Simple Method for interpolating combat values

[RLW]

As any one who has played PG knows   there are  always those times when one can only muster say  29 combat value for a Direct Fire shot which rounds down to 22 being just 1 lousy  point from 30. I have found a simple way to  address this  effect by using a die roll  to interpolate between the listed  combat values in the  various fire effect charts.

The way it works is if the total is equal to a listed value then treat as usual. But if it falls between two listed values, say  it is 25 then take the difference between the  listed value that is higher from the one that is lower (e..g for 25 on the direct fire table that would be 30 - 22 = 8) and roll a  die with that difference (e.g. in the case  one would roll an 8 sided die) and add that value to the regular dice roll the treat that new total as normal (i.e round down). Thus say one rolled in the above example a 4 on the 8 sided die then the new total would be 25 + 4 = 29 which rounds down to 22. But if one rolled say a 6 on the 8 sided die then the total would be 25 + 6 = 31 which rounds down to 30. 

If the  n sided die used to get the interpolation  additive value  starts with zero then use the numbers printed on that die. If it starts with 1 then treat the  highest number (e.g. 8 for an 8 sided die) as 0. 

Thus is say  one has an original  total of 23  the only way to  get it to bump one up to 30 (for direct fire) is to roll a 7 on the  8 sided die. But if one has a original total of 29 any roll but  8 (which  is to be treated as 0) would  bump one up to 30. So it always pays  statistically to add a point or two  to the original total using this method vs the standard method. This method works for  Direct Fire, Bombing fire, Assault fire fire, but is not applicable to AT fire.

This method does require one to buy  a number of n sided die. For example a have a collection n sided die that include  2, 3, 4 , 5 , 7 sided, 8, 9, 10, 11, 12, 13, and 15 sided . But say if one does not want to buy that many special n sided die one can use a larger one as a substitute for a smaller. For example one can use  a 6 sided die for a 5 sided and just reroll whenever one rolls a 6 (and a five roll would be treated as a 0  as per the above rule).  But I have found doing that adds mental calculations and it is much simpler to buy the  full set of n sided die.

Even though one has to roll more die I find this to be pretty easy to use and  eliminates that other problem (that seems pretty gamey) of having to  get those extra points to  make that 29 total go over the top to 30. It does make the game slightly more lethal in that on the average  one will have more shots  that  bump up. One could address that by coming up with a method that would round both up and down. But that would add more complexity, and who wants to make the game  less lethal anyway. 

But it helps both sides so I don't think it would affect play balance too much other than  having a 18 OB  vs 17 OB artillery factor would benefit the 18 where  with the normal method bot would  round down to 16 and thus tend to be a wash (unless added with other arty shooters). So it could have some small effect on balance, but that might be good in that it better  rewards the  side with that higher  factors (e.g. an 18 should be better than a 17 vs both rounding down to 16).

At nay rate I have enjoyed using this method to interpolate  dice rolls and thought I would share it here in case anyone else might find this interesting or possibly  enjoy it likewise..might enjoy using it themselves.

BTW, here are some sites where one can buy n sided die (and there are  more ) so they are pretty easy and affordable to buy.

http://thedicelab.com/d120.html

http://www.ebay.com/itm/Purple-7-Sided-D...1290182330

https://mathartfun.com/d357.html

One more note. Once one  adds the interpolation die roll and gets the adjusted  combat value (rounded down to the  listed values on the  CRTs) the one adds  shifts as normal. And the +3 and -2 limit for shits  does not apply to the interpolation  in that it is not a shift but is an adjusted roll. So  if one bumps a 17 to a 21 by rolling say a 4 on the 5 sided die for a direct fire shot that is not treated a a shift from 16 to 21 but simply that  one rounded up to 21 rather than rounded down to 16 by adding the  interpolation  die roll value and the rounded down to to the  nearest listed value. Thus one could still get a +3 shift  in this case. That way  small round ups , e.g. a 29 to a 30 do not prevent one from getting a further +3 shift.

