Thursday, 24 October 2013

The lost units at Grunberg

While I was preparing the table game for Grunberg, the next Lasalle project, I realized that the bridge over the Floha could channel the play towards that area, delaying the crossing of the French units to the main playing area. Evidently, that was a situation that frequently arose in real warfare, but in this case and according to the Nafziger's narrative, the Austrian units in the northern bank were outflanked by the French and forced to retire towards the Grunberg area. To model these events, some of the French units that could start the game on the table, are allowed to enter upstream in later turns (see the optional Gruberg rules here).
However, the presence of the wooded areas in the banks of a stream can add some additional and  interesting effects: some units could lose its way in the wood while probing for fording sites, and make their apparition in an unexpected site unknown in advance. This seemed to me a very interesting idea to add more spice to mi solo gaming, so I decided to model a such situation with light cavalry units, because these were usually forming the advance-guard of the armies, and such were more liable to suffer these problems. After some cogitation, and using my experience as chemometrician, I designed the following optional rule to be tested in the Grunberg Scenario.

The lost unit (optional)
Light cavalry usually formed the advance guard of the Napoleonic armies. In this Scenario, one of the French light cavalry brigades may act in that way, and it will start the game being hidden in the wooded northern bank of the Floha stream. To add more spice to the game, the exact turn and location of its exit from the southern border of the wooded area, will be unknown in advance.
Turn of exiting. Roll two D4 at the start of the turns 3, 5, 7 and 9. If their total roll is smaller than the current turn number, the unit has exited from the wooded area.
Location of exiting (see the table map)
   Turn 3. The unit exits at the point 3
   Turn 5. The unit exits in any location between 5 and 5’
   Turn 7. Idem between 7 and 7’
   Turn 9. Idem between 9 and 9’
When the unit exits from the wooded area in the turns 5, 7 or 9, the exiting point is found by dividing the exit area in 11 parts, numbered from 2 to 12, and rolling two D6. Their total rolling marks the exact exiting point

The reasoning behind that rule is as follows:
1) Turn of exiting. The sum of two D4 dice produces a triangular probability distribution. The respective probabilities of exiting at each turn are:
Turn 3 : 6%
Turn 5: 38 %
Turn 7: 81 %
Turn 9: 100%
So the probability of an unit leaving the wood, increases with the Turn number.
2) Location of the exiting point. The distance travelled by the units will be proportional to the time that they remain in the wood, so the exit zone becomes progressively larger when time passes. However in this case, the units don't will never lose totally their way because they will be always searching for the maximum slope (down and up). Therefore, they will tend to exit in the central zone (near the point labeled '3' in the map) although with a probability progressively smaller towards the extremes of their allowed exiting zone. This can be well modeled with the usual 2D6 roll that produces a triangular distribution.

I hope this rule will works adequately!

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