that observation Zetacron would probably lose one life, get another shot at Q9, and then be destroyed. Even if that is against mathematical probability. This is of course in a one on one perspective, if you tied up Q9 with something resilient (rats probably) and then used Zetacrons superior range you could probably manage to destroy Q9 unscathed (Zetacron at least, not the rats).

Whether to believe or disbelieve, it is a wicked thing to take away men’s hope.

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Old May 3rd, 2008, 04:25 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

Quote:
Originally Posted by rym View Post
I'm not a math guy like some of you here, but wouldn't Zeta's 4 defense help out against a 3 attack? Especially in the second case where Zeta has the height advantage over Q9? I mean, that's 5 defense right there. Certainly he would live long enough to at least get a second, and possibly, a third shot, right?
Great point. I was just assuming before. Let's find out!

If neither one has glyphs or Height advantage:

If Q9 attacks with his regular 4 attack:
Zetacron takes 0-2 wounds with the following probabilities:
2(or more) wounds: 27.78%
1 wound: 27.78%
0 wounds: 44.44%

More likely, Q9 uses his special (3 attack, 3 times):
For each shot, Zetacron takes 0-2 wounds with the following probabilities:
2(or more) wounds: 14.81%
1 wound: 25.93%
0 wounds: 59.26%

After three shots, Zeta's wound probabilities look like this:
2(or more) wounds: 51.88%
1 wound: 27.31%
0 wounds: 20.81%

Wow. That's better than I thought it would be. About half the time, Zeta is around for a second shot...(Or, even if Q9 engages first, Zeta will have a chance to fire back.)

edited to add: The 'expected' number of wounds on Q9 after taking two Deadly shots is 1.18. (Worth 53.1 points). Doesn't make up his points, even if he gets to fire the first shot.

-----------

If Zetacron has an extra defense die:

If Q9 attacks with his regular 4 attack:
Zetacron takes 0-2 wounds with the following probabilities:
2(or more) wounds: 21.40%
1 wound: 24.90%
0 wounds: 53.70%

More likely, Q9 uses his special (3 attack, 3 times):
For each shot, Zetacron takes 0-2 wounds with the following probabilities:
2(or more) wounds: 10.70%
1 wound: 21.40%
0 wounds: 67.90%

After three shots, Zeta's wound probabilities look like this:
2(or more) wounds: 39.09%
1 wound: 29.60%
0 wounds: 31.31%

Wow. So he's got a 60.9% chance of surviving 3 full queglix shots. And nearly a third of the time, Q9 won't lay a single bullet on him. I'm surprised. I was looking at that 2 life and thinking he had no chance, but the high defense makes a big enough difference.

edited to add: The 'expected' number of wounds on Q9 after taking two Deadly shots is 2.44. That's worth 109.8 points. But this is assuming Zetacron has height both times. (Or a glyph or whatever.)

Thanks for asking, rym!

Last edited by fomox; May 3rd, 2008 at 04:47 PM. Reason: adding expected points taken
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Old May 3rd, 2008, 04:28 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

I guess the math is for his survival... I didn't actually do the math, just assumed.

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Old May 3rd, 2008, 04:35 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

It's worth repeating that I was originally assuming Zeta gets the first shot.
(They each have 5 move, but I figure Zeta's range advantage means he'll get first shot more often.)

The match-up calculator ollie mentioned (thanks, by the way, I hadn't seen that) appears to have a different take, assuming it's a toss-up as to who will get first strike. I think the real odds that Zeta gets first strike would be greater than 50% (like the calculator assumes), but less than 100% (like I assumed).
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Old May 3rd, 2008, 04:43 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

Quote:
Originally Posted by fomo6 View Post
It's worth repeating that I was originally assuming Zeta gets the first shot.
(They each have 5 move, but I figure Zeta's range advantage means he'll get first shot more often.)
Don't forget that Q9 has a normal attack of range 8 too.

Quote:
Originally Posted by fomo6
The match-up calculator ollie mentioned (thanks, by the way, I hadn't seen that) appears to have a different take, assuming it's a toss-up as to who will get first strike. I think the real odds that Zeta gets first strike would be greater than 50% (like the calculator assumes), but less than 100% (like I assumed).
If you look at some of the other data that the calculator spits out, you'll see that there is data there regarding who gets first shot, and at what point of the round it is. Maybe thoes numbers will help? It really is a nifty tool.
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Old May 3rd, 2008, 05:05 PM
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Re: Zetacron vs. Q9: A basic statistical analysis

That is a cool calculator!

Some playing around:

Lets see if Zetacron can give the Major 2 wounds (90 points).

(If the calculator did fractions of a wound, we could look at 60 points worth of wounds, but oh well.)

Setting Q9's life to 2, you can see that Zeta will get two wounds on Q9 over 58% on the time if he goes first with height. (That's two big ifs, though. Well, getting height is, anyway.) That's earning one and a half times his points. If you take off height, the odds go down to 40-something.

---
Also, ollie, you are right about Q9's regular attack range. So half the time Q9 could get in the first attack, it just that it would likely be a regular one. Hmm. The search for a Q9 killer continues..
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