There are clues in the use of hands(and heads/tails/up/down) in the combative showdown between Richard and Red; and these clues link up with and explain why at the beginning of the episode Dougie was trying to hide his left hand while looking at the cowboy with the gun, but later in the office with his boss, he does not die but gets tough while looking at the 'toughest' boxer poster, hesitantly raising his left hand after gulping in fright(fright at losing control and being trapped by Laura again).

  The gun sign was previously made by Red to Shelly, seducing her and her friends at the expense of James, the dark green.  Thus there is a connection between Red and Cooper about who is controlling the green(background community, state/government) and the effect of desire(Red) on the green.  There is then the closely connected topic which differentiates these two well positioned characters (cooper/dougie and red), based on how they manage the connection with the paradoxical and antinomical void that is the infinite red room, so as to properly utilize its power. 

   The clues about the hands/arms: right is stable assertion of conscious control, what is on the surface controlling the nightmare-infinite lying below, then navigating the world.  Left arm is unconscious, clues that surprise/come out of nowhere, unexpected obstacle and 'blue rose' impossible antagonisms; and dealing with unsolvable deep traumas gives rise to surplus-gain(gold) alongside the shit of failure(brown, infinite impossibility, etc.).

    The top/heads is associated with Gold, which is surplus-enjoyment which comes from positively dealing with 'blue rose' unsolvable impossible antagonisms.  How these antagonisms are dealt with by people changes reality itself, including the inner core of people, and both Red and Cooper/Dougie are aware of this.  An example of Red's surplus-Gold gains are seducing Shelly and her friends at James expense, and humiliating Richard.  Gold as success becomes 'electricity-becoming-changing' (white, silver etc. on top, controlling what becomes, in the green etc.), determining the law, reality itself, what people desire, etc., how this is accomplished is 'magic', it is not guaranteed, which is why Red seems uncertain and hurt during certain times of his boxing match with Richard, who does not know of these magic powers explicitly(only vaguely as a young kid only could).  For example, Red acts like being hit in the liver by Richards left, then puts his hands behind his head as if he is under arrest, since Richard's hidden(left arm) strength was unexpectedly strong and resilient(he recovered from Red attacking his deepest core, his enjoyment/women and power in Twin Peaks).

The bottom is associated with shit/brown, absolute/infinite failure which is unsurpassed, garmonbozia(pain/suffering) bringing radical guilt and the drive to black/destruction of what is here that is not fit for us as capable of infinite proper desire(red song in episode 4) and rational thinking beings which infinitely create, capable of making a 'blue rose' situation just, solve the unsolvable, etc..

   Red's coin/dime is important here: the coin is Red's silver/power, which he made Richard choke on, accept as connected to his core, then snatch from his right hand, it is out of his conscious control.  What followed from this coin was Richard's shit spilling out infinitely from the inside:  Red showed Richard the tails/bottom side in his open right palm, in his conscious control/right had, that he has brought to the conscious surface and controlled Richard's source of surplus power; tails, infinite, what we are conscious about, Richard loses, his has been hit with black/symbolic death of his inner core, etc..  Now when the heads side is on Reds closed left first,  Red seems less sure of himself and more hesitant(knowing he cannot fly right into the surplus like richard Gold to shit, back to gold, etc. etc., but control it, art of kung fu, etc.), when dealing with the infinite, there is always an amount of contingency('dont bet the farm on anything', and this is why the dwarf was rolling dice).  The heads side, the top gold-surplus and electricity must not connect directly with the left arm, the fist must remain closed limited.  Heads Red wins, maybe, and only for now.... 

   Also, notice how this limiting of surplus was indicated to change in a different way for Carl(electric pole), who was desiring(sitting the red bench) green/community/government(looking at the trees), got spooked, was happy by the kid and mother, then encountered gold surplus after he saw the kid killed.  This entire process all started in the brown colored scene with Mickey where he and Carl are complaining about the government(green).  That change itself was coming was indicated by the truck driver who waved on the kids with his right hand, with both a gold tassle next to a tassle with white/change on top and black/void on the bottom, indicating an infinite change in the gold taking something out of the void and into the green(reality/government/community, etc.).  The truck driver's conscious assertion/right hand displayed this sort of surplus to green/community, enjoying the simple act of manners/law, etc.,  but his left hand is stiff and absent, meaning that he can never 'bet the farm', even this is not guaranteed, there is always some unexpected obstacle which can change everything.....