It's understandable that sometimes players want to have some sort of logic for making a play. Sometimes, it can be difficult to come up with an explanation for why a given play makes sense. This may be one of those plays.
If you have BJA3 and THLCCS, then you already know that this play is one of the I18 and that it contributes more than 1% of the available gain in SCORE in a 4.5/6 deck game and almost 1.5% of the available gain in a 62/104 (2 deck) game. So it is unquestionably a valuable play. As for why? I can tell you that, in the case of 4.5/6 S17 deck games, the EV of doubling over hitting at TC=4 is about 2.1% higher and that you gain approximately an additional 5% in EV for every higher true count beyond that. That is, the value of making this play increases rapidly once you're at the index and beyond.
My visual guide to index play (a companion to THLCCS) is a great resource for visually understanding individual index plays:
With these graphs, you never again have to wonder why one play is superior to another in blackjack for various holdings. Please note: These are downloadable PDF files
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