D12 vs 2D6

[Charistoph]

This isnt a quibble about 2d10 being bad--I am trying to show that the bell curve of both is identical, as is any 2dx roll, when you appropriately scale the modifiers.  3d6, indeed any 3dx, is a different bell curve-- as is 1dx and 4dx.

Congruent would be a better term than identical, I think.

No matter how hard you try, 13s are impossible on 2D6, while 12s are much more easy to hit with 2D10s.  But that's to be expected when you go from a range of 2-12 to 2-20 (or 0-18, depending on how one's dice are set up), or in other words, 11 results with 36 chances and 19 results with 100 chances.  The 2D10 is going to be much bigger, with its average result being that much higher. 

Now the percentage slopes would be a little bit different.  The center distribution of a 2D6 (i.e. 7) is about a 16.7% probability, while the the center point of 2D10 (i.e. 11) is about a 10% probability.

[Daryk]

I proposed a way to smooth out those cliffs at the ends of the bell curve here.

[Cannon_Fodder]

The basic premise for our system:

Target Base (rather than just hexes moved): (Pilot's DEX+INT+Sensor Operation Skill Level)/3 if walked /2 if running, round fractions down. +1 per hex moved capped by Piloting Skill level.

Attacker: +1 Walked, +3 Ran, +5 Jumped
Ranges are +0S/+3M/+6L +1per hex under range
Woods: +2 Light /+4 Heavy

When making rolls you get the Skill Level AND AToW Link Bonus, Plus 10's explode.

With this system an Ace pilot in a Marauder can be harder to hit than a barely competent FNG Locust pilot.

[DevianID]

No matter how hard you try, 13s are impossible on 2D6

Charistoph, the issue is when you scale the modifiers (the prerequisite) then 13 on 2d6 is 21-22 on 2d10, AKA just as impossible.

If you look at your chart, the slope of the distribution is the same, just streched out.  The stretching is the modifiers being scaled.  Thus the 2d6 distribution has the same curving slope of 2d10, but 3d6 has a different slope (when modifiers scaled) as the tails are further out.  1d6 doesnt have a slope, just a flat line.

Cannon_Fodder, the biggest system change you pointed out is adding an additional modifer to the target, and an additional modifer to the attacker.  On the base 2d6 system you would add a 'sensor' defensive skill to each mech in standard btech, and add exploding 6s to the attacker.  Exploding 6s add ~+1 to a 2d6 roll (1.167), so the sensor skill would range from +0 to +3 to make a green locust (max TMM +4, +0 sensor) easier to hit than an elite marauder (TMM+2, sensor +3).  After that, RPG characters tend to have better gunnery than normal pilots, so having a 2 better gunnery than non-PC characters tracks for the sensor bonus to cancel the exploding die bonus and the AToW link bonus.  Now, the RPG system has all the modifiers scaled already; im not saying you should switch, im just showing that because all 2dx rolls have the same curve, anything you can do in one system you can do in the other presuming you get the modifiers scaled correctly.

EDIT: more clearly.  In Btech the base to hit is 4 for regular pilots.  This can be expressed as -1 (gunnery regular skill) -1 (pilot link attributes) +1 (enemy regular sensor skill) +2 (pilot int) +3 (pilot dex) for a total of 4, which is how your system seems to get to a base to hit chance if it was only using btech modifiers; since in Btech everyone has the same DEX/RFL/INT and sensor skill, with only gunnery able to change (it is RPG lite).

[Charistoph]

Charistoph, the issue is when you scale the modifiers (the prerequisite) then 13 on 2d6 is 21-22 on 2d10, AKA just as impossible.

If you look at your chart, the slope of the distribution is the same, just streched out.  The stretching is the modifiers being scaled.  Thus the 2d6 distribution has the same curving slope of 2d10, but 3d6 has a different slope (when modifiers scaled) as the tails are further out.  1d6 doesnt have a slope, just a flat line.

And you bypassed the important parts to come to this, picking out one single sentence to criticize out of context.  They are not identical bell curves, but they are congruent (maybe not the best word, but the closest I could come up with).  One reaches higher points than the other, but they otherwise have the same shape.

Then one needs to consider the probabilities of something happening, which is why I brought up the percentage chance of it happening.  It is far easier to hit that '7' than it is to hit that '11', even though there are more opportunities to do so, and far harder to reach a '2' or '20' with 2D10 than it is for a 2D6 to get a '2' or a '12', the maximum amount.  All those additional numbers reduces the chances of a certain number coming up as other numbers come in to play.

[assaultdoor]

It is far easier to hit that '7' than it is to hit that '11', even though there are more opportunities to do so, and far harder to reach a '2' or '20' with 2D10 than it is for a 2D6 to get a '2' or a '12', the maximum amount.  All those additional numbers reduces the chances of a certain number coming up as other numbers come in to play.

