Center Torso or Floating Crit on a "2" Location Roll

[OatsAndHall]

The math of how it really works out does depend on if the two critical slots are free or not and how strict to the rules of determining critical hits one is being.

Going super strict according to the rules of how one is supposed to resolve critical hits(also works if there are no roll again locations):

Since the Center Torso is two sections and the Gyro occupies 3 in the first section that is a 1/4 probability total(1/2 for first section *1/2 for how much of that section the gyro occupies.  Since one of four lies in the second section we add a 1/12 probability.  So it would be about a 1/3 total probability.

Now yes if there is one or two roll again results you can argue that effectively the probabilities do change and I won't actually put up that much of a fight because the actual final probability does not actually change as it has to land on a gyro location not enigne, something else that can be critically hit, or Roll Again but for the sake of argument it is close enough to fudge and we often do take short cuts in such scenarios.

In the specific case of the Timber Wolf Prime it only has one Roll Again slot in the Center Torso.

So it's close enough probability would be 1/4+1/10 or 35%.

Now the Right Torso of the Timber Wolf Prime and it's ammunition there from the Front/Back by that same consideration though but adds in that the floating critical must also land on the Right Torso. So 5/36*1/4 or a whopping 3.47222...% chance.

I knew Torso math would get interesting but didn't think it would be that interesting.

I only included the filled critical spots in my calculations, not the "roll again" slots. Seeing as these are mutually exclusive probability events, hitting a "roll again" doesn't affect the probability of hitting a filled slot as you just keep rolling.

However, I didn't think about the "top/bottom" rolls. So, let's plug that out on Timber Wolf's CT:

You have a 50% chance of rolling top and you do so. 50% of the top slots have gyro slots, so you're looking at a 25% chance of hitting a gyro.
You have a 50% chance of rolling bottom and you do so. 20% of the bottom slots are taken up by a gyro so you have a 10% chance of hitting that gyro.
All and all, you have a 35% chance of popping a gyro using CT rules.

Let's take a look at top/bottom probability with the RT ammo bins. You have a 17% chance of hitting the RT, a 50% chance of rolling "bottom" and a 33% of hitting the ammo slots in the bottom. So, you have a 2.8% chance of hitting that ammo (17%*50%*33%).

[monbvol]

I only included the filled critical spots in my calculations, not the "roll again" slots. Seeing as these are mutually exclusive probability events, hitting a "roll again" doesn't affect the probability of hitting a filled slot as you just keep rolling.

However, I didn't think about the "top/bottom" rolls. So, let's plug that out on Timber Wolf's CT:

You have a 50% chance of rolling top and you do so. 50% of the top slots have gyro slots, so you're looking at a 25% chance of hitting a gyro.
You have a 50% chance of rolling bottom and you do so. 20% of the bottom slots are taken up by a gyro so you have a 10% chance of hitting that gyro.
All and all, you have a 35% chance of popping a gyro using CT rules.

Let's take a look at top/bottom probability with the RT ammo bins. You have a 17% chance of hitting the RT, a 50% chance of rolling "bottom" and a 33% of hitting the ammo slots in the bottom. So, you have a 2.8% chance of hitting that ammo (17%*50%*33%).

First correction I see I did 5/36 for hitting the Right Torso, that is wrong and you are correct that is a 1/6 chance so close enough to 17% for our purposes.

So yeah our numbers do line up once correcting for that.

[Charistoph]

Depends on if you're Floating or not.

If not Floating, there are 4 directions you're hitting the CT, while only one for the RT.

And while a Gryo hit is a Bad Thing, an ammo hit is always worse as it takes out Structure (and with the Timber Wolf Prime) provides 2 Engine Hits automatically.

Still, I prefer Floating Crit, because instead of that high chance at a Engine or Gyro Hit, we could be looking at a weapon or Arm Actuator just as much.

[Hellraiser]

Only 2 of 9 crit spaces have ammo in the RT of the Prime. But you're right, there are 4 gyro spaces out of 11 in the CT.

It wasn't the 22% that I questioned, that is 2/9.
It was the RT starting figure, you have 17% (1/6) but its 14% (5/36).

[Hellraiser]

The math of how it really works out does depend on if the two critical slots are free or not and how strict to the rules of determining critical hits one is being.

...........

