PokerStars, $3.92 + $0.48 - Badugi Pot Limit - 150/300 - 7 players
Replay this hand on Pokeit

UTG: 9,265 (31 bb)
MP: 4,413 (15 bb)
MP+1: 6,595 (22 bb)
CO: 600 (2 bb)
BU: 6,434 (21 bb)
SB: 3,150 (11 bb)
BB (Hero): 9,081 (30 bb)

Deal: (450) Hero is BB with K 9 3 A
UTG calls 300, 5 players fold, Hero checks

Draw One: (750) 3 A 8 J (2 players)
BB (Hero) draws Kd 9h, UTG draws 1
Hero checks, UTG checks

Draw Two: (750) 3 A 2 3 (2 players)
BB (Hero) draws 8h Jd, UTG draws 1
Hero bets 375, UTG calls 375

Draw Three: (1,500) 2 4 3 A (2 players)
BB (Hero) draws 3d, UTG draws 1
Hero bets 750, UTG raises to 3,750, Hero???

I wouldn't bet the river. He pretty clearly has a crappy hand and doesn't have showdown value with his 3cd

makes sense, check/call then?

Pot instead of 375

In the little PL badugi I've played, I generally bet pot to charge max when value betting and give max fold equity when bluffing, but I'd be curious what others think.

I guess the flop lead seems pretty good to charge a likely crappy 1 card draw, although if villain is at all thinking, he's likely to bet whole range after 2/1 so maybe we can check/raise. Gets extra money in there and maybe extra fold equity. Also we have a better sense of villain's range when it goes x/x.

RolldUp's logic on river makes good sense to me. I'd probably just check/fold river given villain is likely to be passive, but check/call is probably fine, and mandatory if we've seen villain bluff any rivers.