Silver Bayonet - Theorycrafting Tea Time
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This article documents an experiment I'm conducting on game mechanics related to small scenario design.
The main idea is that really small scenarios should provide the statistically likely outcome as a Draw condition, with statistical outliers favoring each side determing Win/Lose conditions.
Apparently this activity is known as "theory crafting" within certain communities. I've always called it "statistical analysis."
For this first attempt, we'll be using Scenario #6 "Tea Time" from GMT's Silver Bayonet. Tea Time is a 1 or 2 turn scenario with about a dozen counters, and demonstrates only the assault combat mechanics of the game. The initial goal is to play this scenario several times recording the outcome for all die rolls.
Tea Time has two variations. The first is a single turn with 10 Air Points for the FWA defenders, the second is two turns with 10 Air Points for the FWA defenders each turn.
Result of 6 plays
I played the Catecka Tea Plantation scenario six times back to back, recording the results of every phase of the Turn Sequence. The results are given in the following table:
| FWA step loss | PAVN step loss | Winner | |
|---|---|---|---|
| Game 1 | 0 | 2 | FWA |
| Game 2 | 1 | 2 | FWA |
| Game 3 | 2 | 1 | FWA |
| Game 4 | 1 | 1 | FWA |
| Game 5 | 3 | 3 | PAVN |
| Game 6 | 3 | 1 | PAVN |
Each play follows a turn sequence reduced from the full turn sequence, as neither side need (or can) move.
Game 1
Turn 1
Situation at the beginning of the turn.
Per the setup, the FWA have an HQ and a 155 in the tea plantation hex. Neither of these units are going to move, they have to just sit there and take the punishment.
Initial Phase
1) Adjust FWA Air Points [11.0]
FWA receives 10 AP.
2) Remove "First" and "Final" Fire markers for BOTH sides.
Not necessary for 1 turn variant.
PAVN Player Turn
PAVN player's plans for this turn.
The VC is the first player this turn, plan is to assault the HQ and 155 arty in the tea plantation hex.
Combat Declaration Phase [6.1]
1) Declare all assault and maneuver combat by placing markers.
Assault by all VC on tea plantation hexes.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
This is where the Scenario 6 formally begins. The VC mortar unit declares bombardment on tea plantation.
2) Declare and resolve ADF [14.0].
3) Resolve Bombardment.
The VC have 2 bombardment points from a mortar unit. There do not appear
to be any DRM firing into the tea plantation, so the VC need a natural 1
roll to get a step loss, a 1 or 2 to get an F. The roll here is a 4,
which is 1, which is no effect with tea plantation TDV 2.
Combat Coordination Phase
1) Attack Coordination [7.0] which may negate declared Maneuver Combat declarations [8.0]
The VC are PAVN, and here operating outside the range of a HQ. The coordination roll need to be 3 or less to acquire assault coordination. The roll is 9, so no coordination.
Assault Combat Phase [9.0]
1) Defender allocates and resolves air and/or artillery for Defensive Bombardment [10.2]
FWA uses all 10 air points for defensive bombardment. PAVN ADF roll 10,
No Effect. FWA rolls 7 for 2, with TDV always 2 on defensive
bombardment, the VC take a step loss.
2) Defender rolls first on Assault Combat Table, applies DRMs and applies results immediately.
FWA defending with 3, gets a -1 DRM for attacker uncoordinated, roll 3 - 1 for an attacker step loss.
3) Attacker rolls on Assault Combat Table, applies DRMs and results.
VC assaulting with 11, roll 8 + 1 (uncoordinated) - 1 (more than 2 hexes attacking) for no effect.
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 roll 10 for ER check on second round, FWA rolls 9, so no second round of assault combat for either side.
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.
Failed efficiency check, no second round.
6) If Defender is eliminated, Assaulting units must advance.
Defender still occupies tea plantation.
FWA Player Turn
FWA player's plans for this turn.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
No bombardment as all Air Points used in defensive bombardment last turn.
