Reserves mathhammer

There has been discussion in other threads about reserves manipulation.  Taking an Autarch for the +/- 1, taking the standard FOC to get the fortification for a comms relay, etc..  So I thought I would go through the numbers of the various choices we have for reserves manipulation.  We have 4 choices:  nothing, comms relay, autarch, and comms relay with autarch.  Also, we have 2 different reasons for reserve manipulation: we want a unit to come in, and we don't want a unit to come in.

1) Nothing:  We have a 2/3 chance of a unit coming in and 1/3 chance of it not coming in.  Nothing more to see here.

2) Comms relay:  2/3 chance of a unit coming in and a 2/3 chance on the re-roll equals 8/9 chance of the unit coming in.  1/3 chance to not come in with a 1/3 chance on the re-roll of a successful roll equals a 5/9 chance to keep a unit off if we don't want it.

3) Autarch:  5/6 chance to get the unit in and 1/2 chance if we don't want the unit.

4) Comms + Autarch:  5/6 chance plus a 5/6 chance on the re-roll equals 35/36 chance to get a unit in and 1/2 plus 1/2 on the re-roll equals 3/4 chance if you don't want the unit

I put everything together in a table showing the chance out of 36 for each occurrence for comparison.

Type                          In        Not In
Nothing                   24/36     12/36
Comms                   32/36      20/36
Autarch                   30/36     18/36
Comms + Autarch    35/36     27/36

The comms relay is slightly better than the Autarch (2/36) in both instances while comms + Autarch is almost automatic for bringing units in and a significant upgrade over the individual options for leaving units out.  I will leave thoughts and opinions for a separate post, just wanted to get the data out here for everyone.