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.

Action at Fox's Gap - Another Attempt

Following the Federal defeat at Fox Gap in my most recent game (see: Action at Fox's Gap) and a rules' clarification from Norm regarding Line of Sight to and from elevated terrain, a new Federal plan of attack surfaced.  With both artillery sections capable of bringing their tubes to bear from the beginning of the battle, the Federals may finally have the punch necessary to properly soften up the Rebel positions on the heights.  

As I formulated the Federal response, Norm, the author of Two Flags-One Nation, gave the Fox Gap scenario a try (see: Fox Gap 1862 On A Smaller Grid).  Norm's battle result was the same seen in previous outcomes.  That is, the Federals were unable to take and hold the high ground long enough to claim victory.  Undaunted by another Federal loss, I stuck to the revised Federal plan of attack.

The Federal plan was to compromise Bondurrant's gun position early on and then maintain a steady bombardment on the heights until an opportunity arose to breach the Confederate defensive line.  Key to the plan was to use the Division Commander, Cox, aggressively to bolster Federal chances of success.  Recall, the scenario does not provide a Divisional Commander to the Rebels so this is an advantage to be used to further Federal goals.

The battle opened up with both Federal batteries firing.  The Ohio Light Artillery (OHLA) targeted the small, raw 12 NC in the center of the Confederate line causing one Heavy Casualty (HC).  The 12th NC passed its Capability Test (CT).  Gibson's guns opened up against Bondurrant's guns but did no damage.  For the success of the Federal plan, this is a bad omen!  The WV Cavalry across the field from the Rebel guns manages to cause light casualties.  Bondurrant stands firm.

Federal opening attacks

With Cox leading the 30 OHa on the Federal right with 30 OHb following in support, the Ohioans use the cover of the woods to mask their approach and then pop out of the woods on Bondurrant's flank.  As Cox emerges from the woods, Bondurrant turns a gun to face his attackers and gets off a few rounds.  Bondurrant's impulsive fire misses the mark.  Cox and his Ohioans crash into the guns causing two HCs on the guns while taking one HC.  Bondurrant limbers and retires through the Confederate lines.

Bondurrant's guns are driven off

Garland's boys return fire from their solid defensive position lining the stonewall.  With no artillery to bring to bear, the Rebels must rely on small arms.  The 12 OH takes one HC while the 30 OHb suffers two HCs and falls back in disorder.

Rebels return fire

Having driven off Bondurrant's guns in the center, Cox leaves the 30 OH and rides over to join the 12 OH.  The Federal guns maintain their bombardments of the Rebel positions in anticipation of Federal attacks.  OHLA puts two HCs upon the 12 NC while Gibson's guns gift the 5 NCb with three HCs.  Three hits on three dice.  Fine shooting! 

Gibson finds the range!

Not only are the 5 NCb and 12 NC drawing fire from the guns but a hail of lead is also aimed in their direction.  The 30 OHa hits the 12 NC with one more HC.  Its nerve fails and the 12th retreats back into the woods.  The 5 NCb takes a fourth HC but stands its ground.  With the 5 NCb weakening, Cox leads the 12 OH up the ridge.  The 12 OH gives better than it takes and the Tarheels are pushed off the ridge having sustained a total of six HCs.

12 OH (foreground attacks the 5 NC

Notice in the photo above that the center victory hex is unoccupied.  Due to the stickiness of Enemy Zones of Control (EZOC), a Federal regiment could not move into the empty hex.  No movement from EZOC to EZOC is allowed.

The 12 OH regiment's success is short lived.  At canister range, Pelham's guns open up on the Ohioans as they clear the stonewall.  The 12th suffers heavy casualties (four more HCs) but remains undaunted.  Off to the 12th's left, Rebel dismounted cavalry open up causing a further HC.

Rebels pound the attackers

The Ohioans can take no more!  They recoil back down the slope looking for any cover they can find.  Rebel musketry does not end there.  The 23 OHa suffers two more HCs while the 30 OHa absorbs four HCs.   

