Category Archives: Scenario Design Module

Video Walk-through of the Army, Map & Scenario Editors

I‘ve just uploaded a video of a walk-through of the General Staff: Black Powder Army Editor, Map Editor and Scenario Editor. These applications are completed. We will be using Steam for distribution. While we are registered with Steam, and they have given us ‘our space’, we still have to build it out and make arrangements for download keys for early backers. We (why do I keep using ‘we’, it’s just me here) truly appreciate your patience.

I will be posting a gameplay video of General Staff: Black Powder next. As always, please feel free to contact me directly.

A Human-Level Intelligence at Gettysburg, Day 3

Screenshot of MATE analysis of Gettysburg, Day 3 from the Red (Confederate) position. Click to enlarge.,

General Lee, at Gettysburg, said: “the enemy have the advantage of us in a shorter and inside line and we are too much extended.” – quoted by Major General Isaac Trimble.¹⁾Isaac Trimble, Southern Historical Society Papers, Vol. 26, Richmond, Virginia: Reverend J. William Jones, D.D., MATE, the AI behind General Staff, came to the exact same conclusion:

A portion of MATE’s analysis of Red’s position at Gettysburg, Day 3. Here MATE recognizes that Red has exterior lines and the enemy has a decided advantage.

I have been porting TIGER ²⁾Tactical Inference GenERator, the AI behind my doctoral thesis and my DARPA sponsored research from C++ to C# and integrating it into the General Staff: Black Powder wargaming system. I have been doing this via the method of first creating a scenario typifying a specific attribute (exterior lines, exposed flanks, choke points, etc.) and then porting the actual code over and feeding it the scenario for analysis. Gettysburg, Day 3, is the canonical example of exterior and interior lines.

92.9% of Subject Matter Experts agree! The Union (Blue) lines at Gettysburg, Day 3, exhibit the attribute of being Interior Lines. Interior lines are good. Exterior lines are bad. From author’s doctoral thesis.

So, first a significant number of Subject Matter Experts (combat commanders, tactics instructors at military academies, etc.,) agree that there is an attribute called ‘Interior Lines’ and that it is exhibited by the Union (Blue) forces at Gettysburg, Day 3. We then create an algorithm that can detect such an attribute and convert it from C++ code to C# code (and substantially rewrite and improve said algorithm in the process) . We then create a Gettysburg, Day 3 scenario using the General Staff Army Editor, the General Staff Map Editor and the General Staff Scenario Editor and feed the scenario³⁾In Computer Science lingo programs are machines that consume data / tokens to MATE, the General Staff: Black Powder AI. These are the results:

MATE analysis text output (with author’s commentary) of Gettysburg, Day 3, from the Red (Confederate) position. Click to enlarge.

The first time that I presented the Gettysburg, Day 3 scenario as Red to MATE it refused to attack. The enemy has interior lines (1.4, or 40% greater is pretty significant value), you’re attacking uphill (slope > 7%), your attacking units are under enemy ROI (mostly batteries of 12 lb. Napoleon canon shooting explosive shot and then canister and then double-shotted canister) for over a kilometer. Attacking is not a good idea. To get MATE to attack I had to go back to the Map Editor and create a number of new Victory Points; specifically the places where significant roads (Emmitsburg Road, Cashtown Road, Baltimore Pike, etc.) enter the map. Then I went in to the Scenario Editor and assigned appropriate values and current ‘ownership’. Saved it all and fed it back to MATE and the, above, is what I got.

The only way for MATE to win (as Red) is to attack large Victory Point areas (Cemetery Hill and Cemetery Ridge) and hope to destroy significant numbers of Blue (Union) forces along the way to meet the victory conditions set in the Scenario Editor:

Gettysburg, Day 3 Victory Conditions. Screenshot General Staff Scenario Editor.

Anybody who has built a wargame scenario (and I suspect there are more than a few among the readers of this blog) know the drill of going back to edit the OOBs, starting positions, victory conditions, etc. I would just like to say it’s pretty painless using the General Staff Wargaming System. The various editors all integrate seamlessly like Microsoft Office products (they were written in Microsoft WPF by Andy O’Neill who is a Microsoft Gold Developer).

But, the real question that this raises is: why did Lee attack on Gettysburg, Day 3? Blue (the Union) not only had interior lines, an elevated position, but they also had anchored flanks (see #22 above). MATE is running out of options at this point. If you look at the top screenshot you will see yellow numbers in yellow circles. These represent MATE’s three ‘weakest points’ in Blue’s line and it’s not much.

