OTR you need to put in a further $2.37 to win what is then a pot of $7.27
So you're getting pot odds of roughly 3:1
Therefore, you need to win roughly once out of 4 to be totally break-even
I think either fold or call OTR would be OK here, especially since SB has a lot of Ax in his range (he called the flop and turn)
If he is a thinking player, and hold A♠: the river shove is +EV for him, since you might fold weaker flushes
Other hands that are quite likely are worse sets.
I think 52o and 75o are not normally likely, but this is 5NL GGPoker
I put a guess at a range for him into Equilab and got:
OTT
Board: 4♦K♠3♠ A♥
Equity Win Tie
SB 24.76% 24.76% 0.00% { AA, QQ, 66-33, AQs+, KQs, 75s, 52s, AQo+, KQo, 75o, 52o }
BB 75.24% 75.24% 0.00% { KhKc }
OTR you're a very slight favourite:
Board: 4♦K♠3♠ A♥ 6♠
Equity Win Tie
SB 47.97% 47.97% 0.00% { AA, QQ, 66-33, AQs+, KQs, 75s, 52s, AQo+, KQo, 75o, 52o }
BB 52.03% 52.03% 0.00% { KhKc }
If we remove the trash hands, and limit his Ax hand to only having the A♠: you're getting 3:1 equity advantage, which would point to a call.
Board: 4♦K♠3♠ A♥ 6♠
Equity Win Tie
SB 26.82% 26.82% 0.00% { QQ, 66-33, AdAs, AhAs, AsAc, KQs, K4s, 75s, 52s, AsQs, AKo, KQo, AsQd, AsQh, AsQc }
BB 73.18% 73.18% 0.00% { KhKc }
Note: You could have (possibly) avoided by raising 4x pre-flop.
You might consider posting this hand to the Hand discussions for No Limit -- people there know much more about NLHE than I do.
Cheers,
VS