Good observation. In shoe games hit 3,3 vs. 8 since your max bet is out & splitting is risky towards your BR. The player's advantage for this hand is about -23, you wanna minimize losses. You will likely bust one or both & the dealer rarely busts 8.
A 3 would only help if it's in the hole, the...
Level 2?
You say you wonged which leads me to believe you are using a level 1 count (hi-lo). You also say you have two deeply dealt games you play. May I suggest a level 2 count to take advantage of the great penetration you have available, White Guy (esp. DD)? However, you won't be able to...
3,3 ≠ 21
Eureka! Earlier I posted a single-deck index of 0. Gramazeka's sims show a TC os 4.7 for shoe games. It's because the pair of 3's robs the dealer of the opportunity to make 21. tthree posted that a side count of 7,8 would be valuable. I thought so too, but it appears 2's & 3's are more...
According to Professional Blackjack 1974 edition. Table A1 -- High-Low, One-Deck, Dealer Hits Soft 17, for Player's hand of 3-3 vs. Dealer 8, split if double down allowed shows an index of 0. Table A2 -- Four-Deck, split 3-3 vs. 8 DAS at a TC of 4.