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A Fix To Convergence And Pin Point High Alpha Builds


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#21 Master Q

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Posted 30 July 2013 - 08:27 AM

You failed reading comprehension so I'll fill in the blanks.

View PostPraehotec8, on 30 July 2013 - 08:11 AM, said:

1.) No arm actuators doesn't change anything. You still need to be able to aim your weapons SOMEWHERE right? Mechs can still turn and torso twist. People would know where to aim to get right arm PPCs where they want, then where to aim to get left arm PPCs where they want. You're still just artificially enforcing chain firing basically.


GOOD!
You do realize that in TT, an "alpha strike" is defined as "A pilot firing each of his weapons sequentially in a span of 10 seconds", right?

It is not an all-at-once. Every weapon is individually aimed and fired.

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Sure, it prevents single-strike quad PPCs, etc..., but the current heat penalty is already starting to do that. I guess I don't see what makes this idea better, or even unique among the many cries for less convergence.

I'll explain the point of it.
  • It makes facing-time important. When you are pointed at an enemy, your torso faces to them. If you can "alpha-turn, alpha-turn" as the current Meta encourages, you are at an advantage against someone who has to hold you in their sights (laser beam time, missile lock-on time, AC/2 or Machine-gun firing cycle times). If on the other hand you have to chain-fire, you are pointed at them just as long as they are pointed at you.
  • Preventing a single-strike means you have to aim individually. Sure, you COULD potentially hit the same panel all 4 times but reality says that the pace of combat, motion of your mech, motion of their mech, motion of other mechs around you, chance of one of you passing terrain or another mech getting in the way means you will either strike another panel or miss entirely at least part of the time.
  • This leads you to a choice. Either:
    • take the alpha, and spread damage over more of your enemy or:
    • take your time but take the commensurate exposure/aiming risks there as well.
That makes for a better tactical game all around with actual depth rather than "pew pew surgical strike LMAO those noobs still use missiles don't you know this is PPCWarrior Online?"

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2.) I don't want to play TT. Apparently elite pilots in the 31st century couldn't manage to aim despite years of combat.


Oh, they could aim. It's just that aiming is supposed to be HARD to do, not "whee I gotz me a 2000dpi mouse and aimbot software." You want to try what they are doing? Sit in the bed of a pickup truck with a paintball gun and off-road your way past a set of 10 foot diameter targets at 200-meter distance while the platform you are sitting on bounces around. See how many you can hit.

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It works out alright for TT because you aren't aiming yourself and you only see the effects, and can imagine mechs dodging and twisting, etc. Why would you bother to install weapons that can't ever hit the same spot? Penalties to reach convergence, heat penalties to convergence, etc. I can buy, but pure inability to aim my weapons?
...
Again, I'm not trying to belittle your idea, it's interesting but I just don't think it really would improve the game much.


See above. I'm pretty sure you just don't know what you are talking about.

#22 James The Fox Dixon

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Posted 30 July 2013 - 08:35 AM

View Post3rdworld, on 30 July 2013 - 08:27 AM, said:


Where do you gather this? If I rolled the correct number I could put a full alpha on the same location. Weapon A hitting the CT does not make it impossible for Weapon B to do so as well.

Moreover shot rolls had to do with averages to account for pilot skill. That is not needed in a First Person game.


The probabilities of you hitting the same location with all your weapons is almost impossible in TT. This is because all of the weapons are rolled for location separately. There is no grouping of weapons in TT.

Edited by James The Fox Dixon, 30 July 2013 - 08:36 AM.


#23 Master Q

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Posted 30 July 2013 - 08:41 AM

View Post3rdworld, on 30 July 2013 - 08:27 AM, said:

Where do you gather this? If I rolled the correct number I could put a full alpha on the same location. Weapon A hitting the CT does not make it impossible for Weapon B to do so as well.


And the mathematical chance of two weapons hitting the spot is increasingly unlikely.

2d6 probabilities spread as follows:
2d6 Probabilities
2 X
3 X X
4 X X X
5 X X X X
6 X X X X X
7 X X X X X X
8 X X X X X
9 X X X X
10 X X X
11 X X
12 X

1 result each can possibly lead to a 2 or 12 (snake eyes / boxcars). 6 results can give you a 7, which is a CT hit (assuming front arc shot).