So why did Lee attack?

James Longstreet’s From Manassas to Appomattox states absolutely that

All that I could ask was that the policy of the campaign [Lee’s invasion of the north] should be one of defensive tactics, that we should work so as to force the enemy to attack us, in such good position as we might find in his own country, so well adapted to that purpose, – which might assure us of a grand triumph. To this he readily assented as an important and material adjunct to his general plan. [p. 331]

So, Longstreet, in his autobiography, is saying that Lee agreed that at some point in Pennsylvania, the Army of Northern Virginia would find a good solid defensive position and let Hooker (they didn’t yet know that Meade was the new commander of the Army of the Potomac) smash his army to pieces upon it. James McPherson in, To Conquer a Peace: Lee’s Goals in the Gettysburg Campaign writes:

“In a conversation with General Isaac Trimble on June 27, when most of the Army of Northern Virginia was at Chambersburg, Pa., and when Lee believed the enemy was still south of the Potomac, he told Trimble: “When they hear where we are, they will make forced marches…probably through Frederick, broken down with hunger and hard marching, strung out on a long line and much demoralized, when they come into Pennsylvania. I shall throw an overwhelming force on their advance, crush it, follow up the success, drive one corps back on another, and by successive repulses and surprises, before they can concentrate, create a panic and virtually destroy the army.” Then “the war will be over and we shall achieve the recognition of our independence.”

The argument is that Lee, on the morning of July 3, 1863, found himself in a terrible strategic situation with very few options. It was imperative that Lee must, “destroy the [enemy] army;” nothing less than a great triumph in enemy territory would do. In Lee’s only official report of the battle of Gettysburg, written on July 31, 1863 he states:

The enemy was driven through Gettysburg with heavy loss, including about 5,000 prisoners and several pieces of artillery. He retired to a high range of hills south and east of the town. The attack was not pressed that afternoon, the enemy’s force being unknown, and it being considered advisable to await the arrival of the rest of our troops. Orders were sent back to hasten their march, and, in the meantime, every effort was made to ascertain the numbers and position of the enemy, and find the most favorable point of attack. It had not been intended to fight a general battle at such a distance from our base, unless attacked by the enemy, but, finding ourselves unexpectedly confronted by the Federal Army, it became a matter of difficulty to withdraw through the mountains with our large trains. At the same time, the country was unfavorable for collecting supplies while in the presence of the enemy’s main body, as he was enabled to restrain our foraging parties by occupying the passes of the mountains with regular and local troops. A battle thus became in a measure, unavoidable. Encouraged by the successful issue of the engagement of the first day, and in view of the valuable results that would ensue from the defeat of the army of General Meade, it was thought advisable to renew the attack. . . .

Lee was in for a penny and in for a pound. This was not the defensive battle of Longstreet’s choosing. This was now Lee desperately trying to, “throw an overwhelming force on their advance, crush it, follow up the success, drive one corps back on another, and by successive repulses and surprises, before they can concentrate, create a panic and virtually destroy the army,” but now the enemy had, “retired to a high range of hills south and east of the town.” The Union had flipped Longstreet’s strategy 180 degrees and it was they who had, “force[d] the enemy to attack [them], in such good position as [they] might find.”

I will create some other Gettysburg scenarios including ones with the Union and Confederate cavalry available. While not historical, it might make for some interesting gameplay and Human-Level AI decisions.

As always, please feel free to contact me directly with comments.

References[+]

References
↑1	Isaac Trimble, Southern Historical Society Papers, Vol. 26, Richmond, Virginia: Reverend J. William Jones, D.D.,
↑2	Tactical Inference GenERator
↑3	In Computer Science lingo programs are machines that consume data / tokens

A Human-Level Intelligence at Antietam

“Map of the battlefield of Antietam,” by William H. Willcox. Published in Philadelphia. Lithograph of P. S. Duval and Son, 1862. From the US Library of Congress.

