OBT Forum

for the head you are right, it does not matter, but for the center torso it became a game changer since an upper roll will always result in an engine hit and the lower roll will always result in a gyro/equipment hit.  in a case like that you might as well use a D12, which 1) Changes the D6 centric nature of the game and 2) increases the probability of engine/gyro knockouts.  would it make a difference with a computer based random number generator?  no not really, but when using dice to serve that purposes it does make a statistically significant difference.

what this DOES do is make the pre-done record sheets entirely incompatible with the proper battletech game, thus overriding part of TRO 3063s mission statement.

Uhhh, you are not making sense here.

Lets do the math, lets say you get a CT critical, woot.


Old method, lets assume 2 medium lasers in the center torso, a regular engine and gyro.
First die 1 to 3, second die 1 = 8.33% Chance Engine Hit
First die 1 to 3, second die 2 = 8.33% Chance Engine Hit
First die 1 to 3, second die 3 = 8.33% Chance Engine Hit
First die 1 to 3, second die 4 = 8.33% Chance Engine Hit
First die 1 to 3, second die 5 = 8.33% Chance Gyro Hit
First die 1 to 3, second die 6 = 8.33% Chance Gyro Hit
First die 4 to 6, second die 1 = 8.33% Chance Gyro Hit
First die 4 to 6, second die 2 = 8.33% Chance Gyro Hit
First die 4 to 6, second die 3 = 8.33% Chance Engine Hit
First die 4 to 6, second die 5 = 8.33% Chance Engine Hit
First die 4 to 6, second die 5 = 8.33% Chance Medium Laser Hit
First die 4 to 6, second die 6 = 8.33% Chance Medium Laser Hit

So, total the engine has 6 criticals, the gyro 4, the medium lasers 2.  Thus you have a 6 in 12 chance (50%) of an engine hit, a 4 in 12 (33%) chance of a gyro hit, and 2 in 12 (17%) chance of hitting a medium laser.

Now, lets look at my method:


First die 1 to 3, second die 1 = 8.33% Chance Engine Hit
First die 1 to 3, second die 2 = 8.33% Chance Engine Hit
First die 1 to 3, second die 3 = 8.33% Chance Engine Hit
First die 1 to 3, second die 4 = 8.33% Chance Engine Hit
First die 1 to 3, second die 5 = 8.33% Chance Engine Hit
First die 1 to 3, second die 6 = 8.33% Chance Engine Hit
First die 4 to 6, second die 1 = 8.33% Chance Gyro Hit
First die 4 to 6, second die 2 = 8.33% Chance Gyro Hit
First die 4 to 6, second die 3 = 8.33% Chance Gyro Hit
First die 4 to 6, second die 5 = 8.33% Chance Gyro Hit
First die 4 to 6, second die 5 = 8.33% Chance Medium Laser Hit
First die 4 to 6, second die 6 = 8.33% Chance Medium Laser Hit

So, total the engine has 6 criticals, the gyro 4, the medium lasers 2.  Thus you have a 6 in 12 chance (50%) of an engine hit, a 4 in 12 (33%) chance of a gyro hit, and 2 in 12 (17%) chance of hitting a medium laser.

Would you look at that, EXACTLY the same!!!

Statistically the order of the criticals, or their placement, has ZERO impact to their chances to get hit.

Rolling 2d6 produces a 2 to 12, on a bell curve.  Rolling 1d6 for group and 1d6 for slot produces a result of 1 to 12 on a flat 8.3333% chance per slot.

Statistically there NO difference either way, statistically you could roll a 1d12 instead of 1d6 and 1d6 and it would be the EXACT same.

Now, if you really like the whole "I rolled a 2 on that CT hit, let me roll again.... 4, engine hit, woot!" instead of "I rolled a 2 on that CT hit, since it took no criticals I'll just mark off any engine slot, woot!", well, I can't argue with that, but mathematically it simply doesn't matter where criticals are located.

These are hard numbers, not my opinions, and you can't really argue with that.  Well, maybe in the battletech universe that first die "intended" for you to hit a gyro, but since there is no gyro anymore you have to hit the engine, and now your charma is screwed up.

And remember, engines aren't always the same size, compact engines, compact gyros, HD/XL gyros, etc, are now ALL easier to deal with under my new slots than they used to be.  Engines are ALWAYS all 6 upper, and sometimes 2 or 4 lower, and gyros ALWAYS follow engines, its more consistent.