Now, the chance of two 7's. The chance of a 7 that FIRST time is 6 out of 36 possibilities (1 in 6, or 16.7%).
The chance of two 7's in a row is P(7)^2, 1/6 times 1/6, or 1 in 36 now: 2.8%
The chance of three 7's in a row is P(7)^3, or now 1 in 216: 0.5%
The chance of four 7's in a row is 1 in 1296, or 0.08%

See how rapidly that diminishes? "Can happen" does not mean "will be seen often." In fact, it means we SHOULD NOT see it unless they are chain-firing and individually aiming their shots.

Edited by Master Q, 30 July 2013 - 08:41 AM.


#24 3rdworld

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Posted 30 July 2013 - 08:44 AM

View PostJames The Fox Dixon, on 30 July 2013 - 08:35 AM, said:


The probabilities of you hitting the same location with all your weapons is almost impossible in TT. This is because all of the weapons are rolled for location separately. There is no grouping of weapons in TT.


just need to roll the same 2d6. Not impossible at all. Not even that unlikely considering rolling a 7 or 2 facing a mech is around 20%.

#25 James The Fox Dixon

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Posted 30 July 2013 - 08:48 AM

View PostMaster Q, on 30 July 2013 - 08:41 AM, said:


And the mathematical chance of two weapons hitting the spot is increasingly unlikely.

2d6 probabilities spread as follows:
2d6 Probabilities
2 X
3 X X
4 X X X
5 X X X X
6 X X X X X
7 X X X X X X
8 X X X X X
9 X X X X
10 X X X
11 X X
12 X

1 result each can possibly lead to a 2 or 12 (snake eyes / boxcars). 6 results can give you a 7, which is a CT hit (assuming front arc shot).

Now, the chance of two 7's. The chance of a 7 that FIRST time is 6 out of 36 possibilities (1 in 6, or 16.7%).
The chance of two 7's in a row is P(7)^2, 1/6 times 1/6, or 1 in 36 now: 2.8%
The chance of three 7's in a row is P(7)^3, or now 1 in 216: 0.5%
The chance of four 7's in a row is 1 in 1296, or 0.08%

See how rapidly that diminishes? "Can happen" does not mean "will be seen often." In fact, it means we SHOULD NOT see it unless they are chain-firing and individually aiming their shots.

View Post3rdworld, on 30 July 2013 - 08:44 AM, said:


just need to roll the same 2d6. Not impossible at all. Not even that unlikely considering rolling a 7 or 2 facing a mech is around 20%.


See Master Q's answer for the math. It is nearly impossible to hit the same location with all your weapons in a alpha strike.

Thank you Master Q for doing the math.

Edited by James The Fox Dixon, 30 July 2013 - 08:49 AM.


#26 Master Q

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Posted 30 July 2013 - 08:49 AM

View Post3rdworld, on 30 July 2013 - 08:44 AM, said:


just need to roll the same 2d6. Not impossible at all. Not even that unlikely considering rolling a 7 or 2 facing a mech is around 20%.


You never took statistics 101 in college, did you?

#27 Lightfoot

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Posted 30 July 2013 - 08:51 AM

View PostMaster Q, on 30 July 2013 - 08:15 AM, said:

You're joking right? Making mechs "tougher somehow" by fiddling with armor values DOES NOT CHANGE THE META. It's an across-the-board weapons nerf, and instead of making people more likely to use spread weapons actually makes it MORE necessary to put linked fire into a single panel through repeated pinpoint, frontloaded alpha strikes.
Also you say "these weapons have different travel times" regarding Gauss and PPC, but you DO realize that after the travel speed buffs (that they implemented because of HSR issues) it takes a mere fraction of a second for them to deal damage beyond the game's draw distance, right?



In previous MechWarrior games the Mechs all carried and fired arrays of weapons with group-fire mechanics. That's normal, like it or hate it. You won't escape it because the Clans do it more and better. Lighter, smaller weapons with better heatsinking and higher damage per weapon. That's just the way Mechs in Battletech (our source of Mechs) are made to work. Groups of weapons fired in groups is part of the core balancing between Inner Sphere and Clan tech.

The problem with non-converged weapons is you change the core dynamic of grouped weapons from a single hit to multiple hit-points within an AoE type footprint. It's like turning your loadout into a super-LBX burst which would be impossible for Light mechs to dodge.

However you can achieve roughly the same thing by making the mech hitboxes overlap. Then you retain the single hipoint, but you make it more likely that the damage will go into two sections, kind of like you want, but without the super-LBX effect.