There are many reasons that I am intensely interested in this particular American Civil War battle fought on less than twenty square miles wedged in between the Potomac River and Antietam Creek. The battle of Antietam (September 17, 1862) exhibits a number of significant battlefield attributes which I use as base line cases to test algorithms used in creating a human-level tactical artificial intelligence ¹⁾MATE: Machine Analysis of Tactical Environments. Specifically, Antietam definitively demonstrates ²⁾see http://riverviewai.com/download/SidranThesis.pdf the following attributes:

Choke Points
Anchored Flank
Interior lines of communication
Exterior lines of communication
Restricted Avenue of Retreat
Restricted Avenues of Attack

For example, in a blind survey of Subject Matter Experts (SMEs), it was overwhelmingly agreed that the RED (Confederate) left flank at the battle of Antietam exhibited the attribute of ‘anchored flank‘ ³⁾a flank that is attached to or protected by terrain, a body of water, or defended fortifications. and other positions, such as RED’s (Russian and Austrian) left flank at Austerlitz SMEs overwhelmingly agreed that the flanks do not exhibit the attribute of ‘anchored’ and are, therefore, unanchored. Once we have an example of an anchored flank and another example of an unanchored flank we can begin testing algorithms to detect the attribute of an anchored flank.

In my doctoral thesis (above) I demonstrated the algorithm ⁴⁾see pages 45-6 http://riverviewai.com/download/SidranThesis.pdf for detecting the attribute of anchored and unanchored flanks. I have made a number of substantial improvements to the original algorithm since then which are now incorporated into the current MATE.

We have recently posted analyses of other battles that did not exhibit the attribute of an anchored flank (Ligny and 1st Bull Run, or Manassas). MATE correctly recognized that Ligny and Manassas do not have these attributes.

The tactical situation for Blue at Antietam is quite different than Blue’s positions at Ligny and Manassas (is it not curious how often Blue is the attacker in wargames?). The key difference, of course, is the lack of an open flank to attack. MATE will always attack an open flank if it can. Without an obvious objective, like an exposed flank, MATE will next look at opportunities to fulfill victory conditions. For Antietam, as Blue, MATE sees the situation like this:

MATE Analysis of Antietam from the Blue position. Screen shot. Click to enlarge.

Below is a list of statements, predicates and conclusions generated by MATE during the above analysis with my commentary added on the right:

MATE analysis of Antietam. Click to enlarge.

I recently added a set of algorithms that recognize the composition of battle groups and exploits any possible advantages. For example:

Screen shot showing MATE analysis of BLUE position at Ligny. NB: Battle Group #3 (Pajol’s and Exelmans’ cavalry divisions) are, “snatching the pawn,” at Balatre. Click to enlarge.

At Ligny, above, MATE has recognized that Battle Group #3 and Battle Group #4 are uniquely cavalry (and horse artillery) battle groups and are to be used differently. While Battle Group #4 is held in reserve, Battle Group #3 will snatch Balatre. Though it is valued at only 10 Victory Points, MATE realized that no enemy force could oppose it. That said, I can still hear the voice of my old chess tutor, Mr. Selz, warning me against ‘pawn snatching’; that is grabbing a minor point that can lead to defeat because the position was not thoroughly analyzed. MATE, however, is correct in this analysis and can safely seize the objective.

While, at Antietam, Battle Group #1 (all the cavalry of the Army of the Potomac commanded by Brigadier General Alfred Pleasonton) is frozen ‘in reserve’. This is not a case where MATE can snatch a pawn. MATE looked at the situation and said, ‘nope’, there are no unattended Victory Points to snatch and there is not an open flank to exploit so, the default setting is ‘in reserve’.

This leads to the interesting conundrum: what exactly was the Union cavalry at Antietam doing? Honestly, I had never really thought of it before. Now, when I look into the question I find, Was McClellan’s Cavalry Deployment at Antietam Doctrinally Sound? This monograph argues that McClellan massing his cavalry in the center for a great coup de grâce exploitation of a breakthrough across the Middle Bridge was acceptable within the framework of Jomini’s theories as taught at West Point before the Civil War. But, then it is countered with this:

In Landscape Turned Red, Stephen Sears has this to say: Shortly before noon, McClellan had ventured to push several batteries across the Middle Bridge, supported by Pleasonton’s cavalry and a force of regulars from George Syke’s Fifth Corps. He was nervous about the move-it was taken against the advice of Porter and Sykes-and he cautioned Pleasonton not to risk the batteries unduly. As an afterthought, he asked, “Can you do any good by a cavalry charge?” Pleasonton wisely ignored the suggestion. – Sears, Stephen, Landscape Turned Red: The Battle of Antietam, New York: Ticknor and Fields, 1983. page 271. (as cited in above)

Would a great massed cavalry attack across Middle Bridge have been suicide? Or brilliant? For the first time in memory I took the 1st edition of McClellan’s Own Story off the shelf and discovered… nothing. McClellan died suddenly of heart failure just as he was writing about Antietam and his memoirs end abruptly with very little insight into his side of the story. But, using cavalry to support horse artillery – rather than the other way around – seemed a bit odd.