In the specific case of the Timber Wolf Prime it only has one Roll Again slot in the Center Torso.

So it's close enough probability would be 1/4+1/10 or 35%.

Now the Right Torso of the Timber Wolf Prime and it's ammunition there from the Front/Back by that same consideration though but adds in that the floating critical must also land on the Right Torso. So 5/36*1/4 or a whopping 3.47222...% chance.

I'm not sure why your breaking the tables down into 2 separate D6 tables when its a single table using "effectively" a D-"FilledSlots" die roll.

The example he called out was a T-Wolf Prime, it has 11 Slots filled & 4 of them are Gyros, they all have an equal chance of being hit, so its 4/11.

The example was also shifting a CT (Front/Back) TAC into a RT hit. 
The RT has 5/36 chance of being hit by a Floating TAC from the Front/Back table.
There are 9 slots in the RT of the T-Wolf-Prime and 2 are ammo, so its 2/9, not actually 25% as you used.

[Hellraiser]

You have a 17% chance of hitting the RT,

How are you coming up with 17% of getting a RT hit on the Front/Back table?

17% is 6/36 but the RT slot on the F/B table is on a 5

5/36 is 14%
If you used 2 as a continuous Reroll it would be 5/35 which is still basically 14%.   (I honestly don't recall what happens if you roll 2 a 2nd time)

Oh, I think I've just created a house rule..... "Stacking Floating TACs"
If you roll 2 for the 2nd roll you get a 2nd (3rd+) Crit Rolls chances once you finally roll a location in the 3-11 slots.

[monbvol]

How are you coming up with 17% of getting a RT hit on the Front/Back table?

17% is 6/36 but the RT slot on the F/B table is on a 5

5/36 is 14%
If you used 2 as a continuous Reroll it would be 5/35 which is still basically 14%.   (I honestly don't recall what happens if you roll 2 a 2nd time)

Oh, I think I've just created a house rule..... "Stacking Floating TACs"
If you roll 2 for the 2nd roll you get a 2nd (3rd+) Crit Rolls chances once you finally roll a location in the 3-11 slots.

RT is 6 on the Front Back Table not 5.  5 is Right Leg on the Front/Back table.

I'm not sure why your breaking the tables down into 2 separate D6 tables when its a single table using "effectively" a D-"FilledSlots" die roll.

The example he called out was a T-Wolf Prime, it has 11 Slots filled & 4 of them are Gyros, they all have an equal chance of being hit, so its 4/11.

The example was also shifting a CT (Front/Back) TAC into a RT hit. 
The RT has 5/36 chance of being hit by a Floating TAC from the Front/Back table.
There are 9 slots in the RT of the T-Wolf-Prime and 2 are ammo, so its 2/9, not actually 25% as you used.

Because that is the procedure.

You roll a d6 to determine if it is first section or second.  So that's a pure 50/50 chance.  Then you roll another d6 to determine within that section.

Now what the probability is within that second roll does depend on how many items are in that section and how strict you are about following the procedure.

For Gyro since it takes up 3 of 6 slots in the first section and one in the second.

1d6 to determine section so for the first section that means 1/2*1/2.  Second section is 1/2*(1/4 up to 1/6).  In the case of the Timber Wolf it's close enough to call that 1/5.

Counting only based on how many criticals an item takes up does not develop a complete picture of the probabilities when following the procedure.

So yes our numbers are accurate.

[Daryk]

Personally, I prefer the OG always the torso rule, but all of the groups I've played with recently use floaters.  Whatever! 

[Charistoph]

RT is 6 on the Front Back Table not 5.  5 is Right Leg on the Front/Back table.

I think they meant for 5 results of 36, not on the specific roll of 6.  The note of 6/36 right before that.  17% is 6/36 or 1/6 rounded up.  Pointing out that it is 5, is referencing the 5/36 option which is the chance of rolling a 6 with 2D6.

[monbvol]

I swear I used to be able to math.

So yeah 5/36*1/2*1/3 would be the correct final probability to stop the roll again train on a Timber Wolf Prime's Right Torso ammo bins from the front.