Anyway, if you want to see group-fire you need to be looking at Clan mechs since Inner Sphere Mechs are limited by very heavy weapons and equipment. Inner Sphere employs group-fire poorly, but it's all they have to compete against Clan tech also.

#28 Master Q

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Posted 30 July 2013 - 08:53 AM

Heck, I'll redo it with the "2 or 7" option for you just for fun.

The chance of a "2 or 7" is 7 of 36 per roll.
7/36 = 19.4%
(7/36)^2 = 3.8%
(7/36)^3 = 0.7%
(7/36)^4 = 0.14%

It doesn't change that much. It's the increasing denominator that's the problem, not the numerator. Sequential CT hits, much less sequential hits to any other panel, are statistically unlikely to the point of absurdity.

Edited by Master Q, 30 July 2013 - 08:56 AM.


#29 James The Fox Dixon

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Posted 30 July 2013 - 08:57 AM

View PostLightfoot, on 30 July 2013 - 08:51 AM, said:



In previous MechWarrior games the Mechs all carried and fired arrays of weapons with group-fire mechanics. That's normal, like it or hate it. You won't escape it because the Clans do it more and better. Lighter, smaller weapons with better heatsinking and higher damage per weapon. That's just the way Mechs in Battletech (our source of Mechs) are made to work. Groups of weapons fired in groups is part of the core balancing between Inner Sphere and Clan tech.

The problem with non-converged weapons is you change the core dynamic of grouped weapons from a single hit to multiple hit-points within an AoE type footprint. It's like turning your loadout into a super-LBX burst which would be impossible for Light mechs to dodge.

However you can achieve roughly the same thing by making the mech hitboxes overlap. Then you retain the single hipoint, but you make it more likely that the damage will go into two sections, kind of like you want, but without the super-LBX effect.

Anyway, if you want to see group-fire you need to be looking at Clan mechs since Inner Sphere Mechs are limited by very heavy weapons and equipment. Inner Sphere employs group-fire poorly, but it's all they have to compete against Clan tech also.


What makes you think that they got it right in those titles? The obvious answer is that they didn't.

#30 3rdworld

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Posted 30 July 2013 - 08:57 AM

View PostMaster Q, on 30 July 2013 - 08:49 AM, said:

You never took statistics 101 in college, did you?


there are 36 possibilities roll a 2d6 of which 7 of them result in a CT hit from the front. 7/36 = 19.44% chance.

#31 Praehotec8

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Posted 30 July 2013 - 09:24 AM

View PostMaster Q, on 30 July 2013 - 08:27 AM, said:

See above. I'm pretty sure you just don't know what you are talking about.


1.) Sir, I guarantee my reading comprehension, level of learning/education, and intelligence are at LEAST your equal, so cool it with the personal attacks. I understood very well what the OP meant, I just don't agree with it. Just because you disagree with my points does not make me an *****. Disagree with me, but do not personally insult me, nor patronize me again.

2.) Alpha-firing in the game is NOT sequential firing, it is one-time damage. In the current game it is firing all of your weapons at once. Even if it IS sequential firing, that makes it even more strange that you are arguing with me, as you are stating that pilots can aim each individual weapon where they wish in sequence. As I mentioned before, all the OP's idea does is force sequential firing. Precision aiming can still be achieved, albeit at different times. Again, I fail to see how this improves on any other the other methods that encourage staggered fire. I can make it even simpler if all you want is staggered fire: Limit players to fire only one weapon at a time. Period...problem solved. Is it fun though? That's subjective.

3.) Sure, face-time is certainly important and I understand the idea of making it harder to fire, turn and so on. However, I think it would not be as fun to play a FPS where you aim was not a key factor in where you hit. I think it would bother me to put my crosshair right on the CT, fire, and see laser hit is left leg, my AC5 hit his right arm, and my SRM4 hit one missile to each segment. Why bother to try aiming at that point? Just swivel in the general direction of the other mech, fire, and turn away. I exaggerate, but still, sniping ought to have some role, there just needs to be some balance.

4.) I get what you are saying about aiming while moving, bouncing, etc...but the game needs to remain fun above all. I wouldn't mind a little added bounce to make aiming just a bit harder. Arbitrarily limiting where your weapons can be aimed isn't the same thing.

5.) I don't use a mouse to play this game. As I mentioned before, get your joystick out, use it for aiming, and tell me how easy it is to make pinpoint sniping shots from long distance quickly and accurately (or heck, even consistently hit one segment during a brawl while torso-twisting). It can certainly be done, but requires more trouble. Some degree of player aiming skill should still be rewarded.