[Hugmenot]

Direct Fire will be more lethal using this method because any shift due to die roll will be upward. Also, do you consider this a shift and count it towards the maximum +3/-2 column shift? Despite the increased lethality, I believe this is a reasonable alternative if you're in the camp that believes every factor should count.

Same comment for Bombardment. I may be more likely to use this approach for Bombardment because I would like a 10 increment to be more effective than an 8 increment and see Bombardment to be a little more potent.

Assault will definitely be bloodier.

Keep in mind the added lethality may affect play balance, especially in scenarios where the difficulty is to achieve certain objectives within a certain time frame (eliminate X enemy steps immediately comes to mind). I would be curious to hear your impression as to how it affects the pace of the game.

[RLW]

Of course one can use this (or not use this) how ever on likes, so one can say use it just for bombardment. I do not treat it as a shift so it does not limit the +3 shift in that regard. I haven't really played the same scenario with and without this so I do not have any sense of how bloody it makes the game. However, I find that the losses seem to be pretty much in line with what one might expect based on the thresholds for loosing initiative. The main effect is that how one plays the game in that one no longer has to worry about getting that last combat factor to get the next level on the CR table. So it seems to affect game play more than game results, but it does affect both. I do not that it adds more uncertainty in that one a 4 CF factor for direct fire can become a 5 (with 50% probability), add for a 1 hex OP Fire shot can become an 18. So it makes 4's more of a threat and one needs to be all the more cautious against running up against a 4 than without using this..

[RLW]

It also makes  5s and 6's different that even two 5's is a 10 and two 6's a 12  but both  less than the 13. But with this a 6 has a 25% chance of bumping up to a 7 so it is better than a 5. And  two 5's only has a 25% chance of bumping up to a 13 while two 6's has a 75% chance of doing so. So it rewards having even  a point more fire power.  

Now if one likes the extra resolution but not the increase in lethality one can  roll two interpolation die, one that using the difference for the  two barketing listed  numbers that  adds and the other uses the  difference of the  lower value and the next lowest that subtracts. For example say one has a original total of 15 for DF. Then one would use the 18-13 = 5 die roll to add and the 3-9= 4 sided die to subtract to that that original DR of 15. Say one rolled a 3 for the  5  sided roll and a 1 for the 4 sided roll that would  give 15 + 4-1 = 18 which would bump up the roll. But if say the  4 sided  die roll  was 2 the total would just and round back down to 13. But say the  original value was 14 5 sided  die roll was only 1 and the  4 sided  die roll was 3 then the  be 14 + 1 -3 =  12 and that would round down to 9.

With this method one should roll for even original values that  equal the listed in that there is the possibility of being bumped down instead of being bumped up. So say  one has a 13, that would not be enough to assure that this would not be bumped down by a high roll on the  negative die roll and a low one on the positive one. This would require one more die roll and a bit more mental gymnastics than the other method but would  tend to not so much  increase lethality in that these interpolation rolls could hurt one as well as help one. I might test this out on a game or two and see how well it works.

[edit]
And let me end here with one more thought. The  additional only interpolation method probably in effect raises the over all lethality by in effect creating  (on the average) a +.5 shift. The  additive/subtractive  two die interpolation method bring that average back to about 0 in that it also adds a -.5 due to via the negative roll  that roughly cancels out the +.5. And the hybrid method allows that .5 (on the average ) shift to model things that just don't warrant a full + 1 shift such as perhaps special leader abilities and such. 

And that is this idea in a nutshell (albeit perhaps a somewhat lengthy one at that). But what i set out to do was to devise a method to do linear interpolation of CRT results that did not add  new tables and such  but does add an addition one or two die rolls (based on which method  one might employ). I am sure there are other ways to skin that cat as well, given that cat even needs to be skinned. Now method 1 i have tested and seems to work well, if one does not mind the  lethality boost. I can't really comment  more on methods 2 and 3 until I test them out in actual game play. So I include those other two variants to this basic method here for those that might like the idea but are not happy with any lethality boosts  as a way to achieve that goal without adding too much more complexity to play, and even (perhaps) provide the underlying mechanics to  do other things as well by making that  boost in lethality for method 1 a feature and not a bug. 