30 OH takes four for four!

Having sustained devastating casualties in the center, the Federal attack peters out.  Union guns continue causing casualties to the defenders but only the 20 NC is pushed back from cavalry carbine fire on the right.  

Heavy casualties in the Union center

The destruction in the center is too much.  The 12 OH scatters while the 30 OHa retreats.  The Federal center is gone.  Bondurrant unlimbers his guns along the wall in the center.  With the Federal center gone, only the guns are keeping up a hot fire.  OHLA hits Bondurrant's guns again but the gunners maintain their position.  Gibson hits the 23 NC and it has seen enough.  It falls back from the ridge.

With Cox still leading the 23 OHa, the regiment goes in against the end of the Confederate line.  The raw, 5 NCa manages to repulse the Ohioans and Cox goes down in the clash.  In coordination with the 23 OHa, the 23 OHb charges Bondurrant's wavering guns.  The remainder of the Rebel guns are destroyed.  On the Federal right, the WV Cavalry causes the 13 NC to retire back toward Wise's Farm.

Federals hold two of the three objectives

With two of the three objectives in Yankee hands and a number of Rebel units scattered, the Rebels take an (optional rule) Brigade Cohesion check.  All along the Rebel line, regiment after regiment fails its test and retreats in disorder.  Although battered, the Ohioans have succeeded on this day.

As in the previous contests, this proved to be a bloody affair.  Casualties were high with more than one combat result hitting on all dice.  In the end, the Federal plan worked.  Bondurrant's guns were taken out early and the ridgeline defenses softened up sufficiently so that a concerted attack had a chance of success.  Scammon's Brigade was able to give the Rebel defenders a one, two, three punch on more than one occasion.  First artillery, then small arms, and then finally Close Combat was utilized in sequence to first soften up and then push the Rebels from their defensive position.  Combined arms at its finest. 

For future games, the victory conditions will be modified.  I found the Rebels could take up a "Reverse Slope" tactic and simply attempt to blow away any Federal regiment making it onto the ridge.  Pelham's battery did just such execution against the 12 OH when it took the Ridge Road.  Even though this tactic ultimately failed, a better victory objective criterion is warranted.  To prompt the Rebels to defend these crucial hexes, if at the end of a turn all three of the objective hexes are either occupied by Federal units or unoccupied, the Union wins the battle.  With sticky EZOCs, this is still a difficult task for both in controlling these crucial hexes.

As in the other iterations of this scenario, a lot of action in a little space!

The Action At Fox's Gap

Beachley Farm

In the first playings of Fox Gap using Two Flags - One Nation (TF-ON), the scenario was laid out using a two-inch hex grid.  Since Norm uses four-inch hex grids with his 12mm ACW figures, I placed an order for four-inch hexes to allow more room for the regiments within each hex.  The larger grid allowed me to expand each regiment from two stands each up to three stands each.  Since this is a trial run with four-inch hexes, the hexes have not been prepared with paint and/or flock.  The table will show the hexes in their natural wood state.  

The second change made to the scenario was to compress the playing area.  Rather than a 12x10 two-inch grid, a 6x5 four-inch grid was put into place.  The effect of this rescaling is that only the center of the battlefield is in play.  One benefit is that the playing area is quite compact with the action focused on the central aspects of the Federal attacks against the Confederate positions along the stone-walled road.

Finally, the latest version of Norm's rules will be in play carrying a few significant changes since the battle was last seen.

Initial Dispositions

The action begins with the Federals under Cox opening up against Garland's Confederate positions.  In the opening exchanges, Gibson's battery inflicts a hit on the 12 NC while the dismounted WV cavalry target Bondurrant's artillery deployed ahead of the Confederate line.  Both Rebel units pass their Cohesion Tests (CT) but the 12 NC withdraws.  The Ohioans advance upon the Rebel right.

