The Great Dalmuti is a game where you attempt to get rid of your hand, a climbing card game like Tien len or Asshole. The deck consists of 80 cards, with different point values. There is one '1', two '2's, three '3's, ..., twelve '12's and two wilds that are '13' unless played with any other card. Rounds consist of the Great Dalmuti or whomever won the last trick laying down any number of cards with the same value. Players in clockwise order can either 'pass' or play the same number of cards as the previous player but of a lower value (i.e. if the first player played three '10' value cards, the next player could play three '9', three '8', etc.), or by playing a larger set of the same value as the previous set of cards.
When a player has played the last card from their hand, they score one point for each person they beat, with the last person scoring zero. Going out first or second (becoming the Greater or Lesser Dalmuti) gives another privilege: at the start of the next round, the Dalmutis receive the one or two best cards from the Peons (the two players who went out last), while returning any cards from their hand. (The Greater Dalmuti swaps two cards, the Lesser Dalmuti one.) This gives the Dalmutis significantly better hands: they get better cards, and can get rid of singletons that would slow down their hands. It is very important not to go out last, or second to last.
If you are playing a game to some point value that is quite a few rounds away (lets say 10 or more), what should be your strategy for improving your score? How can you determine if you have a hand that can hold onto control of enough rounds to get rid of your high value cards (in other words, how can you determine if by go off during a turn you will likely improve your seat position or maintain it, instead of ending up going out last).
How do you know when to take control, and attempt to get out of the game?
Does the strategy of shooting for first seat get easier/harder with more/less players?