Poker Dice

In Poker Dice, the aim is to build the best possible poker hand, where straights and flushes don't count. The first person to roll has up to three throws of the dice and after each throw can put aside any dice they wish to use for their hand; also, they can stop after the first of second roll if they wish. After the first person establishes a number of rolls, each successive player may only throw the dice at most that many times. The player with the highest ranking hand after everyone has had a turn wins the game. Is there any way to gain an edge?

1-4-24 (Midnight)

How to play

Midnight is played with six dice where the objective is to get the highest score. Someone starts by rolling six dice. On each roll, you are required to keep at least one of your dice, and you re-roll the remaining ones. You do this until all six dice have been kept. So at most you will roll six times.  For example, you can choose to keep anywhere from one to six dice on the first roll. If you kept two of them, then you'd re-roll the remaining four dice, and you can choose to keep one to four of them. And, so on...

The sum of the six selected dice becomes your score, with one caviat: you must qualify the hand by rolling a one and a four. Therefore a maximum score is twenty-four by rolling 1-4-6-6-6-6, and a minimum score is zero by not qualifying.

When beginning, the order is determined randomly. After a round has been played, the lowest score goes first and the highest score goes last. Clearly, going last has the advantage due to the ability to know when to simply just stop trying for a  higher score while taking on the risk of getting a lower one. Say the first person scores an 8. And, as the 2nd player, your very first roll is 1-4-6-5-1, you can simply stop right there and claim a win with a score of 12.

For a three, four, or more player game, only a single distinct winner can win the pot. So, say in a four player game, two people score 18, one guy scores 15, and another scores a 13. Since there is no distinct winner due to two best scores tying, there is no winner this round. All players ante up again, building the pot. All players are still in the game, and therefore, are eligible to win. You play until there is a single distinct winner, who scoops.

Is there an optimal strategy for this game? If so, what is it?