6.) I did not say the idea is totally worthless, I just don't think it quite fits in a FPS, and I still see some holes in the idea. Honestly a straight up cone of fire for alpha-strikes, or heat related aiming penalties would work better IMO.

#32 FatBabyThompkins

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Posted 30 July 2013 - 10:38 AM

View Post3rdworld, on 30 July 2013 - 08:57 AM, said:


there are 36 possibilities roll a 2d6 of which 7 of them result in a CT hit from the front. 7/36 = 19.44% chance.


Probability time!

Assuming 4 hits, the resulting set is a binomial distribution resolved around the probability of hitting the CT, in this case 7/36. So, the binomial distribution is:

0: 42.11%
1: 40.66%
2: 14.72%
3: 2.37%
4: 0.14%

Again, assuming 4-hits the probability to hit the CT all 4 times is 0.14%. The probability to completely miss the CT (and hit other parts of the mech) is 42.11%. In all, the probability to hit the CT with at least 1 hit is 1-BinDist(0,4,7/36,false), which is 57.89%, or the sum of 1 through 4.

Of course, we are forgetting the probability to hit 4 times, which I do not know the dice rolled nor the probability to hit with said dice rolls. So, the probability is even further lower than it would appear here (0.14% * [Probability to hit 4 times]).

Edited by FatBabyThompkins, 30 July 2013 - 10:39 AM.


#33 Master Q

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Posted 30 July 2013 - 10:41 AM

View Post3rdworld, on 30 July 2013 - 08:57 AM, said:


there are 36 possibilities roll a 2d6 of which 7 of them result in a CT hit from the front. 7/36 = 19.44% chance.

See the rest of the math above. 4 weapons ALL hitting the same spot is improbable to the point of absurdity.

Heck I'll copy it for you again:
The chance of a "2 or 7" is 7 of 36 per roll.
7/36 = 19.4%
(7/36)^2 = 3.8%
(7/36)^3 = 0.7%
(7/36)^4 = 0.14%

It doesn't change that much whether you do "7 of 36" or "6 of 36". It's the increasing denominator that's the problem, not the numerator. Sequential CT hits, much less sequential hits to any other panel, are statistically unlikely to the point of absurdity.

#34 FatBabyThompkins

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Posted 30 July 2013 - 10:48 AM

View PostMaster Q, on 30 July 2013 - 10:41 AM, said:

See the rest of the math above. 4 weapons ALL hitting the same spot is improbable to the point of absurdity.

Heck I'll copy it for you again:
The chance of a "2 or 7" is 7 of 36 per roll.
7/36 = 19.4%
(7/36)^2 = 3.8%
(7/36)^3 = 0.7%
(7/36)^4 = 0.14%

It doesn't change that much whether you do "7 of 36" or "6 of 36". It's the increasing denominator that's the problem, not the numerator. Sequential CT hits, much less sequential hits to any other panel, are statistically unlikely to the point of absurdity.


Although your final result is correct, (7/36)^4 = 0.14%, the previous results are not. You're looking for the binomial distribution, not the permutation with repetition.

Edit: as to the reason why. Given 4 hits, the probability to hit 1 once breaks down to the [probability to hit the CT]*[Prob to miss CT]*[Prob to miss CT]*[Prob to miss CT], which is 10.16%. But you could hit on the first and miss the next three, or miss the first, hit the second, miss the next 2, or any combination resulting in one hit, so the equation becomes [probability to hit the CT]*[Prob to miss CT]*[Prob to miss CT]*[Prob to miss CT]*Combination(4,1), where Combination(4,1) is 4 choose 1, which equals 4.

Edited by FatBabyThompkins, 30 July 2013 - 10:58 AM.


#35 Master Q

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Posted 30 July 2013 - 10:49 AM

View PostPraehotec8, on 30 July 2013 - 09:24 AM, said:

...
2.) Alpha-firing in the game is NOT sequential firing, it is one-time damage. In the current game it is firing all of your weapons at once. Even if it IS sequential firing, that makes it even more strange that you are arguing with me, as you are stating that pilots can aim each individual weapon where they wish in sequence. As I mentioned before, all the OP's idea does is force sequential firing. Precision aiming can still be achieved, albeit at different times. Again, I fail to see how this improves on any other the other methods that encourage staggered fire. I can make it even simpler if all you want is staggered fire: Limit players to fire only one weapon at a time. Period...problem solved. Is it fun though? That's subjective.