I do not know of any other great cavalry charge in the American Civil War than Sheridan at Five Forks (above). Is this what McClellan envisioned at Antietam? Would it have worked? Could American Civil War regiments have formed square against a massed cavalry charge?

Moving on, let’s drill down to the Course of Action (COA) for Blue Battle Group #3 (Burnside’s IX Corps) at Antietam:

MATE tactical analysis for Blue Battle Group #3 at Antietam (Burnside’s IX Corps). Screen shot. Click to enlarge.

The author walking across Burnside’s Bridge in 1966 (age 12).

The above is MATE’s output that concludes with the COA for Burnside’s IX Corps. Perhaps, the greatest mystery of the battle of Antietam is what took Burnside so long to take this bridge (now forever linked with his name)? It is true that there were numerous, futile and bloody attempts to cross it. Note that MATE, above, recognizes the bridge as a critical Choke Point. When MATE sees a Choke Point that is within the enemy’s control (see statement #8, above, “Chokepoint (bridge) is under Red’s Range of Influence ROI = 5958″ and 5,998 is very high ROI value) it brings up artillery (see statements #9, #10, #11, #12, above). All the artillery in the IX Corps is to be within 630 meters of the objective. Why 630 meters? Because at that distance it is guaranteed a 50% accuracy rate. This rate, by the way, was set in the Army Editor:

The accuracy curve for the 1st Division, IX Corps artillery as set in the Army Editor. Screen capture. Click to enlarge.

So, MATE says ⁵⁾I apologize but I find it easier to describe how the AI works using such phrases as ‘thinks’, ‘says’, and ‘decides’. It’s not worth straining over. Trust me, “My objective is a Choke Point. I’m not sending my units into a meat grinder. I’m sending artillery to a point where they are guaranteed a 50% accuracy per volley and have a clear 3D Line of Sight to the target. This is how I’m going to project as much force as I can at the objective.” War is about force projection. MATE knows this. Is this a better plan than what Burnside actually did? Yeah, it is a lot better with a far greater probability of success. I’ve stood on that plain just east of Burnside’s Bridge and thought that nine batteries of 12 lb. Napoleons aimed at the crest of that hill just beyond the bridge would provide a substantial amount of force projection and covering fire. About half an hour of force projection followed up with an infantry assault would probably take the bridge.

I once described good AI as: Don’t do anything stupid, fast. MATE is doing that. I think MATE is on the way to beat most human opponents because humans do stupid things, fast.

We’ll see. Should be an interesting journey.

References[+]

References
↑1	MATE: Machine Analysis of Tactical Environments
↑2	see http://riverviewai.com/download/SidranThesis.pdf
↑3	a flank that is attached to or protected by terrain, a body of water, or defended fortifications.
↑4	see pages 45-6 http://riverviewai.com/download/SidranThesis.pdf
↑5	I apologize but I find it easier to describe how the AI works using such phrases as ‘thinks’, ‘says’, and ‘decides’. It’s not worth straining over. Trust me

General Staff will Ship in 2022

A few of Grant’s unsuccessful attempts to take Vicksburg. Map from West Point Atlas of American Wars. Library of Congress. Click to enlarge.

Grant took Vicksburg on his sixth attempt. He first tried a direct movement, east of the Mississippi, against the city but was forced to turn back after Confederate General Van Dorn’s raid destroyed his supply base. Sherman next attempted a direct assault and failed at Champion’s Bluff. Grant then tried to cut Vicksburg off from the Mississippi by digging a great canal across the neck of a giant oxbow. Unusually low water levels in the river that year caused another failure. Grant also tried more canal digging and river clearing at Lake Providence and the Yazoo Pass without luck.

Col. Theodore Lyman, a staff officer of the Army of the Potomac, wrote of Grant, “He habitually wears an expression as if he had determined to drive his head through a brick wall, and was about to do it. I have much confidence in him.”

Grant finally succeeded with his brilliant amphibious landing south of Vicksburg followed by a series of ‘must win’ battles that concluded with besieging the city on May 22, 1863. Confederate General Pemberton surrendered Vicksburg on July 4, 1863.

The General Staff: Black Powder Wargaming System is comprised of four separate programs: the Army Editor, Map Editor, Scenario Editor and the actual Game Engine, itself. The first three have been done for some time (it’s what I use to produce scenarios for testing the AI). They were written in C# using Microsoft’s Windows Presentation Foundation (WPF) which is often used for creating desktop business applications. This decision made sense because the Army, Map and Scenario Editors function not unlike a suite of business applications that create and share data with a common look and feel. However, while WPF was a good development decision for the Editor programs it turned out not to be a great tool for creating the Game Engine.

