A-7 v A (s17) mathematically
If anyone is a fan of exact calculation of blackjack expected values I have an
online version of my cdca program on my website.
To get a reasonable idea of how to play A-7 versus A when dealer stands on soft 17 relative to Hi-Lo make these inputs:
1. Input 6 decks and don't change any of the initial rules or settings. Program's default is for dealer to stand on soft 17.
2. Go to shoe composition section and remove 12 each of ranks 2,3,4,5,6,7,8,9, and A and 48 of rank T. This will leave you with a 156 card shoe which is equivalent to 3 full decks.
3. Remove 1 each of ranks 2,3,4,5,6 by clicking the '-' button beneath each rank.
4. Add 4 of rank T by clicking the '+' button beneath the rank T textbox 4 times.
5. Add 1 of rank A by clicking the '+' button beneath the rank A textbox once.
6. After inputting the above this will result in a 156 card shoe with 11 each (2-6), 12 each (7-9), 52 (T), and 13 (A). There will be 65 (T-A) and 55 (2-6) so running count = 65-55 = + 10. This is RC before any cards are dealt.
7. Input A-7 for player hand by clicking 'A' and '7' buttons once each in player cards section.
8. Click 'Compute' button. EV for hitting = -10.71%, EV for standing = -9.320%.
9. RC when above EVs are computed needs to be adjusted from the pre-deal RC to account for player hand and dealer up card. Therefore RC at time of player's decision is +8 because 2 aces and one seven have been removed from the initial shoe comp listed in step 6. This means Hi-Lo RC = +8 with 153 cards remaining which computes to a Hi-Lo true count of about +2.7.
The above shows that for a reasonably average 6 deck shoe where about half of the cards have been dealt that a Hi-Lo player with A-7 versus A and a TC of about +2.7 should stand when dealer stands on soft 17 and standing is better than hitting by about 1.4% more or less.
Other shoe compositions also could be computed. If shoe is reset to full and one each (2,3,4,5,6) is removed then player is very slightly better off hitting rather than standing. If one each (2,3,4,5,6,7,8,9) is removed from a full shoe then player is slightly better off standing.
Conclusion is that a Hi-Lo index of +1 is reasonable for this decision.