So you fail to notice that I said the current model of Alpha-firing is a problem. It's a problem because it contributes (one part of a triumvirate of alpha-strike mechanics, perfect aim convergence, and weapons that do pinpoint damage) to the overall high-alpha surgical strike meta issue.

Quote

3.) Sure, face-time is certainly important and I understand the idea of making it harder to fire, turn and so on. However, I think it would not be as fun to play a FPS where you aim was not a key factor in where you hit. I think it would bother me to put my crosshair right on the CT, fire, and see laser hit is left leg, my AC5 hit his right arm, and my SRM4 hit one missile to each segment. Why bother to try aiming at that point? Just swivel in the general direction of the other mech, fire, and turn away. I exaggerate, but still, sniping ought to have some role, there just needs to be some balance.


Which is why many people have suggested a spread crosshair or KNOWN aim offsets. Firing your left-hand Gauss? Aim for the left hand crosshair point. Firing your right-hand PPC? Aim for the right hand crosshair point. Firing both at once? I'm sorry but they will not hit the same point. Imperfect Convergence is not the same thing as Random Number Generator, something that apparently has to be repeated a million times for some people to eventually understand.

Quote

4.) I get what you are saying about aiming while moving, bouncing, etc...but the game needs to remain fun above all. I wouldn't mind a little added bounce to make aiming just a bit harder. Arbitrarily limiting where your weapons can be aimed isn't the same thing.


Ok we'll step it up a notch. Now we give you TWO paintball guns. You get to fire them both at the same time and still try to hit your target. I guarantee you won't have perfect convergence. You just attacked bounce and what you described as random aiming, I'm pointing out that with IMPERFECT RETICLES - in this case your own shaky arms - you're going to get fire divergence anyways.

Perfect Convergence breaks the suspension of disbelief and also BREAKS THE GAME.

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5.) I don't use a mouse to play this game. As I mentioned before, get your joystick out, use it for aiming, and tell me how easy it is to make pinpoint sniping shots from long distance quickly and accurately (or heck, even consistently hit one segment during a brawl while torso-twisting). It can certainly be done, but requires more trouble. Some degree of player aiming skill should still be rewarded.


Goody for you on using a joystick. I use a mouse because it's what is on my desk. The game has to be balanced assuming the "most optimal control setup", otherwise people are just going to whomp up on the joystick users anyways - and that's actually another reason that imperfect convergence needs to be a thing because right now, mouse aiming >>>>>> joystick aiming for accuracy.

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6.) I did not say the idea is totally worthless, I just don't think it quite fits in a FPS, and I still see some holes in the idea. Honestly a straight up cone of fire for alpha-strikes, or heat related aiming penalties would work better IMO.


See, above you complained about "if I put my crosshairs on X and saw the laser hit the leg instead", now you're suggesting cone of fire? You're not even consistent.

#36 LoveLost85

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Posted 30 July 2013 - 10:56 AM

I don't remember playing any game where you have a aiming ret and what you shoot doesn't go there, convergence is not a problem. as the the lack of actuators ect, your aiming ret shows the distance to whatever it is over, EX. 234m, your mechs arm actuators bow out and the gun muzzles point in to match the data so that your weapons WILL hit the same spot. seriously, if some one has a PPC and a GR and the have their cross on you and they hit the fire key why would it not hit you? in a game that you yourself control the aiming and firing of a mech I cant believe im seeing people complain about the shots landing where they are aimed, hilarious.

#37 James The Fox Dixon

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Posted 30 July 2013 - 10:59 AM

View PostLoveLost85, on 30 July 2013 - 10:56 AM, said:

I don't remember playing any game where you have a aiming ret and what you shoot doesn't go there, convergence is not a problem. as the the lack of actuators ect, your aiming ret shows the distance to whatever it is over, EX. 234m, your mechs arm actuators bow out and the gun muzzles point in to match the data so that your weapons WILL hit the same spot. seriously, if some one has a PPC and a GR and the have their cross on you and they hit the fire key why would it not hit you? in a game that you yourself control the aiming and firing of a mech I cant believe im seeing people complain about the shots landing where they are aimed, hilarious.


In all of the FPS I've played there has always been a cone of fire and where you aim at is the general direction doesn't mean you'll hit it.

#38 3rdworld

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Posted 30 July 2013 - 11:00 AM

View PostMaster Q, on 30 July 2013 - 10:41 AM, said:

See the rest of the math above. 4 weapons ALL hitting the same spot is improbable to the point of absurdity.