But for me, having played PG for many years now, adding a bit of extra chrome now and then to it adds new life to a very beloved  and tried and tested system and thus help ms me maintain that same level of enthusiasm I had when I first starting playing the game,  regardless of whether I continue in the future to use that new chrome or not, either way it is fun to devise and test them out to see how well they work... or fail to work. That is one of the (many)  advantages of board games over computer games in that one can easily do that  with board games but (typically) not so easily with computer games where one can try out different  mods to rules and such and see how they work... and to see if it turns out to be one's cup of tea or not. 

And for me the difference between roll playing games and  purely strategy/tactical games is that  in the former one does things to play a roll  even though doing that brings no reward  for doing so in the game mechanics while the later  does. So when I play PG I tend to roll play a bit  to avoid gamey tactics and having a way to make that less of role playing and having the game reward such behavior is a plus, given that it in turn does not bog down game play too much. So that here yet another goal in devising this system to  instill those things that one might do  under the guise of roll playing into the game mechanics so that  there can be a material advantage in adding  that extra point of fire power rather than it being discarded by the (dreaded) rounding down. Thus it makes it easier to do that given that it in turn can buy one some benefit  other than (merely) satisfying one's own sense of proper tactical operation/realisms.

[RLW]

[edit]
BTW, what I found this (that is the method that only can bump up the original combat value (CV) total and nt the second method that can bump a CV up or down)   tends to do is make it more profitable to spread out units. For the potential killing power of a lowly 2 or 4 combact factor goes up a notch (or can with a good roll) and thus they can better  hold ground without having to be staked. This tends to reduce some of the bunching that happens otherwise of super dense  gaggles of stacks and spreads out the combat a bit more, which for me makes the game noth more fun and perhaps more realistic as well.

One other thought here.  increased lethality may not men greater combat losses per se in that it might instead cause units to employ more caution and thus affect game play.

[RLW]

[edit]
BTW, what I found this (that is the method that only can bump up the original combat value (CV) total and nt the second method that can bump a CV up or down)   tends to do is make it more profitable to spread out units. For the potential killing power of a lowly 2 or 4 combat factor goes up a notch (or can with a good roll) and thus they can better  hold ground without having to be staked. This tends to reduce some of the bunching that happens otherwise of super dense  gaggles of stacks and spreads out the combat a bit more, which for me makes the game noth more fun and perhaps more realistic as well.

One other thought here.  increased lethality may not men greater combat losses per se in that it might instead cause units to employ more caution and thus affect game play.

Still one more option that employs a hybrid of the two methods I described above. to further add subtle factors that might not have a huge impact on the game outcomes  but give the game extra  crunch, albeit at the expense of a bit extra work.  The idea is to  use these two methods to employ  less  dramatic effects than a hole column shift, which may be too much of a benefit can use  the plus only  in some situations to give the unit an extra  benefit.  to give to some  effects. The idea is that one  might employ the  use of the two interpolation die (plus and minus) option normally but  may use  the plus only as a reward fro certain situations or the minus only die as a penalty.

BTW, in this hybrid method one probably would be best off to treat the maximum roll not as a zero but use that maximum value when  rolling against  listed values.  Thus a 7 roll for a 7 sided die would be read as a 5 and not a 0 if applied to say an 11 on the DF table so that it would have  a chance to be bumped up to a 16 by rolling a 5. This  then would give all CVs a chance to be bumped up (the down side is that the listed value and the  CV one greater would have equal probabilities of getting a bump up..



 Alternatively  when rolling for a listed  CV one could use  the next highest  sided die, such that instead of a 4 sided die, roll a  5 sided, and still treat the maximum roll as  zero. That would make rolling for one higher Cv a bit better. For say rolling for a 9 assault  instead of using the 13-9 = 4 sided die one would use  a 5 sided die (with 5 being read as zero). That way a 9 would have a 1/5 chance of being bumped up but a 10 would have a 1/4th (slightly better than the 1/4 as it should with  10 being greater than 9).  The  other firt mentioned method would cause both the 9 and the 10 in this example to have a 1/4 chance of being bumped thus offering no advantage of the  10 over the 9 , thus i think this  second method to be the better of the two. 

