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Sunday, March 1, 2020

Peering Into the Charge Sequence of TF-ON

Two Flags - One Nation (TF-ON) is Norm Smith's grid-based ACW rules (see: Battlefields and Warriors).  In a recent replay from Sound Officers Call's Seminary Ridge game (see Seminary Ridge), rules' questions led to a discussion of the charge sequence.  After Norm's clarifications, I sat down to put pencil to paper intent on investigating the math within.  For those not interested in probability theory and a brief look into computational statistics, you have been warned.

First, the steps of the Charge Phase before entering Close Combat include:
  1. Attacker declares charge
  2. Attacker takes Capability Test to assess if charge is FULL or HALF-HEARTED
  3. Defender takes Capability Test to react
  4. If Defender passes test then likely fires on charger
  5. Attacker takes Capability Test if receiving at least one hit
  6. Attacker closes for Close Combat or is stopped short
Given the above sequence, the Charge Phase will require either two or three unit Capability Tests (one for the defender and either one or two for the attacker) before combatants actually cross swords.

What was I hoping to unearth?  I was in search of a tactic for improving my play!  I wanted to know the probability of an attacker successfully charging into Close Combat against a defender.  If successful, was this charge going in as a Full or Half-Hearted charge?  With the two or three Capability Tests required and a comparison between Modified Capability Levels of attacker and defender, the answer is not immediately obvious or easily computed.

The diagram below illustrates the process flow for the Charge sequence.  In the flow example, the Attacker and Defender's Modified Capability Level is 6.  What is a Modified Capability Level (MCL)?  This is the unit's Capability Level modified by any situational modifiers that may be applicable.  A smaller Capability Level is preferred to a larger Capability Level.  MCL is then used in a unit's Capability Test.  Probabilities shown are based on one sample of 10,000 trials.  Different samples with differing number of trials may yield slightly different results.  The probabilities shown in the diagram are reasonable approximations to the theoretical probabilities for each event.  
The first decision point is whether the attacker's charge goes in as Full or Half-Hearted.  In this example, the split is 73% Full/27% Half-Hearted.  

Next, the defender tests to see if it responds.  To affect the attacker's ability to close, it is not sufficient for the defender to simply pass this Capability Test.  To have any chance at repulsing the attacker, the defender must pass the test and inflict at least one hit on the attacker.  Without this hit, the attacker makes no second Capability Test and goes into Close Combat with certainty.

If the defender is successful in both passing its test and inflicting at least one hit on the attacker then the attacker must make a second Capability Test.  If the attacker passes this test, it closes with the defender.  If not, the attacker is repulsed and no Close Combat ensues.

After computing the outcomes for these assorted possibilities, we see that the attacker is expected to enter Close Combat with a Full Charge about 61% of the time, Half-Hearted Charge 23% of the time, and repulsed 16% of the time.  Is this result surprising?

How do these computations change if the MCL for attacker and defender varies?

First, consider the attacker's probability of failing to close with the enemy as shown in the chart below.  As expected, for any attacker's MCL, the probability that the attacker fails to close decreases as the defender's MCL increases.  Two take-aways from this chart are,
  • A smaller attacker MCL is always preferred across all defender MCLs to a larger attacker MCL.     
  • The probability trend of failing to close across the span of defender MCL steepens as attacker MCL increases.
When examining the attacker's charge disposition of either Full or Half-Hearted charge, results are interesting here too.  In the example of Attacker MCL=6 and Defender MCL=6, we saw that the attacker attacks at Full Charge about 61% of the time and Half-Hearted Charge about 23% of the time. 

