The original design for the Delay procedure is linear. The curve of distribution of chances is a low flat one (at least for a 0 Delay DRM). It changes with different DRM because the maximum and minimum die rolls are 1 and 6 (look at the table).
Note: how to read the table. The column represents the starting Delay DRM for the unit in the Delay Box. For each Delay DRM you can ready in the row the chances (in percentage) you have to receive the unit in the corresponding number of turns.
Delay | ||||||||||||
Turn | -5 | -4 | -3 | -2 | -1 | 0 | +1 | +2 | +3 | +4 | +5 | Turn |
1 | 100 | 83.3 | 66.7 | 50 | 33.3 | 16.7 | 0 | 0 | 0 | 0 | 0 | 1 |
2 | 16.7 | 16.7 | 16.7 | 16.7 | 16.7 | 16.7 | 0 | 0 | 0 | 0 | 2 | |
3 | 16.7 | 16.7 | 16.7 | 16.7 | 16.7 | 16.7 | 0 | 0 | 0 | 3 | ||
4 | 16.7 | 16.7 | 16.7 | 16.7 | 16.7 | 16.7 | 0 | 0 | 4 | |||
5 | 16.7 | 16.7 | 16.7 | 16.7 | 16.7 | 16.7 | 0 | 5 | ||||
6 | 16.7 | 33.3 | 50 | 66.7 | 83.3 | 100 | 6 |
Sal Vasta proposed a House Rule for an Alternate Delay Track, mathematically modified by Jay Muchnij (see picture).
This design adds a considerable amount of tension and uncertainty surrounding units that are "in Delay". On the other hand, while trying to keep the average delay times close to the original design it has some drawbacks.
While mathematically speaking it mimics very well the 'flat' distribution curve, the new curve opens up at the ends. So gamewise speaking, with a +4 Delay DRM you have a 40% chance of getting the unit back in 3 or 4 turns, and 25% in 7 or more turns. Or with a Delay DRM of 0, you still have about 10% chance to get your unit back in more than 6 turns! (Don't ask Sal to try this one! ;-) (see table below.)
Delay | ||||||||||||
Turn | -5 | -4 | -3 | -2 | -1 | 0 | +1 | +2 | +3 | +4 | +5 | Turn |
1 | 100 | 83.3 | 66.7 | 50 | 33.3 | 16.7 | 0 | 0 | 0 | 0 | 0 | 1 |
2 | 16.7 | 22.2 | 27.8 | 25 | 22.2 | 25 | 5.6 | 8.3 | 0 | 0 | 2 | |
3 | 7.4 | 13 | 17.1 | 19.9 | 24.5 | 24.1 | 13.9 | 15.3 | 13.9 | 3 | ||
4 | 2.5 | 5.6 | 10.7 | 15.2 | 18.4 | 23 | 22 | 24.3 | 17.4 | 4 | ||
5 | .8 | 2.3 | 6.3 | 10.4 | 12.5 | 17.3 | 19.1 | 20.7 | 20.8 | 5 | ||
6 | .3 | .9 | 3.5 | 6.6 | 8.1 | 11.8 | 13.9 | 14.9 | 16.9 | 6 | ||
7 | .1 | .3 | 1.9 | 4 | 5 | 7.6 | 9.2 | 9.9 | 11.9 | 7 | ||
8 | .1 | 1 | 2.3 | 2.9 | 4.6 | 5.8 | 6.3 | 7.8 | 8 | |||
9 | .5 | 1.3 | 1.7 | 2.7 | 3.4 | 3.8 | 4.8 | 9 | ||||
10+ | .7 | 1.4 | 1.9 | 3.3 | 4.4 | 4.8 | 6.5 | 10+ |
I abandoned the idea to track the Delay of the unit, and decided to try a different approach (actually it is only the reverse of the coin): instead of the delay, you track the time spent by the unit in production (so the Delay Box could be considered a sort of Production Track).
Here it is my personal design:
A unit enters the Delay Track in the '1' box. Each Delay Segment roll one die for each unit (starting from the box with the greatest number, going backward), modified by the current Delay DRM for it: if the modified DR is less or equal to the number printed in the box you receive it, otherwise move it ahead one box. Units in the '6' box automatically arrive (or the '10' box for 'Long Delays').
Download now a printable version of my Alternate Delay Box in Adobe Acrobat format
This design has some pros and cons:
Delay | ||||||||||||
Turn | -5 | -4 | -3 | -2 | -1 | 0 | +1 | +2 | +3 | +4 | +5 | Turn |
1 | 100 | 83.3 | 66.7 | 50 | 33.3 | 16.7 | 0 | 0 | 0 | 0 | 0 | 1 |
2 | 16.7 | 27.8 | 33.3 | 33.3 | 27.8 | 16.7 | 0 | 0 | 0 | 0 | 2 | |
3 | 5.6 | 13.9 | 22.2 | 27.8 | 27.8 | 16.7 | 0 | 0 | 0 | 3 | ||
4 | 2.8 | 9.3 | 18.5 | 27.8 | 27.8 | 16.7 | 0 | 0 | 4 | |||
5 | 1.9 | 7.7 | 18.5 | 27.8 | 27.8 | 16.7 | 0 | 5 | ||||
6 | 1.5 | 9.2 | 27.7 | 55.5 | 83.3 | 100 | 6 | |||||
Optional 'Long Delays' House Rule | ||||||||||||
6 | 1.5 | 7.7 | 18.5 | 27.8 | 27.8 | 16.7 | 6 | |||||
7 | 1.5 | 7.7 | 18.5 | 27.8 | 27.8 | 7 | ||||||
8 | 1.5 | 7.7 | 18.5 | 27.8 | 8 | |||||||
9 | 1.5 | 7.7 | 18.5 | 9 | ||||||||
10 | 1.5 | 9.2 | 10 |
And now for a comparison of the various designs, look at the following table with the average turn number of re-entry for each Basee Delay DRM:
Average Turn Number | ||||
---|---|---|---|---|
Base Delay |
Original | Sal's | Jay's | Prana's |
-5 | 1 | 1 | 1 | 1 |
-4 | 1.167 | 1.167 | 1.167 | 1.167 |
-3 | 1.5 | 1.433 | 1.5 | 1.391 |
-2 | 2 | 1.773 | 1.875 | 1.695 |
-1 | 2.667 | 2.264 | 2.622 | 2.132 |
0 | 3.5 | 2.887 | 3.46 | 2.772 |
+1 | 4.333 | 3.402 | 4.020 | 3.757 |
+2 | 5 | 3.588 | 4.824 | 4.665 |
+3 | 5.5 | 3.705 | 5.129 | 5.388 |
+4 | 5.833 | 4.023 | 5.407 | 5.833 |
+5 | 6 | 5.022 | 5.740 | 6 |