2) Declare and resolve ADF [14.0].
3) Resolve Bombardment.
Game Record Phase
1) Reset FWA Air Points counter to 0. 2) If last turn assess victory, otherwise advance Game Turn marker.
This is a clear FWA win.
AAR for first game
First, the game is brilliant, no question, and no complaints.
However, I've played Silver Bayonet with a couple of fairly experienced opponents as well as solo, and all three of us have had some trouble with interpreting the Terrain Effects Chart. On the chart, column 6 is titled "Attacker Combat Effects." Apparently, this column is referred to as "Defender Combat Effects" in Section 4.2.1 of the rules (as shipped and v1.1 pdf).
Question: what's the correct column title, "Attacker Combat Effects" or "Defender Combat Effects?"
This point of confusion for us leads to the next question: is this column (whatever it's titled) used for combat DRM, or is the TDV value used for combat DRM? (FWIW, we have been using the TDV value.)
Apologies if this is explained in errata or elsewhere. I did some poking around and wasn't able to find anything.
Game 2
Turn 1
Situation at the beginning of the turn.
Initial Phase
1) Adjust FWA Air Points [11.0]
FWA receives 10 AP.
2) Remove "First" and "Final" Fire markers for BOTH sides.
Not necessary for 1 turn variant.
PAVN Player Turn
PAVN player's plans for this turn.
The VC is the first player this turn, plan is to assault the HQ and 155 arty in the tea plantation hex.
Combat Declaration Phase [6.1]
1) Declare all assault and maneuver combat by placing markers.
Assault by all VC on tea plantation hexes.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
This is where the Scenario 6 formally begins. The VC mortar unit declares bombardment on tea plantation.
2) Declare and resolve ADF [14.0].
None.
3) Resolve Bombardment.
The VC have 2 bombardment points from a mortar unit. There do not appear
to be any DRM firing into the tea plantation, so the VC need a natural 1
roll to get a step loss, a 1 or 2 to get an F.
Mortar rolls 10 on Bombardment table, no effect.
Combat Coordination Phase
1) Attack Coordination [7.0] which may negate declared Maneuver Combat declarations [8.0]
The VC are PAVN, and here operating outside the range of a HQ. The coordination roll need to be 3 or less to acquire assault coordination.
The roll is 7, so no coordination.
Assault Combat Phase [9.0]
1) Defender allocates and resolves air and/or artillery for Defensive Bombardment [10.2]
FWA uses all 10 air points for defensive bombardment.
- PAVN ADF roll 10, No Effect. (Same roll as first game!)
- FWA rolls 7 for
2, with TDV always 2 on defensive bombardment, the VC take a step loss. (Again, same roll as first game. Weird.)
2) Defender rolls first on Assault Combat Table, applies DRMs and applies results immediately.
FWA defending with 3, gets a - 1 DRM for attacker uncoordinated, roll 4 - 1 for an attacker step loss. (Different roll, same result as first game.)
3) Attacker rolls on Assault Combat Table, applies DRMs and results.
VC assaulting with 11, roll 9 + 1 (uncoordinated) - 1 (more than two hexes attacking) for no effect.
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 roll 3 for ER check on second round, FWA rolls 7, PAVN gets a second assault round, FWA does not.
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.
PAVN rolls 4 which is a step loss, almost surely have to take the step as the artillery unit, need to read the rules on this. (12.4.4 HQs must be the last steps chosen as combat losses.)
6) If Defender is eliminated, Assaulting units must advance.
Defender HQ still occupies tea plantation.
FWA Player Turn
FWA player's plans for this turn.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
No bombardment as all Air Points used in defensive bombardment last turn.
2) Declare and resolve ADF [14.0].
3) Resolve Bombardment.
Game Record Phase
1) Reset FWA Air Points counter to 0. 2) If last turn assess victory, otherwise advance Game Turn marker.
