Silver Bayonet 22 - more theorycrafting

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Several years ago I did a deep dive into how the very short Tea Plantation scenario (6a) worked out in practice, specifically, how well balanced is it? Preliminary results from six plays indicated the scenario favors FWA 2:1, that is 4 of 6 plays to the FWA, PAVN winning the other two plays. At that time, I made an attempt, on paper, to work out the probabilities of various courses of action and results thereof. That effort was only partially successful.

The following plays pick up where those left: quantifying the probabilities.

Game 1 (22)

Turn 1

There is only 1 turn in Scenario 6a.

Offensive Bombardment Phase [10.1]

1) Declare Bombardment using air points or artillery.

Mortar fires at 2 strength, roll 8 for -.

2) Declare and resolve ADF [14.0].

N/A.

3) Resolve Bombardment.

VC Mortar, roll 10, no effect.

Combat Coordination Phase

1) Attack Coordination [7.0] which may negate declared Maneuver Combat declarations [8.0]

For this we VC ER is 3 when out of range, roll 9, uncoordinated,

Assault Combat Phase [9.0]

1) Defender allocates and resolves air and/or artillery for Defensive Bombardment [10.2]

  • All 10 Air points for Defensive Bombardment.
  • Air Defense is viable as VC have 16 steps adjacent the the Tea Plantation which is the Mission Hex in this case. Roll 10, no effect.
  • Air Bombard, roll 3 which is 3F, one step loss with the Fatigue marker ignored in Defensive Bombardment (10.2.3).

2) Defender rolls first on Assault Combat Table, applies DRMs and applies results immediately.

US defends with 3, rolls 10 - 1 (UC) = 9 for no effect.

3) Attacker rolls on Assault Combat Table, applies DRMs and results.

VC bringing attack 12, roll 5 + 1 (UC) - 1 (3 attacking hexes = 5 for 1, step loss from B/6/14.

4) If units on both sides remain, both sides roll against highest ER in their stack for Efficiency Check. A roll less than or equal to the ER passes the Efficiency Check.

  • VC ER check roll 4, fail.
  • US ER check roll 8, fail.

5) Units passing their Efficiency Check may roll again on the Assault Combat Table. This roll is simultaneous, results are not applied until both sides (if possible) have rolled.

6) If Defender is eliminated, Assaulting units must advance.

N/A.

Games 23-26

Here's a set of four games with just the essential mechanics extracted. The games were recorded on a dedicated spreadsheet, and the results copied here.

Game 23

FWA win.

Phase Description VC total hits FWA total hits
Offensive Bomb Roll 4, no effect. 0 0
Attack Coordination Roll 3, coordinated. 0 0
Defensive Bomb 10 Air points, roll ADF 1, hits, roll 6 no change. Roll 4 for 3 which is 1 hit on VC 1 0
Defensive Assault Roll 9 on Assault 2-3 for no effect. 1 0
Offensive Assault Roll 10 - 1 on Assault 10-12 for no effect 1 0
ER Check VC roll 9, US roll 3. 1 0
Defensive Assault Roll 2 on Assault 2-3 for 1 VC hit. 2 0
Offensive Assault N/A 2 0

Game 24

FWA win.

Phase Description VC total hits FWA total hits
Offensive Bomb VC roll 3 for no effect. 0 0
Attack Coordination Vc roll 7, uncoordinated 0 0
Defensive Bomb ADF roll 6, no effect. Roll 9 for 1 VC hit. 1 0
Defensive Assault Roll 1 for 1 VC hit. 2 0
Offensive Assault Roll 1 + 1 (Uncoordinated) - 1 (3 hexes) for for 2 hits, B/6/14 eliminated. 2 2
ER Check VC roll 1, US roll 1. 2 2
Defensive Assault Roll 7 - 1 = 6 for no effect. 2 2
Offensive Assault Roll 10 + 1 = 11 for no effect, bummer, VC had a 60% chance of winning this one. 2 2

Game 25

FWA win.