The answer from Dan Eastwood (http://giantbattlingrobots.blogspot.com/)


Bad_Syntax  post #63 has the math right. Further, if one of those slots is a "Re-roll" the 8.33% probability is distributed equally among the remaining 11 locations. This create a Discrete Uniform distribution, and every crit-slot has an equal probability of being hit. It doesn't matter how you arrange the slots, only how many total slots there are.

@ JP_Arbiter post #64: There is no bell curve here, because the two dice are not being added together. The only way this could matter is if you are not doing critical hit location rolls/re-rolls right in the first place.

And more:

This does _not_ alter the probability, unless maybe they are somehow doing it wrong in the first place. It is important to re-roll BOTH dice if they get a re-roll slot (or empty, or already destroyed), and if they aren't doing that they ARE wrong to start with.

The method of assigning critical hit locations creates what is called a Discrete Uniform distribution (http://en.wikipedia.org/wiki/Uniform_distribution_(discrete)), and each slot has an equal chance of being hit, no matter where that slot is, or what is in that slot.
 
OK, I think Ashley is onto why people see this differently: It's because with all the engine crits in the first six slots the second roll may not do anything. That is, if the first die gives you "upper", then you don't really care which upper it is (they are all the same). It does not matter, each slot has the same probability of being hit, so long as the correct re-roll procedure is used.

Dan

I have an email to my Statistic's for Behaviour Sciences Professor in college as well to double check my assertion.  if it turns out I am wrong I will gladly admit it.

I have an email to my Statistic's for Behaviour Sciences Professor in college as well to double check my assertion.  if it turns out I am wrong I will gladly admit it.

Actually, even if you are wrong here, you have pointed out something we did not take into account.

This is an issue of intimidating looks.

The problem isn't in the actual chance of hitting a given slot - it lies in the fact that you need three engine hits to kill a 'Mech, but only two gyro hits to neutralize it.

With the engine slots bunched at one end and the gyro slots at the other, they appear vulnerable - isolated, a sort of 'all the eggs in one basket' syndrome if you will, despite the lack of actual statistical evidence. 

It doesn't matter if the odds are actually different - in a game where people curse their luck with the dice and regularly relate stories of miracle headcaps, it just has to appear as though it were more vulnerable. 

And it does, even to me.

I have approached the programmer to see (a) if he is willing to change this, (b) if it is even possible and (c) how much work it will entail. 

JPArbiter, it would be nice if you would unsay those hard words you had for Bad Syntax earlier.  They were unwarranted.  He may be a scalawag, but he is not a maniac.

Cent13

Quote from: Centurion13 on September 07, 2012, 05:00:14 PM

I have approached the programmer to see (a) if he is willing to change this, (b) if it is even possible and (c) how much work it will entail. 

JPArbiter, it would be nice if you would unsay those hard words you had for Bad Syntax earlier.  They were unwarranted.  He may be a scalawag, but he is not a maniac.

What???  Hard words for me???  Baaah, I'm married, and get those every time I don't do dishes (which is nearly every day). 

As I'm the programmer.....

I made the change so the engine/gyro is split, the new record sheets are generating now.  I'll release them as soon as we can get JP to acknowledge that mathmatically the chances are the same, even if if he just hates them aesthetically

In fact, aside from a few bugs and the slots, nobody has said one thing, positive or negative, on my *completely* remade record sheets   Ya'll like the logo being on there?  What about the BF/QS stats?  Hows about the way I did the heat sinks so you knew which ones were internal?  Or the labeling of the slots/weapons?  How about circle placement (I'd like to distribute them better, but that is a LOT harder)?  etc, etc...

Surprising when soooo many want a mech/etc editor, soooo few have input when it comes to making one   I am probably the only person who would ever write something like a mobile structure, base, or character generator, and in fact the only one who has ever written an infantry platoon creator, oh well, I'm writing one for Strike Legion now

You know I like it.

As for the others, I suspect the only time you will hear from them about the record sheets is when there's something they *don't* like. 

In this matter, as with so much else in modern American life, no news is good news.

Cent13

https://www.opendrive.com/files/61132515_inISD_f819/RS%20TRO3063%20Mk32.pdf

The Center Torso change has been made.  You guys should have no problems with it now.

Cent13

Quote from: Dragon Cat on September 07, 2012, 07:55:33 PM

Not just because of how they look but because I know the players I play with (semi-regularly/sometime   ) wouldn't accept these as acceptable sheets purely because the layout is so different from what they are used to.

Was it the Center Torso issue that concerned you?

Cent13

CT and Head were my two main issues, otherwise it looked real good