Getting exactly 7 on 2d6 is a lot more likely than getting exactly 11 on 2d10 (16.67% vs 10%), but in BattleTech you usually want to roll at least a 7 on 2d6 or at least an 11 on 2d10. Those chances are reasonably similar (58.33% on 2d6 vs. 55% on 2d10).

Hitting extreme values on 2d10 is indeed harder than on a 2d6, so either you leave, say, the HVAC/UAC failures as 2 on 2d10 and find certain weapons are a little more reliable (1% chance of failure vs. 2.78%) or you adjust it so that they fail on a 2 or 3 (a 3% chance of failure vs. 2.78%).

If you scale carefully, you should be able to get similar (but not identical) results. For example, there's about an 8.33% chance of rolling 11+ on 2d6. Your options for 2d10 are either 18+ (6%) or 17+ (10%). Likewise, there's about a 41.67% chance of rolling 8+ on d2d6. Your options for 2d10 are either 13+ (36%) or 12+ (45%).

Scaling the to-hit modifiers helps, but now you're scaling things by roughly 1.68, so there's going to be a lot of rounding. At least, I assume you'd use 1.68, since that's the ratio of the standard deviations. There may be a better option, but it's probably still going to involve a lot of rounding. Do you round each modifier? In this case, +1 on a 2d6 turns into +1.68 on a 2d10 and then gets rounded to +2, which means that two +1s get converted to +4. Or do you round total modifiers? In this case, two +1s on 2d6 turn into 3.36 on 2d10 and then get rounded down to 3?

You aren't going to replicate the 2d6 system on 2d10. You can get pretty close in most cases, but it won't match up completely. On the other hand, if you look at BattleTech's to-hit modifiers and think "We need a bunch more of these," then it's easy to reduce the importance of some modifiers to fit new ones in. It won't match up with BattleTech's 2d6 system, but that's the point.

[Charistoph]

You aren't going to replicate the 2d6 system on 2d10. You can get pretty close in most cases, but it won't match up completely. On the other hand, if you look at BattleTech's to-hit modifiers and think "We need a bunch more of these," then it's easy to reduce the importance of some modifiers to fit new ones in. It won't match up with BattleTech's 2d6 system, but that's the point.

After doing an Alpha Strike Campaign game last Saturday, I've wondered how much lighter the game would be to run Total Warfare with the same modifiers instead of all the accumulations.  All that would be left would be simplifying the PSR modifiers like the Gunnery modifications are.

[DevianID]

Alpha strike begins by eliminating the +2 shooter penalty for running (and knocks 2 off jumping), but after that most of the core modifiers are the same (range, TMM, ect.)  The individual weapons +/- is handled with damage changes, so the net is basically the same.

Thus, in core Btech if you reduce everyone's movement penalty by 2 you approximate the level of hits you see in alpha strike.  -2 changes the metric of what is good due to how the bell curve works; now you want to run/jump every turn as it doesn't penalize you outside heat, while in standard btech you often sit still for multiple turns to maximize your hit chance.  It makes for a more mobile game, but light units that had to run every turn anyway get a little better as now they dont have a movement penalty--they still die too easy versus elite pulse monsters though.  The archer wasn't moving before, but now can run, so he is a little harder to hit versus before if he can spare the heat.

Edit: Assaultdoor you get it exactly about scaling modifiers.  It isnt exactly perfect like you said, as +2 in btech x 1.68 is 3.36, but the game changed the base formula anyway so they didnt match as is.  You can also multiply your 2d6 dice by ~1.58 to find an approximate 2d10 roll and hit percentages pretty close, but you couldnt multiply 2d6 by 1.5 to find an approximate 1d20 or 3d6 roll as the tails spread out much slower/faster.

[Charistoph]

Alpha strike begins by eliminating the +2 shooter penalty for running (and knocks 2 off jumping), but after that most of the core modifiers are the same (range, TMM, ect.)  The individual weapons +/- is handled with damage changes, so the net is basically the same.

Thus, in core Btech if you reduce everyone's movement penalty by 2 you approximate the level of hits you see in alpha strike.  -2 changes the metric of what is good due to how the bell curve works; now you want to run/jump every turn as it doesn't penalize you outside heat, while in standard btech you often sit still for multiple turns to maximize your hit chance.  It makes for a more mobile game, but light units that had to run every turn anyway get a little better as now they dont have a movement penalty--they still die too easy versus elite pulse monsters though.  The archer wasnt moving before, but now can run, so he is a little harder to hit versus before if he can spare the heat.

Alpha Strike knocks 1 off of Jumping, actually, and pretty much eliminates Running as an option (movement is 2*Walk inches, which is the Miniature Rules standard for Walking Conversion, but turning is no longer an issue), plus provides -1 for standing still. 

For all intents in purposes, conversion would apply a -1 to current AMM standards.  Running would then be just a +1 at that point instead of a +2.

Also consider that the TMM would be that of unit's full Walk capability rather than just how far they moved that turn, so long as they actually moved one hex.