[DevianID]

Without the floating crit rule, we see less diversity. Everyone fields laser boats with the arms and side torsos packed.

oats it should be the opposite.  WITH the floating crit rule, ammo anywhere on the mech can be hit, with the normal CT rules ammo in the side torso can be kept safe as long as you keep the mech front facing (thus the standard TAC rule has more player skill/agency).  Thus, crit packed laser boats benefit more from floating crits as no other location except head hits can destroy the zombie.  WITH the normal CT rule, ammo explosions go down a tiny bit thanks to no floating TAC to the ammo, and zombie mechs get disabled at the same rate as ammo mechs in the CT.

Overall floating crits mean all mechs die/get crippled slower thanks to so many useless crits like lower arm actuators compared to engine/gyro.  But zombie energy mechs benefit more then ammo mechs, which we dont need to emphasize further with any optional rules like floating TAC.

[Hellraiser]

You have a 50% chance of rolling top and you do so. 50% of the top slots have gyro slots, so you're looking at a 25% chance of hitting a gyro.
You have a 50% chance of rolling bottom and you do so. 20% of the bottom slots are taken up by a gyro so you have a 10% chance of hitting that gyro.
All and all, you have a 35% chance of popping a gyro using CT rules.

Let's take a look at top/bottom probability with the RT ammo bins. You have a 17% chance of hitting the RT, a 50% chance of rolling "bottom" and a 33% of hitting the ammo slots in the bottom. So, you have a 2.8% chance of hitting that ammo (17%*50%*33%).

RT is 6 on the Front Back Table not 5.  5 is Right Leg on the Front/Back table.

Because that is the procedure.

You roll a d6 to determine if it is first section or second.  So that's a pure 50/50 chance.  Then you roll another d6 to determine within that section.

Now what the probability is within that second roll does depend on how many items are in that section and how strict you are about following the procedure.

For Gyro since it takes up 3 of 6 slots in the first section and one in the second.

1d6 to determine section so for the first section that means 1/2*1/2.  Second section is 1/2*(1/4 up to 1/6).  In the case of the Timber Wolf it's close enough to call that 1/5.

Counting only based on how many criticals an item takes up does not develop a complete picture of the probabilities when following the procedure.

So yes our numbers are accurate.

Sorry, I'm still not seeing how your method is accurate.
I'll use a new example for simplicity.

New Example.   
Assuming you've already rolled location as Side Torso & you have 7 slots in this new example.

Upper 6 = 3-XL Slots + 3-DHS Slots
Lower 6 = 1-MedLas +  5-Empty/Roll Again

Using your formula the odds of hitting the 7 slots in the breaks down below.
XL = 50% Top * 50% (3/6 Slots) = 25%
DHS = 50% Top * 50% (3/6 Slots) = 25%
MedLas = 50% Bottom * 100% (1/1 Slots) = 50%

I know its been 25 years since I took any sort of Math or Statistics course but I do know you don't have a 50% chance of hitting a ML when its 1/7 slots in either Side-Torso location.

It looks like your procedure isn't accounting for Roll Again Slots which is making the 50/50 top bottom role irrelevant and all slots equal.

You have 7 slots on what is effectively a D12 Roll using 2 D6's to determine the D12.  Each slot has an equal chance of rolling thanks to the roll again.

[Cannonshop]

CT for simplicity of play.  That is, even in advanced play, the more die you have to roll more often the longer it takes to resolve a turn and the less likely you are to actually GET to the end of the battle in a single evening.  (By 'end of the battle' I mean "reach the point where the outcome, barring god's own intervening hand on the dice or cheating, is pretty much over.")

Risk appetite is something you have to deal with in a game.  Too little, and you might as well shelve the mapsheets and go watch sportsball.

[monbvol]

Sorry, I'm still not seeing how your method is accurate.
I'll use a new example for simplicity.

New Example.   
Assuming you've already rolled location as Side Torso & you have 7 slots in this new example.

Upper 6 = 3-XL Slots + 3-DHS Slots
Lower 6 = 1-MedLas +  5-Empty/Roll Again

Using your formula the odds of hitting the 7 slots in the breaks down below.
XL = 50% Top * 50% (3/6 Slots) = 25%
DHS = 50% Top * 50% (3/6 Slots) = 25%
MedLas = 50% Bottom * 100% (1/1 Slots) = 50%

I know its been 25 years since I took any sort of Math or Statistics course but I do know you don't have a 50% chance of hitting a ML when its 1/7 slots in either Side-Torso location.