In the center, Pelham fires on Gibson's artillery forcing the guns to limber up.  A lucky hit and CT failure!  The 5 NC, anchoring the extreme right of the Rebel line, stops the advance of the 23 OH.  The 23 OH is forced to withdraw back through its supports.  The 23 NC hits the 30 OH as it advances upon Bondurrant's artillery position.  This is not a good start for the Federal attack.  

Opening Exchanges

West Virginia Cavalry attempts to soften up Bondurrant's artillery before the 30 OH goes in against the battery with cold steel.  The West Virginians cause a casualty on Bondurrant before the Ohioans go in.  In the clash, the Ohioans suffers two hits while the artillery takes one more casualty.  Having taken more hits than the artillery, the Ohioans are forced back.  Since their retreat path is occupied by friendly troops, they continue falling back through their supports.

Charge of the 30 OH repulsed.

For their fire, the Rebels pour fire into the 23 OH on the Federal left.  The 23 OHb suffers two hits from Pelham's artillery but holds its ground.  The sister regiment sustains one hit from the 5 NC.  The other half of the 5 NC charges off the high ground to engage the 23 OH.  The attack devolves into a close range firefight with neither yielding.

Firefight intensity increases

Gibson's guns, having unlimbered, counter battery fire into Pelham causing two hits.  Pelham remains calm.  The West Virginians continue pounding Bondurrant with short range carbine fire.  Bondurrant's gunners have had enough.  Taking one more hit, the guns limber and retire.  On the Federal right, the 30 OH attacks the 20 NC forcing the Tarheels back, disordered, through their supports.

Casualties mount

On the Federal left, the 23 OH resumes pressuring the 5 NC.  With half of the 5 NC falling back from the high ground, the Ohioans attempt to turn the Rebel line.  

Bondurrant and 20NC retreat
 while Confedrate right is threatened.

All along the Rebel line, Confederate guns and muskets ring out.  The 23 OH, 30 OH, and 12 OH all suffer casualties as the close range fighting continues.  Trying to reform the Rebel right, the 5 NC charges into the disordered 23 OH.  In the close range firefight, the 23 Ohioans are bested.  The Ohioans fail their Cohesion Test and retreat back to Beachley Farm passing through their supports. 

23 OH Retreats!

In an attempt to regain lost ground before the 5 NC could get firmly emplaced, the other half of the 23 OH attacks the unsure Rebels.  Suffering heavy casualties, the Tarheels are driven back into the woods.

Federals regain lost ground

Federal success is short lived. Both Pelham and 5 NC pour fire into the 23rd.  Both halves of the regiment suffer casualties and retreat.

23 OH is sent reeling

As the 30 OH prepares to assault the Rebels behind the stone wall, the West Virginian cavalry supports their assault.  The 23 NC suffers at the hands of the cavalry carbines and falls back from the stone wall.  

That is exactly the support the Ohioans needed!  Leading the 30 OHb, Cox has the regiment fire into the 13 NC before clamoring over the stone wall to gain the road.  A victory objective is taken!

30 OH takes an Objective!

Pelham and the 5 NC continue punishing the 23 OH on the Federal left.  Both suffer additional casualties and both fail their Cohesion Tests.  Both halves of the 23rd have surpassed the Heavy Casualty mark.

The Federal left crumbles

While the Federal left crumbles, the Federal right is seeing some success.  Half of the 30 OH, having been occupied in supporting its sister regiment in taking the stone wall, redirects its fire onto the 13 NC.  The 13 NC takes heavy casualties (two hits) and retreats from the field.  Seeing this success, the other half of the 30th charges into Bondurrant's wavering guns.  Unfortunately for the Ohioans, Bondurrant had moments before unlimbered his guns and got off a close range blast of canister.  This was enough to discourage the Ohioans from pressing any farther.  Disordered, the 30th retreats back down the embankment.   

Heavy casualties plague the Federal left

30th Ohio attacks Bondurrant's guns

Having regained the stone wall, the Rebels began to dig in.  Seeing his left streaming from the field and his right wavering from having been repulsed from the high ground, Cox calls off the attack.  His force is spent.  With the troops at hand, not enough offensive strength remains for another assault despite the weakened Confederate positions.  Garland and his Tarheels are victorious!

