How is EV defined for doubled and split hands

[assume_R]

Let's say this is a scenario (the actual numbers and cards don't matter; they are just for an example):

I want to know if, at a certain count, one should hit a 7,7 v 8 or split a 7,7 vs 8.

You have a $10 bet out.

1. If you hit, on average you get a total of $14 back (so your bankroll goes up $4).

2. If you split, you will have $20 out (since you had to increase your wager to split the hand), and on average you will get back a total of $26 (so your bankroll goes up $6).

Now here is my question:
In 1. you increase your bankroll by $4 on average, and won 40% of your bet.
In 2. you increase your bankroll by $6 on average, but only won 30% of your bet.

Which is the better play?

Also, same question, in principle, for doubled hands.

 

[psyduck]

I say play 2 is better. I think this is the basis for doing split and double down - to inrease your advantage based on the initial bet. Although the advantage based on total bet drops, in the long run you win more money.

Just my understanding.

 

[assume_R]

Thanks, psyduck.

Also, sleightofhand was able to explain to me that in case 2, your TBA is defined as 30%, but your IBA is defined as $6/$10, or 60%. That's the difference between the IBA and TBA.

Yet even though your TBA is 30%, you essentially double your # of hands for a given round, thus winning more money for a defined time period.

Hence, we seem to be in concurrence that in this simple, made up example, splitting would be correct

Also this is assuming EV-maximizing indices (or perhaps I should say IBA maximizing), not RA indices.