It looks like your procedure isn't accounting for Roll Again Slots which is making the 50/50 top bottom role irrelevant and all slots equal.

You have 7 slots on what is effectively a D12 Roll using 2 D6's to determine the D12.  Each slot has an equal chance of rolling thanks to the roll again.

And it would not be 50%.

This is why I do prefer using my strict methodology as it does communicate that clearer.

The Roll Again slots do introduce an effective OR probability in a way though and I'll admit it makes it seem like that it would be a 50% when taking that into account.

[OatsAndHall]

Sorry, I'm still not seeing how your method is accurate.
I'll use a new example for simplicity.

New Example.   
Assuming you've already rolled location as Side Torso & you have 7 slots in this new example.

Upper 6 = 3-XL Slots + 3-DHS Slots
Lower 6 = 1-MedLas +  5-Empty/Roll Again

Using your formula the odds of hitting the 7 slots in the breaks down below.
XL = 50% Top * 50% (3/6 Slots) = 25%
DHS = 50% Top * 50% (3/6 Slots) = 25%
MedLas = 50% Bottom * 100% (1/1 Slots) = 50%

I know its been 25 years since I took any sort of Math or Statistics course but I do know you don't have a 50% chance of hitting a ML when its 1/7 slots in either Side-Torso location.

It looks like your procedure isn't accounting for Roll Again Slots which is making the 50/50 top bottom role irrelevant and all slots equal.

You have 7 slots on what is effectively a D12 Roll using 2 D6's to determine the D12.  Each slot has an equal chance of rolling thanks to the roll again.

I did miscalculate.
You need a "6" for the right torso, which is a 13.88% chance on 2d6.
Accounting for the "roll again spots: 2/3 viable slots is a 67% chance.
And, the 50% needed to roll "bottom".

13.88%* 67%* 50%=4.6% chance of hitting those ammo bins.

In your example:
13.88% chance of hitting the RT * 50% chance of "bottom" * 100% (you can ONLY hit the medium laser if everything else is "roll again")= 6.9%. And, with floating crit rules, that's pretty high because the medium laser is the only viable slot in that area.

Since we're talking about floating crits, you need to include the probability of hitting different locations as that drastically lowers the probability. With CT crit rules, you don't have that extra roll which dramatically increases the chance of doing tearing up an engine or a gyro. Even with all of the tinkering with multiplication, you're typically looking at a 10x greater chance of hitting a gyro under CT rules than hitting something critical with floating crits. Bear in mind that taking out a big weapon with a lot of slots is much more probable with floating crit rules. Let's look at taking out an LRM in that Timber Wolf Prime with floating crit rules:

13.88% chance of LT* 50% of hitting "top"* 50% chance of hitting the LRM= 3.5%
13.88% chance of LT* 50% chance of bottom*50% chance of hitting LRM= 3.5%
13.88% chance of RT* 50% chance of "top" *50% chance of hitting LRM= 3.5%
13.88% chance of RT *50% chance of "bottom" * 33% chance of hitting LRM= 2.3%

3.5%+3.5%+3.5%+2.3%= 12.8%

[monbvol]

Add in that even if you roll that 2 float or not you do still also have to roll on the determining critical hits table.  This becomes another layer of consideration for Floating Criticals because it now matters more how many criticals actually result.

[OatsAndHall]

Add in that even if you roll that 2 float or not you do still also have to roll on the determining critical hits table.  This becomes another layer of consideration for Floating Criticals because it now matters more how many criticals actually result.

Yeah, I've been operating under the assumption that at least 1 crit gets rolled. You have about a 36% chance of getting at least one crit.

[monbvol]

Yeah, I've been operating under the assumption that at least 1 crit gets rolled. You have about a 36% chance of getting at least one crit.

And that's fair enough for specific examples involving torso locations.  But start talking limbs and how rolling a 12 when determining critical hits changes what happens, well that becomes quite the consideration to take into account.

[OatsAndHall]

And that's fair enough for specific examples involving torso locations.  But start talking limbs and how rolling a 12 when determining critical hits changes what happens, well that becomes quite the consideration to take into account.

Yup, blowing off limbs is something to consider.

But, the last thing to consider in that math is rolling a 12 which has a 2.77% probability. So, all of the calculations you figure before hand will be knocked down significantly by the probability of that roll.

