Quote Originally Posted by Mr. Ed View Post
How much EV do you sacrifice by giving up EVERY double/split opportunity? Even if I am still in positive EV territory, it would be more profitable to go home, and come back another day with a replenished session bankroll, so I do not have to make this sacrifice. I would NEVER bet my last session dollar.

…even if there is only one hand left in the shoe.

…this is my “opinion”. Sorry - that was snarky…this is my preference.
Let's look at your AA vs 7 example.
The Frequency of the hand AA vs 7 is 0.00027830 but we will settle for a conservative 0.0003 at +5
The Frequency of a +5 count or more in a 6 decks, S17, DAS, LS is about 0.02765
So, you will encounter this particular hand at this particular count (+5 or more) about 0.000008295 or once every 120 155 hands. Say once every 1 200 hours of play.

Now, what's the EV for Splitting AA vs 7 at +5 ? It is about 61% of your initial bet.
What's the EV for Hitting AA vs 7 at +5 ? It is about 12% of your initial bet.

You bet $300 and get that hand. Fine, you'll make on average $183
You bet your last $600, and get that hand. Fine, you'll make on average $72

There is no negative EV here, you will only win less. Why leave the table ?
However, you have to weight it against all other hands where you could get 18, 19, 20 and BJ + all the hands you could simply hit with +EV, etc.
No clear cut answer here...