On the other hand, having 2 Light Woods between you would mean the same as having just 1 Light Woods between you, and the only way to improve that is to have Partial Cover or block LOS all together.

[DevianID]

If TMM is full walk, and we dont pay for turns, then you need to run to turn and keep the full walking TMM.  Hence why I knocked 2 off movement (but you are right it is only 1 from jumping)  Sprinting is also only 1.5x movement, thus the base move in alphastrike is closer to a run than a walk.

Unless you mean just get rid of running and give free TMM, like alpha strike did.  Im fine with that as a simplification, much more fine with that than keeping running but giving free turns or free TMM based off running MP.

Terrain between the systems is different, as they have a very simplified set of terrain but also check actual LOS.  In btech we dont check LOS but have more terrain modifiers to make up for this.  Thus I wouldnt change btech terrain rules for mapsheet play as mapsheets use different rules for blocking LOS.

[Charistoph]

If TMM is full walk, and we dont pay for turns, then you need to run to turn and keep the full walking TMM.  Hence why I knocked 2 off movement (but you are right it is only 1 from jumping)  Sprinting is also only 1.5x movement, thus the base move in alphastrike is closer to a run than a walk.

I never said that TW should drop paying for turns.  It was only how it treated the Modifiers themselves which I was bringing up.

The Movement doesn't change if you run or not, and it is limited to Miniature Rules of the Walk of the model, i.e. a Centurion's 4/6/0 is just 8", while a Spider's 8/12/8 is 16"j.  Nothing changes the TMM, either, except for Jumping.

Unless you mean just get rid of running and give free TMM, like alpha strike did.  Im fine with that as a simplification, much more fine with that than keeping running but giving free turns or free TMM based off running MP.

That would be closer, but there is no reason to give free turns or setting a "default" TMM to Running MP.  TMM isn't quite free in AS, as one has to literally move the equivalent of 1 hex in order to gain it.  Movement still has its benefits in Battletech, even if how fast one went determines how hard you are to hit.  It's mostly affects what location direction you'll hit, but it can affect LOS as well.

Terrain between the systems is different, as they have a very simplified set of terrain but also check actual LOS.  In btech we dont check LOS but have more terrain modifiers to make up for this.  Thus I wouldnt change btech terrain rules for mapsheet play as mapsheets use different rules for blocking LOS.

Look up the Miniature Rules, and you'll find them rather similar to Alpha Strike's rules in many areas.

And we check for LOS in Battletech all the time.  In fact, trying to avoid it is a key tactic for Lights who are trying to maneuver to a better position to strike from.  Just get some terrain +2 Levels over what the Mech is standing on between it and what can shoot it, and it's blocked.  Plus there is the density of Woods to consider, with 3 Light Woods blocking LOS.

Unless you're meaning a "True Line of Sight" concept like 40K's been trying to do for a decade now.

But we should probably stop this direction of thought here, as it's probably better suited down in Fan Designs.

[Stormy]

I’m enjoying that math, but the one place I can see d12 shining is by taking away the need for multiple rolls on packaged critical hit tables.

[Kovax]

I’m enjoying that math, but the one place I can see d12 shining is by taking away the need for multiple rolls on packaged critical hit tables.

There are situations where a flat probability line is more useful than a curve, and places where you want a heavily center-weighted "bell shaped" probability curve.  The first can be done with a single die, the latter benefits from more dice.  2 dice is a compromise which works passably well in either case, depending on how you combine them (such as simulating a D12 by using the first die to generate a "band" of possibilities for the second die, as used in allocating critical hits, versus adding the two digits).  3 or 4 dice offer a much sharper difference between the means and the extremes, where the tails at either end are VERY unlikely compared to the middle region.  That works well for finer variations in probability near the center (good for shooting odds, such as a 53% chance versus a 58% chance), or for limiting the occurrence of extremely unlikely events toward the ends (critical hits, gun jams, and breakdowns with a 1% or less chance to happen).

BT's use of 2D6 puts it in the "middle of the road" range of granularity, with a moderately weighted probability curve (more like an inverted "V" than a curve with only 2 dice).

A game like Warhammer with a 1D6 roll has terrible granularity and a totally flat probability curve, so even a single +1 or -1 modifier is fairly drastic.  Warhammer gets its granularity by having separate rolls to hit, to wound, and to save, producing a pseudo-3D6 system to "kill" a figure, but where a modifier on the initial 1D6 roll can have a far more significant impact than it would on a straight 3D6 roll.

In essence, there are times to use 1D, 2D, or 3D rolls to control probability at the center compared to the edges, and the size of the dice determines the granularity of the system.  A fine-grained system (bigger dice) allows for subtle variations and minor differences between fairly similar things, while a coarse-grained system can only distinguish between large differences in probability.  A system which can use different numbers of different size dice for various situations can produce far more "realistic" chances of an outcome, assuming that the base odds and modifiers are properly thought out.  The down side is carrying all of the different size dice and knowing how many of which of them to roll for each situation.