[Daryk]

And they are inevitably SPECTACULAR when they happen. 

[MoneyLovinOgre4Hire]

As is getting a center torso TAC and destroying the engine with a single hit from an AC 2.

[garhkal]

OR a head crit blowing off the head (or killing the pilot) from a stray LRM round...

[OatsAndHall]

It's been fun to plug those numbers. I knew it was difficult to pull catastrophic rolls but some of these numbers are insane. We've had many games where the cockpit has been blown out on a head shot. The probability of those two rolls is literally .55%. But, this math also speaks loudly to one other thing: the more rolls, the better.

[Col Toda]

Battletech is a game of out maneuvering your opponant and deliberately attacking right left or Rear. The existing rules claiming 2 being a critical on the facing torso rewards the more maneuverable unit with less weapons to bring down an opponent with finesse  . You have to work at it to get the desired result of light or XL   engine hits or ammo hit or head hit with a light MG array 4 with the eye to knocking out the pilot and recovering a largely intact mech . 

Floating crit anywhere  just rewards crude player who has the most guns slug fest where quantity is all that counts not relative postion and tactics are not rewarded . This is supposed to be a tactical combat game .

It also damages specific Zombie designs a that fact your Center torso has a compact engine and Compact gyro with 2 Inner Sphere Double Heat sinks and a medium  X pulse laser in which 7 out of 12 center torso hits are neither Engine or Gyro. So it is manifesly obvious if you want a mech less vulnerable to center torso crits feild it be it custom or the 2 or so stock . Design is supposed to be a compromise between durability and performance.  I designed a 100 ton Zombie  with 2 Heavy PPCs and 5 Medium X-Pulse lasers and 32 heat dissipation . More than half the time you have to Core it to kill it .

Very against floating crits anywhere instead of facing torso it kills much of the finesse mauvering aspect of the game And it makes near pointless the sacrifice in tonnage and firepower in units designed not to care about center torso crits much at all.

[MoneyLovinOgre4Hire]

I'm sorry but no, even a 100 tonner with an armored compact engine and armored compact gyro is generally going to be better off soaking TACs to some other hit location besides the center torso.  Floating crits do not "punish" you for taking a zombie mech, they increase its zombieing ability.

And TACs, like headshots, are good but not something you should be relying on for your victories.  They're rare and that's by design, it's very easy to go entire games without that hit location come up- if you're relying on them for victory you're going to have problems.

[OatsAndHall]

Battletech is a game of out maneuvering your opponant and deliberately attacking right left or Rear. The existing rules claiming 2 being a critical on the facing torso rewards the more maneuverable unit with less weapons to bring down an opponent with finesse  . You have to work at it to get the desired result of light or XL   engine hits or ammo hit or head hit with a light MG array 4 with the eye to knocking out the pilot and recovering a largely intact mech . 

Floating crit anywhere  just rewards crude player who has the most guns slug fest where quantity is all that counts not relative postion and tactics are not rewarded . This is supposed to be a tactical combat game .

It also damages specific Zombie designs a that fact your Center torso has a compact engine and Compact gyro with 2 Inner Sphere Double Heat sinks and a medium  X pulse laser in which 7 out of 12 center torso hits are neither Engine or Gyro. So it is manifesly obvious if you want a mech less vulnerable to center torso crits feild it be it custom or the 2 or so stock . Design is supposed to be a compromise between durability and performance.  I designed a 100 ton Zombie  with 2 Heavy PPCs and 5 Medium X-Pulse lasers and 32 heat dissipation . More than half the time you have to Core it to kill it .

Very against floating crits anywhere instead of facing torso it kills much of the finesse mauvering aspect of the game And it makes near pointless the sacrifice in tonnage and firepower in units designed not to care about center torso crits much at all.

The math shows that you don't have work for it; roll a "2" and you have a much higher chance of crippling a mech because you don't have the second location roll. Playing with floating crit rules has forced us to be more tactically minded as we've pulled much of the crit-seeking out of the game. When we played with torso crit rules, we had LBX and SRM spamming across the board; people knew rolling multiple "2"s in a round would probably cripple or outright kill a mech. We saw a whole lot more laser boats as well; people avoided any mech with ammo in it's torsos. Don't get me started with the number of head hits we were seeing in these situations either.