No, I am thinking even better one need not roll at all  for the  single die case when the original CV total equals a listed value on the CRT. The advantage it gains is that  not having to roll the negative  die roll it can never ve bumped down, even if it neither can ever be bumped up as well. So am am striking out the other two options above in that this  one is both the simplest to employ and  seems to work the nest as well. 

For example  the  special leader benefits  rules that  give leaders additional powers such as rifle, MG, night fighting, urban combat and such could be  backed down a notch from giving a  full shift to  just giving a plus interpolation with no minus. 

For example if a leader is  in an assault and has urban combat special ability rather than that giving  the assault a full +1 shift instead would relax the requirement for the negative extrapolation die roll. Say the original combat factor is 14. Without that special power the assault would roll both the plus extrapolation 5 sided die (18-13 =5) and the negative 4 sided  die (13-9 =4) which could bump it up to 18 with a 4-0 roll or bump it down to a 9 with a 0-3 roll of each, or just round it down to 13 for most other  rolls. 

But if that leader has that urban combat special power then it would only need to  roll the  5 sided additive die and not the  4sided  negative and have a much better chance of being bumped up and no chance of being bumped down to a 9. And if the original CV for that assault was say a 13 (which is a listed value in the assault CRT, and the leader had that extra power then  it still would have a 1 in 5 chance of being bumped up if it rolled a 5 (where as per the rule above) that 5 would then be read as a f5 on the 6 sided die and not as a 0 as in normal extrapolation rolls for non listed original CV. This could give nuance (i.e  more crunch) to the game (albeit at extra work) without giving it too much, as the original rules seems to do.

So one could use this hybrid method as a way to add resolution to combat rolls without adding to the over all lethality using the add/ subtract two die roll option but  also provides a way to give a smaller bonus than a  full +1 shift  for things that might add nuance such as special leader abilities and such. One I might consider adding is that if an assault has a turreted AFV it gains in addition to the +1 (given the  plus only  extrapolation advantage but not if it only has non turreted AFV, thus giving  turreted  AFVs a slight advantage over non turreted ones in assaults. Another  such bonus could be given to units that fire on moving units using OP Fire  that if that unit moves more than one hex one gets the  plus only benefit. And there are many others I am sure one could dream up and add if they wnat more crunch and nuance and don;t mind the added complexity that goes with them.

So  I am suggesting three variants here for  using the method for interpolation, 

1. the single additive die roll option that is the simplest and easiest to use but does up the over all lethality of the game a bit,
2. the two die roll additive/subtractive that adds another bit of complexity but shouldn't  affect the over all lethality too much, and
3. the hybrid method described above that  employ both methods  using the single  die roll option as a bonus (but less than a blanket full +1 shift) for having certain leader  skills or equipment or tactics or such.

I have only tested option 1 above so I am not sure if there might be a few bugs in options 2 and 3 that might need to be further ironed out. But I might do some testing of these to see how well they work and if they are worth the additional effort to employ by either raising the  realism, crunch factor and/or fun level of the basic game enough to justify ever using them. 

[RLW]

I thought I would make a table that  captures (my latest) interpolation dr conditions  YES means that it is a applicable dr condition - means that  it is a minus only interpolation dr condition and  blank means  neither. FG = fire group and applies if any  unit in FG has condition. OP = opportunity fire, units is used  hereto  refer to combat units and not leaders, in assault "against" refers to the one receiving the AF and "by" refers to the  side  conducting the AF. These conditions have no effect on other normal shifts and are in addition to them.

Having two  or more plus conditions gives the exact same result as only having one, except that the max die roll is treated  as its presented value and not as zero. Same for negative conditions. For example if one had a FO with special abilities and and arty leader with special abilities (see table below) then that plus die roll would  treat  say a 5 rolled on a 5 sided die as 5 and not as 0 (given there were no minus die roll conditions as well).

