This format was developed by Jim McCarthy for Cutthroat Racquetball tournaments at New Mexico Tech (NMT).
Some years later it was used for running Cutthroat Pool tournaments at NMT (see BAC Tournaments).
Note that foursomes are required for both of the above.  The threesomes and fivesomes that may be referenced below can't be used for McCarthy style Cut Throat competitions.
For simplicity the explanation below will use the schedule for 32 players .  The examples use four people per group (foursomes).  Match Point tables for Three-somes, Four-somes, and Five-somes will allow for using this format with some different size groups.
Note: Please keep in mind that the following description is geared toward running a Cutthroat Pool tournament.  In particular any times shown in the accompanying tables are used for various Cutthroat Pool tournaments.  Those times would be altered (or discarded) for other situations.  The restriction of just three people playing at a time is definitely tied to Cutthroat.
Each player will play in a foursome.  Only three of the players will play at any given time, but they are competing with all other players of their foursome.  The foursomes do not compete. The self-seeding aspect of this format comes from players moving about between the foursomes from one round to the next.
A player's performance in the first two rounds will determine what foursome they play in for the 3rd-round.  So by the 3rd-round they are playing against players more-or-less on their level.
The 1st-round is seeded by random draw.  The foursomes are split into two pools; one called RED, the other called GREEN.
The 2nd-round foursomes are based on the results of the 1st-round of play.  It reseeds players by moving them between the foursomes of their respective pool.  A player's performance in the first two rounds will determine how they are grouped with players of the same relative performance from the other pool for 3rd-round play.
The 3rd-round is the first elimination round.  In the 3rd-round players will no longer be in a RED or GREEN pool.  Players will be moved into an "A" or "B" division based on their performance in the first two rounds.  Only 1/2 of the 3rd-round players will advance to the semi-final round.
The 4th-round is the semi-final round.  Players will be grouped according to their performance in the 3rd-round.  That may change which foursome they're in but it will not change the division they play in.  This round will see the field cut in half again.
The 5th-round is the final round. It will see each division with one foursome.  The players in these foursomes will be playing for their rank in the tournament.
(Note: this is just for Cutthroat.)
The different rounds of the tournament use games of differing times.
 See Round Time Schedules
for the charts and which rounds they apply to.
Below are "Flow Tables" (with sample schedules) for various numbers of: players, tables, and days.