FWA prevails, still occupying tea plantation with single step. PAVN down 2 steps.
Game 3
This game the FWA gets a forced F result on the PAVN mortar
bombardment.
Turn 1
Situation at the beginning of the turn.
Initial Phase
1) Adjust FWA Air Points [11.0]
FWA receives 10 AP.
2) Remove "First" and "Final" Fire markers for BOTH sides.
Not necessary for 1 turn variant.
PAVN Player Turn
PAVN player's plans for this turn.
The VC is the first player this turn, plan is to assault the HQ and 155 arty in the tea plantation hex.
Combat Declaration Phase [6.1]
1) Declare all assault and maneuver combat by placing markers.
Assault by all VC on tea plantation hexes.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
This is where the Scenario 6 formally begins. The VC mortar unit declares bombardment on tea plantation.
2) Declare and resolve ADF [14.0].
None.
3) Resolve Bombardment.
The VC have 2 bombardment points from a mortar unit. There do not appear
to be any DRM firing into the tea plantation, so the VC need a natural 1
roll to get a step loss, a 1 or 2 to get an F.
Roll 2 for 1F result, the 155 arty will take the Fatigue result.
Combat Coordination Phase
1) Attack Coordination [7.0] which may negate declared Maneuver Combat declarations [8.0]
The VC are PAVN, and here operating outside the range of a HQ. The coordination roll need to be 3 or less to acquire assault coordination.
The roll is 9, so no coordination.
Assault Combat Phase [9.0]
1) Defender allocates and resolves air and/or artillery for Defensive Bombardment [10.2]
FWA uses all 10 air points for defensive bombardment.
- PAVN ADF roll 6, No Effect. (Same roll as first game!)
- FWA rolls 9 for
NE, with TDV always 2 on defensive bombardment, the VC takes no step losses.
2) Defender rolls first on Assault Combat Table, applies DRMs and applies results immediately.
FWA defending with 3, gets - 1 DRM for attacker uncoordinated but + 2 for the F on greater than or equal to 50% of steps, roll 2 + 1 for an attacker step loss.
3) Attacker rolls on Assault Combat Table, applies DRMs and results.
VC assaulting with 12, roll 3 + 1 (uncoordinated) - 1 (more than two
hexes attacking) for 2, FWA takes the howitzer off the field.
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.
Neither side passes EC. Game is over for FWA win.
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.
FWA Player Turn
FWA player's plans for this turn.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
2) Declare and resolve ADF [14.0].
3) Resolve Bombardment.
Game Record Phase
1) Reset FWA Air Points counter to 0. 2) If last turn assess victory, otherwise advance Game Turn marker.
Another FWA win. Geez.
Game 4
This game the PAVN gets their coordination roll.
Turn 1
Situation at the beginning of the turn.
Initial Phase
1) Adjust FWA Air Points [11.0]
FWA receives 10 AP.
2) Remove "First" and "Final" Fire markers for BOTH sides.
Not necessary for 1 turn variant.
PAVN Player Turn
PAVN player's plans for this turn.
The VC is the first player this turn, plan is to assault the HQ and 155 arty in the tea plantation hex.
Combat Declaration Phase [6.1]
1) Declare all assault and maneuver combat by placing markers.
Assault by all VC on tea plantation hexes.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
This is where the Scenario 6 formally begins. The VC mortar unit declares bombardment on tea plantation.
2) Declare and resolve ADF [14.0].
None.
3) Resolve Bombardment.
The VC have 2 bombardment points from a mortar unit. There do not appear
to be any DRM firing into the tea plantation, so the VC need a natural 1
roll to get a step loss, a 1 or 2 to get an F.
Roll 2 for 1F result, the 155 arty will take the fatigue.
Combat Coordination Phase
1) Attack Coordination [7.0] which may negate declared Maneuver Combat declarations [8.0]
The VC are PAVN, and here operating outside the range of a HQ. The coordination roll need to be 3 or less to acquire assault coordination.