Having both plus and minus condition  cancel  each other out. So if one has one plus condition and one minus then they cancel each other out and  one rolls both plus and negative die. But if  one has two plus and only one  negative then one would employ the plus only roll, etc. If none of the conditions exist (which will typically be the case) or that the number of plus conditions equals the number of minus conditions so as to  cancel each other out then both the plus and minus die are rolled and added together for the purpose of interpolation. 

If a situation applies to some units in a stack but not all only one interpolation dice  roll is made but the results would be applied to each unit as to what conditions apply to that unit. Thus say a stack of three one unit might be bumped up to the next column, one bumped down, and the other not affected. This is in addition to any normal shifts. BTW if this ever gets too messy one might need to write down on a note  the interpolated results for each unit. 


Interpolation results do not count against +3/-2 shift limits for DF.


Plus Conditions______________________________________DF---DF OP----BF----BF OP-----AF (attacker)---- AF (defender)
1. DF Op fire against  a target that moves greater than 1 hex..................YES                      
2. Assault against a wheeled vehicle (but not MC), 
OT, or non turreted AFV............................................................................... .......................................................YES..................... YES  
3. DF against  target that is lower and adjacent to the firing unit..............YES......YES
4. DF with a MG (in FG) that has a leader with MG special ability................YES.....YES
5. DF if FG has INF and leader has rifle special ability.................................YES.....YES
6. Spotter  has FO special skill ...........................................................................................YES.......YES
7. Arty leader has Arty special skills.....................................................................................YES.......YES 
8. AF by ENG unit on non first AF (see note 1 and 7)............................................................................................YES..................... YES
9. BF against targets in woods (to reflect air burst).............................................................YES......YES
10. AF by leader that has applicable urban or rural leader ability.......................................................................... YES......................YES
11. AF against first AF (see note 1 & 6) ............................................................................................................................................YES
12. BF against wheeled vehicle (includes MCs) or OT AFV.....................................................YES......YES

Minus Conditions _____________________________________ DF---DF OP---B---BF OP----AF (attacker)-----AF (defender)
1. DF against any target in terrain limiting hex (that has no other DF shift). YES    YES
2. AF by any OT AFV  against INF (see note 9).....................................................................................YES........................YES
3. (2x) AF by any non turreted AFV (see note 8)  ................................................................................YES........................YES
4. DF by scouts or Cav (not just horse cav)  at range greater than 1 hex..... YES
5. DF and BF against dug in targets in woods (see note 2)...........................YES....YES......YES.....YES
6. AF against withdrawing  units.............................................................................................................................YES
7. Unit firing at max range ...........................................................................YES....YES......YES.....YES
8. AF against  units all in non good order................................................................................................................YES......................YES
9. AF with INF with no AFVs/inherent AT fire against AFV in clear terrain..................................................................YES
10. DF at INF in river hex (major or minor)...................................................YES.....YES
11. First assault fire. (see note 5)............................................................................................................................YES
12 AF by no leaders or none  in good order............................................................................................................YES
13. Air attack against hex adjacent friendly units (see note 4)........................YES
14. DF fire against IG or Arty with gun shield.................................................YES

note 1. In addition to normal shifts.
note 2. only effect of having  dug in counter in woods (e.g. no +1 shift or first fire). Thus using this rule one can dig in in woods but it only helps one in regard to the  interpolation roll and provides no other benefit. It would cancel out the other rule (rule 9 in the plus conditions).  
note 3. The negative only  die role condition  1 gives terrain that offers no DF shifts such as fields (in season) at least some protection from DF fire . But if the terrain has  one or more negative  shifts this condition does not apply. 
note 4.  This condition reflect the fact attacking from the air targets close to friendlies is difficult and more caution has to be employed.
note 5.  The attacker in an  assault has to be on the move. But less so as the assault develops
note 6. In an assault The defender does not have to move where the attacker initially does so this condition reflects that.
note 7. It always pays to have guys with demo charges (regardless of the terrain), but they have to get close first and hence  this rule only applies to subsequent AF and not the first.
note 8. This conditions counts double, i.e it can cancel out two plus conditions and thus invoke the battle of the zeros rule and give any plus dir roll that boost by reading its max  value as presented and not as zero).
note 9. the idea here is that an OT vehicle  near enemy inf would be so worried about them that it would likely hamper their offensive ability a bit.