This was a close fight.  While the rules tend to favor the defender with reduced hit possibility in cover, the Federals very nearly turned the Confederate right while managing to breach the center.  The 30 OH temporarily crossed the stone wall to take an Objective hex but could not hold it when the Ohioans were emboldened to attack Bondurrant's guns.  While the Federal dismounted cavalry was a stabilizing force in the center and eventually forced Bondurrant's guns to retire, its presence in the center blocked Federal artillery Firing Arcs.  With the cavalry's central position, Federal guns never seemed to get both batteries into the action at once.  This is a mistake that the Federals need to correct in order to present more fire onto Confederate positions.  Since artillery fire is not hampered by Cover, two batteries in action every turn would likely soften up the entrenched Rebels with more ease.

The reduced battle footprint (in hexes) promoted are a more focused attack and the value of each BMU was enhanced through this heightened importance.  Fox Gap turned out to be a slugfest and Garland's North Carolinians were the champions on this day although their position and resolve were increasingly looking untenable.

The latest rule changes worked well and Close Combat resolution was speeded up because of these amendments.  I liked the reduced hex count.  A battle footprint of 6 x 5 seemed appropriate for a small, intense action.  Very suitable for solo play on a small table.  Fox' Gap was good fun and worthy of another replay. 

For Two Flags - One Nation rules, please visit Norm's blog, Battlefields and Warriors.

Fox's Gap - An ACW BatRep in 10mm

The Action at Fox Gap had another outing on the gaming table using Two Flags-One Nation. After the first bloody fight (see: Action at Fox Gap Conclusion) that ended in a bloody draw, I wanted to give the scenario a rematch after a post-mortem of the rules, scenario, and play development.  Units were returned to their starting positions and the battle was joined.

Battle map

In translating the battle map to the game table, notice that I have dispensed with the entanglement of trees that hindered play in my first game.  My sleeve and arm were constantly catching a tree as troops were maneuvered through the dense foliage.  In place of the forest of trees, forest green hex tiles have been laid down to represent these woods' areas.  Model trees are placed sparingly to give the look of a united forest.  I like the look and improves play.

Initial deployments with troops on table

0900: At 0900, the action at Fox's Gap transforms from a probing operation into a full contact operation.  Seizing the initiative, Union General Cox joins the 23 OHa as it skirts Beachley Farm and closes with the 5 NC hunkered down along the Ridge Road on the Confederate right.  With Cox attached, the Ohioans can fire and move.  Unfortunately, their fire at long range is ineffective. 

The battle opens

Ohioans advance on the Confederate right

Perhaps being a bit brash, the Federal West Virginian cavalry advances upon Bondurrant's Rebel guns.  The Rebel guns deal death to the dismounted cavalry and they suffer heavy casualties.  Since cover does not diminish the effect from artillery, the troopers receive the full brunt of the cannonade.  Not able to stand up to the belching fire, the troopers fall back in disorder.  On the Confederate right, men from the 5 NC fire upon the 23 OH as the two Federal units close upon Rebel positions.  Both Federal units suffer casualties on the approach.

WV cavalry suffer mightily from Bondurrant's guns

Troopers fall back, disordered

5 NC fired into advancing 23 OH

0912: Cox slips over from the 23 OHa to join the 23 OHb.  Having unlimbered, Gibson's Federal battery brings Bondurrant's guns under fire.  The Rebel guns suffer only light casualties and dismiss the fire.  Both wings of the 23 OH fire upon the 5 NC before 23 OHb, under Cox's leadership, advances to the foot of the ridge.

Federals open up the firefight

Firefight in front of Beachley's Farm

Rebels respond

0930: As Cox hustles from one wing of the 23 OH to the other, the Confederate line braces for Cox' threat to lead an assault against the defenders lining the Ridge Road.  To distract Bondurrant, Gibson's guns keep the Rebel guns under fire while the 30 OHa brings the guns under small arms fire as well.  Bondurrant suffers more casualties but maintains his position.

