The key decision was the turn Call of SB's check-raise. With 8 outs and only 700,000 behind, jamming was better than flatting, though the call wasn't a big error. The preflop Call, flop Bet and river All-in were all fine.
Street-by-Street Analysis
Preflop (8/10)
Defending K♣4♣ in the BB against a min-raise with a big-blind ante in the pot is correct at 20 BB. The price is too good to fold a suited king.
Flop (6/10)
Your hand is just the board pair of 3s with backdoor draws. As a pure bluff, this 0.4x-pot Bet needs 26.3% folds, and the backdoors only lower that slightly. Leading into the preflop raiser with two players to act is a low-frequency play; checking was also fine. SB's check-call keeps 6x, 5x, 4x and pocket pairs in his range.
Hindsight: SB held 6♠6♣, a full house on the flop, so you were already drawing dead.
Turn (6/10)
The 5♥ gives you an Open-Ended Straight Draw (8 outs). As a pure bluff, your 0.3x-pot Bet needs 20.0% folds, and the draw puts the real requirement well below that, so the bet is reasonable. SB's check-call then check-raise on 3-3-6-5 is a strong line, but it leaves you only 700,000 behind, so you can't fold. Jamming adds fold equity to your 8 outs; calling lets SB see the river cheaply and choose his line.
Hindsight: against 6♠6♣, every line lost the same chips.
River (10/10)
You made a Straight (6 high), which is not the nut straight. It beats 833 combos and loses to only 40 (7-high straights, full houses and quads). Putting your last 700,000 in against the 800,000 Bet is mandatory.
Hindsight: SB showed 6♠6♣ for a full house. That is a cooler you could never get away from at this stack depth.
