Anyone ever play the game 31?

Rules:

Each player is dealt 3 cards face down, discard/draw piles in middle. Each player has option to take face up card or draw and must discard after hand, like gin. Goal is to get highest total; cards are counted like blackjack but must be suited, with the exception that a set counts 30.5. AsTsTs = 31 wins instantly; all other hands must knock. Knocker lays 2:1 that he can beat at least one other player; each other player immediately following knock has one final turn to improve. Low hand loses.

Questions:

I'm struggling with the exact probabilities to find a) at what total one should knock first hand, dependent upon position [note that the 'UTG' player, upon knocking, would limit opps to one additional card each, while the 'button' player would face two chances - albeit only one where the opps knew the finite horizon] and b) what a reasonable rate of improvement would be over the course of several rounds of a hand [how quickly does a particular holding devalue?]

Any help, or just random thoughts, would be highly appreciated.

Cheers!