A flow chart of the General Staff: Black Powder Wargaming System. Files created in the Army Editor and the Map Editor are combined in the Scenario Editor to create a scenario or simulation. Click to enlarge.

What the Game Engine does is it takes data created in the three Editor programs, displays them in a visually exciting way, enables the user to make input (orders), and simulates those orders (as well as the AI’s orders) and the resulting combat to the highest degree of accuracy possible. That sounds like a lot, but it really isn’t. And the heavy lifting that the Game Engine is being asked to do is all visual: making everything look good on the screen.

Recently, I’ve been looking at Grand Tactician: Civil War which is an immersive voyage into 19th century American typography, cartography, tactics and grand strategy. I eagerly look forward to having the time to do more than gaze upon it in amazement ¹⁾Full disclosure, the developers were kind enough to give me a review copy of Grand Tactician and, damn, it looks fantastic.. I reached out to Ilja on their development team and he convinced me that we should complete the General Staff Game Engine in Unity (which is what they used for Grand Tactician). What they accomplished visually with Grand Tactician was precisely the look and feel that I wanted for General Staff ²⁾I’m talking about the typography and the UI, not thousands of tiny 3D soldiers on the battlefield; which look really great, but, General Staff is not that kind of a wargame..

Consequently, we are officially announcing that we are abandoning writing the General Staff: Black Powder Game Engine in WPF and, instead, will be creating it using the Unity engine. We believe that this will produce a far superior visual experience ³⁾Please note: we will not being using Unity to create a 3D simulation with tiny soldiers. I like playing those kind of games, but that’s not what General Staff is..

Because Unity is designed to facilitate the creation of computer games, this move will greatly accelerate the completion of the General Staff Game Engine and will allow us to ship General Staff: Black Powder this year.

I am certainly not U. S. Grant, though I like to think I have some of that bulldog determination. Like Grant before Vicksburg, I’ve had to acknowledge that our first attempt will not succeed and we’re moving on to another plan. I am sorry for the delay in the release of General Staff and am confident that, with Unity, we will soon be reporting some good news.

I am also very excited to announce that my good friend, Damien, will be joining the team to specifically work in Unity completing the General Staff Game Engine. Damien lives in Ireland and has been a devout wargamer since playing Arnhem on the ZX Spectrum. When not enjoying a Guinness or a Jamesons, he’ll be playing tabletop or computer games, whether that means pushing cardboard counters across hex boards, drawing LOS between badly painted miniatures on the tabletop, or day-long sessions in front of a computer – where he particularly enjoys playing against a challenging, non-cheating AI. Damien is a 28 year veteran of the IT industry, having worked on everything from telecoms, healthcare and financial systems, across Mainframes, Linux, Unix and Windows, and co-inventor of two messaging system patents. He has a particular passion for language processing and domain specific languages, originating from his interest in the elegance of recursive descent compiler construction.

References[+]

References
↑1	Full disclosure, the developers were kind enough to give me a review copy of Grand Tactician and, damn, it looks fantastic.
↑2	I’m talking about the typography and the UI, not thousands of tiny 3D soldiers on the battlefield; which look really great, but, General Staff is not that kind of a wargame.
↑3	Please note: we will not being using Unity to create a 3D simulation with tiny soldiers. I like playing those kind of games, but that’s not what General Staff is.

I Was Wrong About George Washington

Washington Crossing the Delaware by Emmanuel Luetze. 1851. The Metropolitan Museum of Art. Click to enlarge.

I must confess that I was never much a fan of George Washington’s generalship. Having not studied American Revolution military history I thought that from 1776-1781 the British chased Washington and his sad excuse for an army up and down the eastern seaboard of what was to become the United States until the French Comte de Grasse defeated the British naval forces at the Battle of the Chesapeake and the Comte de Rochambeau at the head of a French army surrounded, besieged and eventually captured, Cornwallis at Yorktown.