BTW, I will try to update this as I play out my test scenario

Obviously any such list as this will reflect one's own personal preferences or biases. But the idea here is not so much on making anything like an definitive list of conditions but rather to just test out the idea in general and see how its works. And most of these I just thought of off the top of my head so no real thought has gone into them, so this is more of a first cut than anything  meticulously thought out and tested. But it shows how having something less potent than a full +1 shift might open the door to  including other secondary factors such as these.

[edit] Here is an optional rule that I  like (but haven't tested yet) that one always rolls both the plus and minus die, but if the situation dictates that only the plus die or minus die is to be used then that other die roll is treated as zero no matter what it rolls. However if it in fact did roll a zero then that other die roll would treat its maximum value not as zero but as its presented value. Thus say the situation called for only a plus die roll of a 5 sided die but that minus die would have been  4 sided die had  the situation called for  both the plus and minus rolls. By this rule one would roll both die but treat the minus die as a zero regardless of what it rolls.

 Say one rolled a 5 and a 3. The 5 (being the max number) would be read as a zero and the 3 (being that the condition did not call for a negative roll) would be read as a zero as well, giving a 0-"0" = 0 result with the " "'s around the zero indicated that is how that die rollis read no matter what the actual roll was. 

But if the minus die roll was a 4 and not a 3 then that would be read as a true zero (being the max value) and that would cause one to read that 5 not as a zero but as a 5 and thus the sum would be 5-0with no " " on that zero for it was a zero that was rolled  . Thus there is a bit more mental gymnastics in this approach but one has the benefit that one always rolls two die  and the conditions  dictate merely how one reads those two die rolls rather than how many die one rolls. thus with this rule there are two ways that the max die roll can be read as that value and not a zero. 

Either form where having two (none countered) conditions  (for either  a plus only or minus only roll) or when one has only one such  (not countered) condition causes that "not rolled" die roll if it rolls a  true zero (i.e. 0) vs merely an assumed zero (i.e '0") to boost that other die roll by replacing its normally read zero with the listed value (e.g. a 5 for a 5dr would be read as a 5 and not as a 0). Also, I just added the case where some conditions count as two (denoted by a 2x in parenthesis in the above table) for this so that if that conditions is present it counts twice in regard to both canceling the other  opposing conditions are  bumping up that other die roll. That said this 2x rule just like the battle of zeros rule  I consider optional in that they  are a bit  more to warp iones brain around when playing, with the basic house rules contributing enough to that  on their own.

And BTW this rule is harder to explain than actual employ. And i like to give each rule a name that helps one remember it so I am calling this optional rule, the battle of the zeros.
  
[edit] I added a new rule 11-14 for conditions to only roll the minus die and cleaned up some of the wording of the other rules. Plus I edited a few more. I guess you can call these living rules, and they ma still be at the represent a bit lively at that, but I imagine that liveliness with fade away after a while.

[edit] BTW, I deleted the previous post in that it is now OBE.

[Hugmenot]

One issue with a plus and minus die is the following:

If the Direct Fire is exactly 22 factor. The plus die is 8-sided but eight is treated has 0 so it can never go to the 30-column. If you roll a "1" on the d8 and a "3" on the d6, the net is -2 and thus the fire would drop to the 16 column. I believe there are several ways to solve this issue.

I think the approach definitely has merits if one believes every factor counts (which is a very valid position in my opinion) and/or wants more variability. It will require a more time to play a scenario but maybe only marginally so after the process becomes routine.

I encourage you to submit the process to Avalanche Press as a potential Daily Content column after you test it out.

[RLW]

Thanks for the comment.

My thought on you example  was that maybe one could use  a 1 plus up for that case and  use the 9 sided die instead of the 8 (see my lined out text). But then i though (for the hybrid method,  even though it could never round up a good roll on the positive die would at least keep it from  rounding down to the 16.  For with the  plus/minus method  the die rolls have three results, bumping the total up a comumn, leaving it at the same column, or bumping it down a column. The later is required to keep the over all average lethality the same.