The roll is 1 (by decree), coordinated assault.
Assault Combat Phase [9.0]
1) Defender allocates and resolves air and/or artillery for Defensive Bombardment [10.2]
FWA uses all 10 air points for defensive bombardment.
- PAVN ADF roll 7, No Effect.
- FWA rolls 3 for
3F, with TDV always 2 on defensive bombardment, the VC takes one step loss and Fatigues a unit.
2) Defender rolls first on Assault Combat Table, applies DRMs and applies results immediately.
FWA defending with 1 with no DRM, roll 10 for -.
3) Attacker rolls on Assault Combat Table, applies DRMs and results.
VC assaulting with 11 (1 step loss, 1 F unit), roll 7 - 1 (more than two
hexes attacking) for 1, 1 FWA step eliminated.
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.
FWA passes EC, PAVN fails.
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.
FWA rolls 3 on the 1 column, no effect.
6) If Defender is eliminated, Assaulting units must advance.
This is another FWA win.
FWA Player Turn
FWA player's plans for this turn.
N/A
Offensive Bombardment Phase [10.1]
N/A
Game Record Phase
1) Reset FWA Air Points counter to 0. 2) If last turn assess victory, otherwise advance Game Turn marker.
FWA win.
Game 5
We try again, but not logging this game or successive.
Turn 1
Initial Phase
1) Adjust FWA Air Points [11.0]
FWA receives 10 AP.
PAVN Player Turn
Combat Declaration Phase [6.1]
1) Declare all assault and maneuver combat by placing markers.
Assault by all VC on tea plantation hexes.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
Mortars.
3) Resolve Bombardment.
Mortars, roll 2 for 1F. HQ takes the fatigue marker.
Combat Coordination Phase
1) Attack Coordination [7.0] which may negate declared Maneuver Combat declarations [8.0]
Roll 2 for coordination.
Assault Combat Phase [9.0]
1) Defender allocates and resolves air and/or artillery for Defensive Bombardment [10.2]
Roll 5 ADF miss.
Roll 3 for 4F, two step losses, take an F on one of the step loss
units.
2) Defender rolls first on Assault Combat Table, applies DRMs and applies results immediately.
Roll 2 for 1, VC eliminates the F unit.
3) Attacker rolls on Assault Combat Table, applies DRMs and results.
Roll 5 - 1 (multiple units) on the 7-9 column for 1, FWA flips
howitzer.
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.
Both pass EC.
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.
- FWA roll 4, no effect.
- PAVN roll 3 - 1 for
2, FWA eliminated.
6) If Defender is eliminated, Assaulting units must advance.
PAVN win, finally.
FWA Player Turn
FWA player's plans for this turn.
Game 6
Not logging this game or successive.
Turn 1
Initial Phase
1) Adjust FWA Air Points [11.0]
FWA receives 10 AP.
PAVN Player Turn
Combat Declaration Phase [6.1]
1) Declare all assault and maneuver combat by placing markers.
Assault by all VC on tea plantation hexes.
Offensive Bombardment Phase [10.1]
1) Declare Bombardment using air points or artillery.
Mortars.
3) Resolve Bombardment.
Mortars, roll 1 for 2F. Howitzer takes the step loss.
Combat Coordination Phase
1) Attack Coordination [7.0] which may negate declared Maneuver Combat declarations [8.0]
Roll 5 PAVN uncoordinated.
Assault Combat Phase [9.0]
1) Defender allocates and resolves air and/or artillery for Defensive Bombardment [10.2]
Roll 9 ADF miss.
Roll 10 for -, PAVN lucky, bad pilots miss everything. Sad!
2) Defender rolls first on Assault Combat Table, applies DRMs and applies results immediately.
Roll 1 on the 2-3 column for 1, PAVN takes a step loss.
3) Attacker rolls on Assault Combat Table, applies DRMs and results.