To make matters worse, years ago I stumbled upon George Washington’s Expense Account which is, frankly, brutal. Washington turned down the magnanimous salary of $500 a month for being Commander in Chief of the Continental Army famously saying,

“As to pay, Sir, I beg leave to Assure the Congress that as no pecuniary consideration could have temped me to have accepted this Arduous employment (at the expense of my domesttic [sic] ease and happiness) I do not wish to make any Proffit [sic] from it. I will keep an exact Account of my expences. Those I doubt not they will discharge, and that is all I desire.” ¹⁾George Washington’s Expense Account, Washington, George & Kitman, Marvin, page 15

If Washington had accepted the salary he would have been paid $48,000 for five years’ service. Instead, his ‘expences’ came to $449,261.51! This book – and it contains a photocopy of every page of Washington’s Expense Account in fine copperplate handwriting along with a humorous explanation of the expense – is damning. Washington’s very first entry for June, 1775 was for $6,214 (over an entire year’s salary at $500 per month) for “…the purchase of five Horses… to equip me for my journey to the Army at Cambridge – & for the Service I was Then going upon – having sent my Chariot and Horses back to Virginia.” There are also numerous expenses for cases of the finest wines and plenty of food while at Valley Forge. Not surprisingly, when Washington offered Congress the same terms when he was elected president (no salary just expenses) Congress insisted that he take $25,000 a year; no expenses paid.

Like most Americans, what little knowledge I had of the battle of Trenton can be summed up in Luetze’s famous painting, above: Washington, posed heroically, crossed the Delaware River on Christmas Eve and surprised a garrison of drunken Hessian mercenaries at Trenton capturing them all without a shot. In reality, not much of that is true. Yes, Washington did attack Trenton but it was on the morning of December 26, 1776, and the Hessians weren’t drunk; they fought bravely and their commander, Col. Johann Gottlieb Rall, died leading them.

Then I discovered (from reading David Hackett Fischer’s Pulitzer Prize-winning Washington’s Crossing) that the amazing part of the story wasn’t the battle of Trenton (which really was an extraordinary tale of a small, poorly-equipped, non-professional army making an audacious amphibious crossing of an ice-choked river) but the campaign that followed the victory from December 30, 1776 to January 3, 1777.

The strategic situation in the Princeton / Trenton area, December 29, 1776. Screen shot from the General Staff Scenario Editor. Click to enlarge.

Washington’s forces had made it safely back across the Delaware River after the Trenton raid but he now faced a difficult decision: terms of enlistment were running out for many units in his army and he feared taking the field again in bitter cold with a diminished force. As always, Washington held a council of war. As the senior commanders of the army advised caution a courier arrived informing them that Brigadier General John Cadwalader with his Pennsylvania militia had already crossed the Delaware and was at Crosswicks itching for a fight with the British (this is the blue force at the bottom of the map, above). After more discussion, one group stated, “tho’ they would not have advised the Movement, yet it being done it ought to be supported.”²⁾Washington’s Crossing, David Hackett Fischer page 266. Eventually, with Washington’s urging, the council voted to support Cadwalader, recross the Delaware and, again, defeat the British in the field.

This was a bold strategy; a defeat of the Continental Army with its back to a river would probably spell the end of the revolution. Washington’s plan was to assemble his forces east of Trenton, in a strong defensive position on ‘good ground’ behind the Assunpink Creek and lure Cornwallis, who was commanding the British and Hessian forces, to attack. This Cornwallis did and was soundly defeated. Washington now moved decisively, sending his forces to capture Prince Town (Princeton) to the north. At the crucial moment in this battle Washington rallied the routed Pennsylvania forces saying, ” ‘Parade with us, my brave fellows! There is but a handful of the enemy, and we will have them directly.’ Washington [then] led his men straight into the center of the battle, within thirty paces of the British line. He was mounted on a white horse, an easy mark for any British soldier.”³⁾Ibid. page 334

Frankly, I cannot comprehend such bravery. The attack, of course, was a success and the Americans captured Princeton and, perhaps more importantly, demonstrated that their volunteer army would fight, could fight and could win. Washington showed superb strategic and tactical vision throughout these ten crucial days⁴⁾See https://tencrucialdays.org/wp-content/uploads/2019/09/eb14b5212fb62dfea8d100f3efd1950f.pdf for a wonderful series of maps that cover this campaign as well as extraordinary personal courage.

I was wrong about George. Washington.

References[+]

References
↑1	George Washington’s Expense Account, Washington, George & Kitman, Marvin, page 15
↑2	Washington’s Crossing, David Hackett Fischer page 266
↑3	Ibid. page 334
↑4	See https://tencrucialdays.org/wp-content/uploads/2019/09/eb14b5212fb62dfea8d100f3efd1950f.pdf for a wonderful series of maps that cover this campaign