Phase Description VC total hits FWA total hits
Offensive Bomb Roll 2 for 1F, fatiigue on HQ. 0 0
Attack Coordination Roll 2, coordinated. 0 0
Defensive Bomb ADF roll 10 for no effect, roll 8 for 0 hits. 0 0
Defensive Assault Roll 7 for no effect. 0 0
Offensive Assault Roll 7 - 1 (3 hexes) on Assault 13-15 for 1 hit. 0 1
ER Check VC roll 1, US roll 1 0 1
Defensive Assault Roll 1 for 1 hit 1 1
Offensive Assault Roll 8 -1 for 1 hit 1 2

Game 26

FWA win.

Phase Description VC total hits FWA total hits
Offensive Bomb Roll 2 for 1F, fatigue on HQ 0 0
Attack Coordination roll 7 uncoordinated 0 0
Defensive Bomb ADF 5 no effect, roll 5 for 1 hit on VC 1 0
Defensive Assault Roll 9 for no effect 1 0
Offensive Assault Roll 2 + 1 - 1 on Assault 10-12 for 2 hits 1 2
ER Check VC roll 8, US roll 9. 1 2

AAR

Combining with the previous study, the win rate for VC is currently 2/11, which seems a little lower than it ought to be. My hunch is that it ought to be around 25%, maybe a closer to 30%. For 2 turn games, I'm pretty the win rate would be much higher, but I need to play a few to see.

More probability

I worked on getting a complete probabilistic analysis for this scenario, but there is just too much complexity to deal with to do it all at once. I'm going to work on back calculating various probabilities to make it easier.

Probability of taking out US on first turn

There several cases, starting with Offensive Bombardment:

  1. Offensive bombardment does not destroy one step, \(O_{BF} = 0.90\).
  2. Offensive bombardment does destroy one step, \(O_{BS} = 0.10\).

Then we need to figure out which column the VC attack on, either Assault 10-12 \(A_{10}\) or Assault 13-15 \(A_{13}\). From the previous article, we can equate the probability that the the VC lose no steps during defensive bombardement \(A_{13} = L_0 = 0.312\).

Again, two cases, coordination succeeds \(P(C_S) = 0.30\) or fails \(P(C_F) = 0.70\).

Supposing bombing failed, then we have \(P(H_3|C_S) = 0.20\) and \(P(H_3|C_F) = 0.1\).

Given a bombing failure \(O_{BF}\) and no VC step loss, we have (and I know the syntax here is likely nonsense)

\[P(H_3|O_{BF}) = P(O_{BF} \cap A_{13} \cap P(H_3|C_S)) \cup P(O_{BF} \cap A_{13} \cap P(H_3|C_F)) = (0.9)(0.312)(0.1+0.3) = 0.0842,\]

or around 8.5%.

My game plays aren't seeing that, yet.

With a VC step loss and bombing failure, I do not see a way for the VC to win in one turn, unless they make the ER check and can go another round of Assault combat.

Next step is compute \(H_3\) for successful bombardment with no VC step loss.

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What to play next?

Deciding what to play next is always a tough call when faced with a closet full of games, all of which were purchased with intent to play. Here's one I'm dealing with the decision.

  • Something New: this means both something new to me and a game which has been published recently, within the last two or three years.
  • Something Classic: I've acquired a number of games properly considered "classic" which haven't yet been played. The current example would be PanzerGruppe Guderian.
  • Something Again: mastery requires constant practice, which means playing games many, many times to allow nuance to appear.
  • Something Vietnam: as I'm on a Vietnam binge. I don't have all the Vietnam games ever published, but I can say that I have a lot of them, and probably more than most people.
  • Something Obscure: as it's fun to poke around in the dustier corners of game design.
  • Something Different: break away from the same old publishers and try a game from one of the new kids on the block. Or, conversely, dip into legacy with a classic tried and true.
  • Something Light: once in a while it's nice to actually finish a game all the way through in one sitting, in an hour or two.
  • Something Heavy: if possible, it's nice to set up something big and complicated which can be left out for days or weeks or even months, for a leisurely stroll through a very large or long game.

There are surely many more ways to choose, but the above method keeps me busy enough, helps me get both breadth and depth into my play, and provides me with a sense of progress.

The odd man out

When there is an odd man out:

  • Have a solo game ready to play.
  • Keep score or advise on a game in progress.
  • Referee a game in progress.