[rfuyrbpj] Draw poker with no betting

Consider the game of draw poker with no betting.  You get dealt some cards then replace some.  The winner has the best hand and scores 1 point.  What is the optimal strategy?  This has probably already been calculated.  It probably depends on number of players.  How does the optimal strategy depend on the observed actions (number of cards wanting to replace) of previous players?

Can we increase the complexity so that skill matters a lot more than luck to make this non-betting form an entertaining game in its own right? Perhaps multiple rounds of replacement, some cards dealt face-up (like upcards in stud).  We are mostly removing the element of bluffing, though you can bluff some by the number of cards you ask to replace.

If more than 1 player tie for the highest hand, does it matter if all get 1 point, or all get 1/N points?  The latter can be done (as an expected value) with a tiebreaker round.

Another variation in scoring: you get 1 point for each opponent hand you beat.

Can we increase the complexity enough that humans can beat computers?  This will be pretty tough because computers can do Monte Carlo simulations well.  We need some concept of strategy, a sequence of non-obvious correct moves from a very large universe of possible moves.