I'd say we're even more tactically minded with our movement. We want to take someone's left, right or rear sides so that we can cluster the damage done more effectively. We can't rely on crits to win a game for us; we have to tear up a mech as best we can.

[Charistoph]

Battletech is a game of out maneuvering your opponant and deliberately attacking right left or Rear. The existing rules claiming 2 being a critical on the facing torso rewards the more maneuverable unit with less weapons to bring down an opponent with finesse  . You have to work at it to get the desired result of light or XL   engine hits or ammo hit or head hit with a light MG array 4 with the eye to knocking out the pilot and recovering a largely intact mech . 

Floating crit anywhere  just rewards crude player who has the most guns slug fest where quantity is all that counts not relative postion and tactics are not rewarded . This is supposed to be a tactical combat game .

It also damages specific Zombie designs a that fact your Center torso has a compact engine and Compact gyro with 2 Inner Sphere Double Heat sinks and a medium  X pulse laser in which 7 out of 12 center torso hits are neither Engine or Gyro. So it is manifesly obvious if you want a mech less vulnerable to center torso crits feild it be it custom or the 2 or so stock . Design is supposed to be a compromise between durability and performance.  I designed a 100 ton Zombie  with 2 Heavy PPCs and 5 Medium X-Pulse lasers and 32 heat dissipation . More than half the time you have to Core it to kill it .

Very against floating crits anywhere instead of facing torso it kills much of the finesse mauvering aspect of the game And it makes near pointless the sacrifice in tonnage and firepower in units designed not to care about center torso crits much at all.

Not as much as you're implying.  Since the the side facing torso has the highest probablity of being hit anyway, maneuver is still being rewarded.  It just reduces the chance from 100% to 22% when compared to not Floating it.

[Col Toda]

That 78 percent chance of not getting the projected desired results with design compromises ment to achieve it . That seems like a huge difference to me .

[OatsAndHall]

That 78 percent chance of not getting the projected desired results with design compromises ment to achieve it . That seems like a huge difference to me .

You're saying that the torsos only contain flaws in the armor that are exploitable. That isn't terribly realistic.

[Col Toda]

No I am saying you see different designs to exploit the floating crit rules . Units with machine gun arrays 4 s . Roll to hit get a 2 . Then roll how many hit exact same spot say 3 . So 3 possible crit rolls in a leg should impair or cripple the mech . head should kill piliot and or sensor or life support . The underlying design philosophy in the game has . I designed an head hunting med mech with 4 Improved Heavy Med Lasers and 3 Heavy Machine Gun array 4s with MASC and a Supercharger  and a targeting computer for the lasers.  Ment to run behind a mech and blow away a rear torso armor and maybe expliot it with multiple 3 points hits . Floating crit instead of doubling down on a Torso it gives an extra chance to kill the head and pilot an gives a 25 + percent chance of eliminating all the actuators inva leg with only 3 to 9 points of armor damage .
My design philosophy tend to have heavy hitting accurate near heat neutral ammo using mechs to achieve brutally short time combat win or lose. The object is to take down between 1 and 3 mechs per turn starting in turn 3 . The object is to have a huge 2 company per side combat be the least time consuming as possible . The standard facing torso rules have the desired effect of making combat take less time so you have an easier time finishing a big fight without having to take pictures over the course of 3 or 4 weekends with the limited time available.  After playing since the FASA days with the writer of Macarrions Armored Calvary and Jade Falcon Sourcebook the days of nearly every weekend free and 16 hour marathon sessions is over . So my style morphed to what it is today . I gut and clearly will best the opposition force in 15 -20 turns or I run out of ammo and become largely toothless and lose .

I can run a company or more of heat neutral mechs amd combat vehicles in the time it takes someone else to run a lance of TSM equiped mechs trying to achieve and keep the magic 9 heat . I have come to a point were if you do not run some or most of your unit with some football like pre planned tactical plays you are wasting unnecessary time.

Sadley my biggest issue with alternate floating crit rules is that I would resent the extra time spent on an extra die roll in a Brigade or larger fight.

I expect anyone who plays this game for 30 + years gaining a cell phone ball and chain so work and spouse and kids puts extra demands on your time other people might sink with my position.  But for the first 10 years or so I do not expect many to agree with me .