Notice the effect as attacker MCL increases above six.  Both the probability of charging Full and Half-Hearted increase at an increasing rate of change with Half-Hearted increasing at an even greater rate.  Does this make sense intuitively?  Fortunately, it does.  As the defender's MCL increases, the defender is increasingly less likely to pass its Capability Test.  With that, an attacker is increasingly less likely to take a second Capability Test, guaranteeing closure with the enemy.  Unfortunately as an attacker's MCL increases, the attack is more likely to go in as a Half-Hearted charge.  
While many of these results may be intuitive, breaking down the probabilities embedded within a ruleset can provide insight into design philosophy and intent.  What can be inferred from this exercise of digging into the Charge Sequence?
  • The first attacker Capability Test to determine either Full Charge or Half-Hearted Charge is independent of defender status.  I think this an interesting point for debate.
  • A smaller attacker MCL is always preferred across the range of defender MCLs to a larger attacker MCL.  
  • As Defender MCL increases, the probability of charging home increases.
  • As Attacker MCL increases, the probability of charging in Half-Hearted increases at an increasing rate.
Will this information change my style of play?  It may.  Charging with an attacker MCL above six, may give pause to reconsider.  What will be interesting, for sure, is to put this analysis into practice on the gaming table to validate decision science at work.

29 comments:

  1. Cedar me Jonathan ....I hope your leg returns to normal functionality soon...I feel you may have just a tad too much time on your hands at preset...LOL! Joking aside...perhaps the intent of rule designers is to discourage charging? My good friend Mark S always says wargames are obsessed with charging when in reality most battles from 1700 onwards were mainly firefights, with very few charges and even fewer melees as generally one side broke before actual hand to hand combat commenced.

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    1. Funny, Keith! My wife wishes for my return to normalcy too!

      You will be pleased to read that I returned to the battlefield yesterday for my first game with the guys since breaking my leg. Games were played at a kitchen table but we got in three games of Commands & Colors Napoleonics in India. Great fun!

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  2. PS...God knows why Blogger decided to substitute "cedar" for my first word, which should have been Dear.....

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  3. A little too deep for me on a Sunday morning, but I do get the overall philosophy. I make up rules without really having any sense as to whether they are fair or balanced. However I don’t have the capacity (maths never my strength) for your expert analysis.

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    1. You were warned, Matt! My suggestion is to roll dice and have fun.

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  4. Too much for my dear old brain this Sunday morn! Still an interesting exercise and read.

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    1. Sorry about that, Steve! It helps to follow along with spreadsheet to see the impact of varying the simulation inputs...I know, not much help!

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  5. Thanks Jonathan for doing all the work that went into that, fascinating for me of course :-)

    I'm actually quite pleased with that outcome, the science does help quantify design intention.

    Keith is in the right direction of things, I wanted the charge to simply represent that last 100 - 200 yrds when one side tries to assert itself over the other, usually by a mix of firing and moving forward or standing steady and imposing an impression of determination and that they will not be the one's to yield ... who's nerve will go first? So the charge is not so much a charge, but a mix of things that is all about competing wills.

    A few things I wanted as design imperative (a) a bit of uncertainty to loosen player control over events (b) a model that showed the benefit of fresh troops and reserves and that how even after a short time exposed to the rigours of war, unit deteriorates and becomes less capable of being trusted to prosecute an assault and finally reaches a point were you dare not push them into an assault. (3) that the first test will always result in a charge, even if only a half hearted one, which I though was better than stopping a charge altogether (4) and then there is that sting in the tail, which is hard to quantify here, but on a close combat, the attacker is open to harm if they roll 1's.

    I recall a charge that went in half hearted and I got 3 attack dice ....I rolled three 1's and the attacker was effectively rendered totally ineffective and would need to be rotated out of the line. Deliciously cruel, some will not like that amount of control wrested from them, but I like friction in a game, especially as I tend to play small games ... things need to happen!



    Thanks again.

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    1. Norm, I hoped you would enjoy and appreciate this exercise in digging into your process and outcomes.

      I understand exactly what you are attempting to model in the charge sequence. When the design supports a gamers’ intuition in process flow and result, the designer has accomplished his goal.

      I enjoy seeing an expansion of your Design Notes here.

      I continue to think that your Close Combat resolution of the attacker hurting himself as well as the defender as a brutally brilliant mechanism.

      Very fun design and THANK YOU!