As far as writing a Daily Content I thought I would  do a lot more testing  before thinking about doing that. Mainly I have done this to enhance my own game experinece. But I posted it here in that I thought maybe others might like it too, or at least  think it interesting. But it does add complexity and that is something that it seems  AP is avoiding  so as not to let requirements creep  rob PG of being in the easy to learn category. So I would think something like this might be a a bit of hard sell to AP, unless the  bagns (i.e. fun level) to bucks (i.e. bogged down game play) ratio turns out to be really high y. For me, I don't really mind the extra complexity and I like the chrome, the nuance, and savoring the narrative as it emerges, vs simple rules and fast paced action. But I have no feel how others might weigh in on that. and take a lot more work than I might be up to doing.

What I hope to do is  continue my test ting on thsi scenario and post how it seems to all work as to ease of play vs  fun level and such. But I am more of a dabbler than a perfectionist so that may be as far as i take this, for onece I get it to I am happy with it that might be as far as I care to take it, where  it may still be a bit shy of being ready for prime time. And I am sure there may be simplifications that might  do the job but easier. But those can be hard to find and take a lot more time and effort than just tossing it out here on the forum for comment. But if  it does seem to work really well and looks like something others may like I might consider doing what you have suggested. 

I might add that I am not so much of a gamer but more of a history buff and like to think of these not so much as a game to be played, won, or lost or to show my mettle as a player  but rather asa reenactment that  lays out little dramas of what happened or might have happened in the said historical situation so as to better understand it. So adding more nuanced makes more nuanced dramas and (perhaps) more understanding, i.e. one can see  why they did what they did or didn't do what they did not do. And what I find is that  the extra die rolls don't so much add  complexity to the game system (to my thinking)  but rather allows that drama to further  be told as one sees if one can get that bump to the next column (or in the two die system avoid a bump down) and thus slows the action down  so that one can better see that drama unfold. 

But i am not so sure others would see this that way and may just see it as needless added complexity with little  addition game play value to show for it. That is what i suppose separates the true game designer form the dilatant dabbler like myself, that feel for what their customers would like and not like, where all I need worry about is whether i like it or not. For I care more about innovation and less about who might like or not like said innovation, not that I don't care, but rather just do not have a good feel for that, so any feedback would be quite helpful in that regard. .. so once again, thanks for the comment.

[RLW]

I am continuing in my play test and I am not trying to give an actual AAR here but rather  do plan to post how this new rule is playing out. with (a few)  actual examples. Also as i play test this  I am making revisions on the rules and I can post these  here   also as one can see below. 

I just (on turn 4) fired 64 BF on the NK armor stack, of a half step T-34/85, a SU-76A, a Ba-64, and a Lt 7-0-0 in a Light Woods hex. I rolled the 15 sided die and got a 6 and the 13 sided and got a 13 which is read as 0. So sure enough  64 +6 -0 = 70 and thus the 55 column was bumped to the 70 columBa-64 (being a wheeled  vehicle as per rule 12 above (which I forgot to add  where  if BF against a vehicle with wheels or an OT AFV  is a condition for using just the plus die for interpolation., but the T-34 and the Lt would.
 
BTW, I rolled a 9 which gave a M2 which affected the Lt but not any of the AFVs. So in this case  this rule raised the drama level with a 70 BF shot but did not affect the outcome.

I fired the NK  20 BF againt  2 INF and a leader in Light woods and the 5 sided roll (5dr) wa 4 and the 4dr ( this being a two die case given none of the  one die situations apply) was 1 giving 20+4-1 = 23 and thus a 21 shot that rolled a 4 giving a M2, which would have been the same without the bump. So one again this rule did not have an effect on the outcome... but sooner or later it certainly will. 

And i did not have to wait long for that case. Two NK 4-2's Op fired at  a lt and US 6-3 and the 4dr was a 3 and there was no ngeative dr as per rule 1, the target moved more than  1 hex and this gave 8+3 = 11 which bumped the roll up to a 11 with no shifts (the light woods -1 canceling the op fire +1). I rolled a 9 and that without the interpolation would have resulted in no effect but with the bump up gave a M... but both units passed the MC anyway so it ultimately did not affect the outcome.. this time. But in moving more than 1 hex the US player did incur a bit more risk so it was a decision that the US player made, and with good results this time.