Heck I'll copy it for you again:
The chance of a "2 or 7" is 7 of 36 per roll.
7/36 = 19.4%
(7/36)^2 = 3.8%
(7/36)^3 = 0.7%
(7/36)^4 = 0.14%

It doesn't change that much whether you do "7 of 36" or "6 of 36". It's the increasing denominator that's the problem, not the numerator. Sequential CT hits, much less sequential hits to any other panel, are statistically unlikely to the point of absurdity.


unlikely != impossibility. The person I responded to, said it is impossible for 2 shots to hit the same location in TT.

That is not true.

Moreover the sequence is irrelevant. In this thought experiment shot 1 has already been rolled, and the question in hand is what is the chance of shot 2 hitting the same location. Well if that is the CT, the chance is 19.44%.

It is the old brain teaser. I flipped 2 coins, coin 1 landed on heads. What is the chance of coin 2 landing on heads. it isn't 25%.

View PostJames The Fox Dixon, on 30 July 2013 - 10:59 AM, said:


In all of the FPS I've played there has always been a cone of fire and where you aim at is the general direction doesn't mean you'll hit it.


so you never played halo, or used the sights on CoD? You must live under a rock.

#39 James The Fox Dixon

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Posted 30 July 2013 - 11:03 AM

View Post3rdworld, on 30 July 2013 - 11:00 AM, said:


unlikely != impossibility. The person I responded to, said it is impossible for 2 shots to hit the same location in TT.

That is not true.

Moreover the sequence is irrelevant. In this thought experiment shot 1 has already been rolled, and the question in hand is what is the chance of shot 2 hitting the same location. Well if that is the CT, the chance is 19.44%.

It is the old brain teaser. I flipped 2 coins, coin 1 landed on heads. What is the chance of coin 2 landing on heads. it isn't 25%.

so you never played halo, or used the sights on CoD? You must live under a rock.


I've played CoD and Halo as I stated that I've played FPS. Even using the sights doesn't mean you necessarily hit where you are aiming at. Using the sights makes the cone of fire smaller, but doesn't get rid of it.

#40 Master Q

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Posted 30 July 2013 - 11:06 AM

View PostFatBabyThompkins, on 30 July 2013 - 10:48 AM, said:


Although your final result is correct, (7/36)^4 = 0.14%, the previous results are not. You're looking for the binomial distribution, not the permutation with repetition.


Incorrect.
Assume we have 4 PPCs. Each has to fire at the target and hit. For ease of use let's assume that they all hit (an invalid assumption given a standard Pilot skill of 4, mechs moving for an average of +2 to target number, and possible intervening terrain or distance modifiers, but whatever).

Now we roll on the targeting table:
Front/Rear
2 C. Torso (critical)
3 Right Arm
4 Right Arm
5 Right Leg
6 Right Torso
7 C. Torso
8 Left Torso
9 Left Leg
10 Left Arm
11 Left Arm
12 Head

So only a result of 2 or 7 will give us the result we want (CT). We look at the possible 2d6 rolls from above; there is ONE result (snake eyes) that can give us a result of 2, but SIX results can give us the 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). So 7 out of the possible 36 results of a 2d6 roll can give us a CT connect.

Probability of a single strike hitting CT will be referred to as P(CT HIT).

Therefore the possibility of four CT hits in a given strike is P(CT HIT) * P(CT HIT) * P(CT HIT) * P(CT HIT), or P(CT HIT)^4.

This is much like flipping a coin. Let's flip one coin: the probability of a Heads result is P(Heads) = 0.5 (one possible result heads, one result tails, we'll dismiss as negligible the "what if it lands on its edge" as astronomically small since on-edge is not normally a valid, stable result and it'll have to fall eventually.)

The probability of two heads in a row is 0.25, because the possible results are: 2 Heads, 2 Tails, Heads+Tails, or Tails+Heads. 4 results, only one of which is 2 Heads. Independent, unrelated events. The Probability of 3 Heads in a row is P(Heads)^3, or (1/2)^3 = 1/6. The probability of 4 heads in a row is P(Heads)^4, or (1/2)^4 = 1/16.

P(CT HIT) = 7/36.
P(CT HIT)^4 = (7/36)^4 = 2401/1679616 = 0.0014294934 = 0.14%

That is the math. They are independent, unrelated events. Not one of them affects the ones that come before or after, BUT the probability of alignment is so small as to be highly improbable.





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