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  6. Jonathan this is great! I love the level of analysis you put into the TFON turn sequence. Now to the gaming table to validate the results! I wonder if 61% odds would be good enough "in real life" to close into close combat (note I mean the close fight and not necessarily melee) if you were commanding in person?

    I think the turn sequence in TFON is brilliant and there is much potential for other erasure. I feel as if your analysis brings that out.

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    1. Erasure? Auto correct strikes yet again!

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    2. Glad you appreciate (and understand) my ramblings!

      Remember that the 61% probability for a FULL Charge is only applicable when the MCL of both attacker and defender are 6. To find the probability of your particular situation, cross reference attacker MCL with defender MCL in the chart(s) above. The Half-Hearted chart is the one I find very interesting.

      Give it a go and see if using these charts enhances or at least alters your play.

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  7. Very interesting. The number of steps/checks and counter checks for this one phase strikes me as novel, and as such, worthy of such analysis. Often (I can't say in this case), I've seen rules where modifiers or steps are put in, but as stand-alone ideas, each perhaps worthwhile on its own, but the interactions of these processes sometimes creates inverse effects. I once worked out that in a friend's homegrown Napoleonic rules, for example, the most effective thing to do to by far to break a square, statistically, was to charge it with cavalry. Doing the math may seem mundane, but in the end, it demonstrates what the rules actually encourage players to do, which, in turn, reflects how the rules work to deliver the feel of the era involved. Thanks for sharing this analysis!

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    1. Ed, good point about interactions and unintended consequences. For me, it is a fun exercise to trust but verify! Breaking down the process and probabilities brings to the front designer intent.

      Good story about those homespun Napoleonic rules and square bashing. Is a corollary to this event similar to "if I only have a hammer, everything looks like a nail?"

      Glad you appreciated the analysis!

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  8. You have given me an idea to do the same thing with DBMM, which is quite a geometric game both in terms of maneuver and in calculating odds against various troop types. I think laying it all out along the lines you have done would help visualise things. Now if only my Excel skills were a little better.

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    1. Great! While I have not played DBMM, I look forward to your analysis of the game mechanisms embedded within.

      Even if a reader is not familiar with Norm’s rules, it is good to see that the approach and analysis are applicable to other systems.

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  9. Good work Jonathan! I ought to do this with my homegrown rules. I say 'ought', but I suspect it'll be a while before I get round to it ;-)

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    1. Thank you! As a rules' designer/developer, this is a useful if not critical exercise, I think. I am sure you will give it a test run before publication.

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  10. I'm glad you qualified this with a warning Still interesting read and really all our games are based on probability with design being the way it is adjusted, with die or cards to try and approximate period tactics, still looking forward to some painted toy soldiers and I'm glad your legs getting better!
    Best Iain

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    1. A warning up front, is only fair, I think.
      Glad you slogged despite the warning and found something of interest.

      Painted toy soldiers up next time.

      Thank you!

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  11. I remember charts from decades ago, made my poor head hurt. I like the vignette, sounds like an interesting set but I am sticking with my old favourite.

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    1. George, not trying to tempt you away from your favorite ACW set of rules. Norm's rules are interesting especially if you enjoy playing on a grid.

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  12. Oh wow! General Freitag analyze again!

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  13. Probability theory? Computational statics? Say it in a slow sexy voice and I’m all in.
    Having a good idea of the maths inside a rule set is a great way to improve tactics when playing a game. You can either dive in with math skills or for those less math inclined just play the rules a lot to get an idea of the important variables. 😀

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    1. Stew, you are so funny!

      Playing the rules a lot to get a feel for the probabilities is a tall order for me. With so many periods, so many rules, and not enough time, I must pursue the mathy way...

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  14. Glad to hear there is progress with the leg and some games played. Seems like an awful lot of steps to me to get to the final result,

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    1. Leg is progressing. Started PT this week and the therapist said I was way ahead of schedule with recovery.

      The steps may be numerous but they are easy to remember and quick to execute. I would likely reduce the attacker tests from two to one, though.

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