Question Relating to Math Theory

Let's say the house EV is .30%.

Round 1: Player advantage: -.30%
Round 2: Player advantage: -.30%
etc.

But what if for the 24th round, I was not 100% certain that I would have a 21.49% (I am sure that my first card will be either an ace or a 10, but I don't know which; courtesy Eliot Jacobson - see link below) advantage, but rather I was 'only' 45% certain that I would have a 21.49% advantage?

So, for Round 24, at the very worst I am still at a .30% disadvantage. But, does being 'armed' with the information that I am 45% sure that I will have a 21.49 percent advantage for this Round 24 help me make money? (Obviously, it would be better to know that, for this round, I will have a 100% likelihood of a 21.49% advantage rather than a 45% likelihood of a 21.49% advantage.).

(As an aside, I realize I may be confusing EV with advantage, but, to keep things simpler, I won't even get into how to vary my bet when I might have a higher-than-normal probability of having a 21.49% advantage.).

So, my question: Is it true that for Round 24, my EV (or maybe I should use the term 'advantage' because I am not incorporating the variable of dollars or units?) will be .45 X 21.49%, or 9.6705%? If not, what IS my advantage for Round 24 if I am indeed 45% certain that, for that particular round, I will have a 21.49% advantage?

Finally, let's assume that for Round 24, my advantage is indeed 9.6705%. (And let's further assume that my advantage for all of the other rounds I play during this short trip session continues to be -.30%.).

Does this mean that if I play a total of a paltry 31 rounds (to include the above "Round 24") during my trip that, on average, in the long run (even though this is a very short trip session), I will be at a very slight advantage for my short trip session because my advantage for Round 24 = 9.6705% while my advantage for each of the remaining 30 rounds continues to be -.30%? So, 30 rounds X -.30% = -9.000, and -9.000 + 9.6705 = .6705, and, after dividing this figure of .6705 by 31 rounds, we get an average slight player advantage of .0216% for this very short trip session. Is this correct?

Everything you wrote is correct. What will vary greatly from the regular game of blackjack is your variance. Since you're getting all of your edge from a single round, per 31, and more than half the time, you don"t have that edge at all, the variance of outcomes will be considerably greater than for the average hand of blackjack (which is, roughly, 1.32 squared units).

Don

I wanted to add that it feels great knowing that I got the math right and that my math thought process was confirmed by such an esteemed expert.

It really seems like you are 'giving back' to those of us 'up and comers' in the blackjack community. So, thanks again!