Roll 2 + 1 (uncoordinated) - 1 (3 attacking hex bonus) on 10-12 column
for 2, FWA eliminated.
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.
PAVN win.
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.
PAVN win, again.
FWA Player Turn
FWA player's plans for this turn.
AAR
I'm inclined to go with having the FWA down to a single step be called a draw. That seems to be a pretty likely case. In 6 games of this scenario, the PAVN have only prevailed twice.
What follows is a first cut at some probabilistic modeling of the how this scenario works. There is a lot more which could be done, and I have a set of notes with more details.
Defensive Bombardment
The scenario grants the FWA player 10 Air Points. A natural question to
ask is "How much damage can these 10 Air Points inflict?" The answer, of
course, is on the Bombardment/Support Table, column 10-14, we see
rolling 1 or 2 results in 4F, which is 2 steps lost for TDV 2 (per
definition of TDV during Defensive Bombardment). On the other hand,
rolling an 8, 9 or 10 results in no step losses for the attacking PAVN.
The PAVN can reduce the odds one or two step losses by getting a hit and damage on Air Defense Fire (ADF). Any damage at all shifts the FWA bombardment to the 6-9 column. Let's calculate the probability of PAVN inflicting damage on the defender's aircraft.
First, we note that rolling 1 or 2 results in a "hit," but since PAVN has a mortar unit adjacent, PAVN gets a +1 DRM. Hence,
\[P(H) = 0.3.\]Given we have a hit,
\[P(D) = 0.4.\]Any damage at all results in a single column shift left. For Shift Left \(S_L\), we have
\[P(S_L) = P(H\cap D) = P(H)P(D) = 0.12.\]For convenience, define \(B_6 = S_L\), that is, shifting the air bombardment 1 left indicates using the 6-9 column instead of of 10-14 column for the Bombardment table. (For 10 Airpoints associated with Tea Time.) Then we have
\[P(B_{10}) = 1 - P(B_6) = 1 - 0.12 = 0.88.\]Probability of two PAVN step losses
Now let's check the probabilities on the Bombardment/Support Table. For
the 10-14 column \((B_{10})\), rolling 1 or 2 results in 4F. On the 6-9 column
\((B_6)\),
rolling 1 results in 4F. For some two step loss \(L_2\),
Now we have
\[P(L_2) = P(L_2 \cap B_6) + P(L_2 \cap B_{10}) = 0.012 + 0.176 = 0.188.\]This result makes sense. If we were rolling only on the \(B_{10}\) column it's easy to see there is a 20% chance of getting 2 step losses. But the small probability of being hit with ADF weights the result into the \(B_6\) column, just a small amount. So the odds are reduced just over 1%, from 20% to 18.8%
Probability of single PAVN step loss
It's easy to compute the probability of losing exactly 1 step:
\[P(L_1) = P(L_1 \cap B_6) + P(L_1 \cap B_{10}) = (0.5)(0.12) + (0.5)(0.88) = 0.06 + 0.44 = 0.50.\]Now that's an interesting result, and one which can be seen by inspection!
PAVN loses at least 1 step
To find the probability of losing at least one step, first compute the probability of losing no steps \(P(L_0)\):
\[P(L_0) = (0.12)(0.4) + (0.88)(0.3) = 0.048 + 0.264 = 0.312\]Now, \(P(L_1) \cup P(L_2) = 1 - P(L_0) = 1 - 0.312 = 0.688.\)
In other words, there is about a 70% chance that Air Bombardment will reduce PAVN by at least 1 step.
This study will be continued with an examination of the Assault Combat Table.
Conclusion
This concludes what I hope will be just the first round of investigation.
I'm interested in digging deeper to get a complete spectrum of outcomes, but that will take more time than I'm willing to spend right now.
Next steps to consider:
- See if this battle is amenable to some sort of spreadsheet system.
- Can it be programmed? Surely so.
- Continue on with Scenario #6b to give the PAVN another crack at it.
Fun times for the future!