The NK 12 mortar shot BF at two  US 6-3's and a leader in a lt woods hex and the 4dr result was 1 and the 3dr result (that is 12-8 =4 but 4dr is already taken by the plus roll hence it is bumped down to a 3dr rolls a 2 and  12 +1 -2 = 11 so the  BF was bumped down to a 8. But the  CRT DR was a 8 so it made no difference (again) in that  that would have resulted in no effect had it not been bumped down from 12 to 8. Note in this case there was no way for the result to have been bumped up to a 16 in that the  Cf  equaled a listed value. But  it could be bumped down and was. But if there had been a situation the  removed the minus roll (e.g. the FO had special abilities), then even though the plus die roll; could not bump it up to a 16 never the less  that situation removed the  possibility of being bumped down and thus had a benefit for the shooter.

And so far play seems pretty  straight forward (other than trying to remember my rules and changing them as it seems appropriate). And probably these are enough examples to better illustrate the idea so I will let these suffice unless something of particular note arises in my test run. But as one can see , these rules do add to the narrative even if they tend to have only a small effect on  the outcomes.. with the real potential of having a quite large one. 

[edit]
BTW, I have just finished playing turn 5 in my test game using the hybrid interpolation system and am really likening it. Here are a few of my observation

I am finding it somehow more satisfying to roll two interpolation die vs one. It is I guess more suspenseful in that will that roll help me, do nothing, or hurt me where with the one die  approach it was  just the first two in question  and not the third.

I really like the  plus die bumps down the negative die if both require the same  n sided die. I devised that rule just so one does not have to buy extra die or make two rolls but have found it quite useful in that it is never a problem  remembering which was the plus die and which was the minus in that with this scheme the plus will always be the die with the higher number of sides. Thus a 5dr and a 4dr one can see that it is the 5dr that is the plus . 

What I am seeing is that  having both the plus and the minus die rolls does still reward every CF point, but often in that having those points above the listed CF in the CRT helps one hand onto that column even if it fails to bump one up from that column. 

Also I am liking those rules for special conditions that removes reduces the two die interpolation role (with both a plus and minus die) to either  a single plus roll or a single minus roll. This I am finding is not at all much mental gymnastics to  track (once one becomes familiar with the all the conditions) in that all it means is when one makes the interpolation roll does one pick up one or two die. 

So I think I am declaring this little experiment in this hybrid  approach a success. in that it seems to work well, produce results that are interesting and add to the crunch  of the game and feels more emotionally satisfying. For example I  in turn 5 had some NK  inf dig in in a woods hex. For  that seems like what they would really do in real life, thinking it would  help them survive. But in PG it does not and is not allowed. But with that rule that  allows one to  dig in  for wood hexes and that still does not help one  in the  normal rules (i.e no =1 shift and no first fire) it never the less  gives one a  condition for only using the minus die for interpolation purposes, hence it buys  the units something in game terms where  without that it would not. 

I can say a similar thing for the condition that reward a AFV for having a turret. For in real life it is much more expensive to build a AFV with a turret so that implies it buys one something. Now I am not sure that in PG having that turret is baked in to its combat values or not. But with this rule it provides some additional tangible benefit that it gives the turreted vehicle a slight edge in assault combat over a non tenured one. 

So the bottom line is I am liking this system and will likely be using  use it for all my solitaire PG gaming in that (for me) it is showing itself to  add to my gaming experience enough to justify the added complexity. 

... so i think this completes my report here on this test game... so back to finish playing it!

...well almost. I just played a turn in my test game where the US player lost two turns due to added fog rule because the commander moved to safety and thus he  lost two MC due to that -1 which caused him to loose firing his arty (all 86 factors) becuase  he thne rolled a bad fog of war that ended the turn. So there was a cost for  having to move that commander, or rather for exposing him to begin with causing him later to half to move. So with this rule don't micro manage with your commander unless you have to.