As anticipated, Cox leads the 23 OH along with the 12 OH in an assault upon the Confederate positions on Ridge Road. 

From the left of the Fedeal line, the 23 OHa clashes with the 5 NCa in the woods.  The Federal assault goes in half-heartedly but the raw 5 NC fails to get off a meaningful volley to stop the Ohioans.  Both combatants suffer casualties but both stand their ground in disorder as the close range firefight continues.  To the right, of the 23 OHa, the 23 OHb charges up the hill to come to grips with the 5 NCb.  The Federals maintain the resolve to close but the raw Tar Heels break for the rear.  The 5 NCb takes heavy casualties and abandons its defensive position behind the wall protecting the Ridge Road.

In the third attack, the 12 OH with Scammon in the lead, charges into Bondurrant's guns.  On the way in, the 12th takes light casualties while the battery suffers casualties in the close fighting.  Seeing the guns holding onto their position in defiance, the Ohioans lose their nerve and fall back in retreat.  Garland fails to rally the 5 NCb. 

Initial Federal assault goes in

In close combat, you win some and lose some

Bondurrant continues dishing out death and destruction

0948: The first Special Event of the game is drawn and produces a "Confused Order" for the Federal troops.  The 23 OHb falls back.  Cox joins the 23 OHb to bolster its resolve.  Gibson's battery fires into Bondurrant's battery in conjunction with the 30 OHa.  Bondurrant suffers light casualties and continues to hold onto his exposed position.

Situation at 9:48

With Cox in the lead, the 23 OHb charges into the 5 NCa.  The Tar Heels take two hits while the Ohioans take no losses.  Scammon attempts to rally the 30 OHa to no avail.

Federals pour fire into Confederate positions

Cox leads the 23 OH into the 5 NC

Bondurrant returns fire on the 30 OHa.  Taking more casualties, the Ohioans are forced to withdraw in disorder.  On the Confederate far right, Rosser's cavalry finally make it into the fray. forcing the battered 23 OHa to fall back to escape the wrath of their weapons.  Also driven back from Confederate small arms fire is the 23 OHb.  Despite support from Rosser's dismounted troopers on their right, the 5 NCa fails it Capability Test and falls back.  In the Confederate center, the stalwart gunners of Bondurrant's battery holds its ground, ambivalent to its mounting heavy casualties.

Federal sent reeling back from the front line

Situation at 10:06

1006: With much of his command falling back from the fight having suffered heavy casualties, Cox calls off his attack.  Garland, having only one regiment badly damaged maintains the high ground and prevents the Federals from taking Fox's Gap on this day.

Rather than a hard fought draw seen in the first game, the second game I call a hard-fought win for Garland and his North Carolinian troops.  The Federals suffered heavy casualties with four of the six Union regiments at 50% casualties or greater.  As in Game One, Bondurrant's battery performed heroic feats while taking on all comers.  With 75% casualties, the Rebel gunners stood their ground unflinchingly.  Amazing display of valor.

On the Federal left, Cox and the Ohioans never managed to turn the flank and ended up in frontal assaults against prepared troops.  Even though raw, the 5th NC put up just enough fight to dissuade the Federals from pursuing a turning maneuver one more time.  Really, the Federal forces were spent without much remaining in offensive capability.

Was it fun? Yes!  Did the game produce tension and drama? Yes!  Did it provide a believable narrative?  I think so.  A lot of action in a small space.  A decision reached in only an hour of game time.  With only a handful of units per side, every unit's behavior and every casualty taken impacted upon the game.

Having several battles under my belt with TF-ON, time to provide my impressions of the game and put down a few thoughts on tactics and the processes embedded within.  That will be for another time, however.  Back to the painting desk for me. 

Note:  A technical error caused only a portion of the BatRep to be published earlier this morning and the original was unrecoverable electronically.  Luckily, a recent blogger "Preview" was displayed on another page.  Many screenshots and transcriptions later, the BatRep has returned (mostly) intact.  Thankfully, all was not lost.