Sorry to not be clear.

I will try to simplify.

Let's say that I am sitting with 5 other players at first base and the final card of the previous round was a 6. Also assume that I believe I am 15.1% certain that the first card of the next round (and the first card of my hand) will be an Ace (because the 6 card was the last card played).

I would like to know my advantage.

We know that, given the double deck rules I specified, if I were 100% certain that my first card were to be an Ace, then I will have a 51.4% (I referenced Eliot Jacobson for this 51.4% figure) advantage for this round if I am seated at first base.

But instead of being 100% certain, I am 'only' 15.1% certain (which is better than we can expect due to chance, which is 1/13 or 7.69%).

Don, you provided me with the explanation some years ago, but I cannot locate it. The solution for my player advantage was straightforward: Something like (.514 X .151) minus (the probability of my first card being something other than an Ace). But I forget how to express that second part mathmatically.

Please disregard the important consideration that the dealer instead of I may receive 'my' Ace. (Hopefully with 5 players this possibility is sufficiently small.).

Again, please provide (and show your work please) my player advantage

1) for the scenario of the final card of the last round being a 6 and my belief that I know with 15.1% certainty that the next card (my first card of the new round) will be an Ace and

2) for the scenario of the final card of the last round being a 10 and my belief that I know with 15.1% certainty that the next card (my first card of the new round) will be an Ace. I was thinking this scenario is trickier than the '6' value card scenario because there are four times as many 10s as Aces - does this fact confound or interfere with one using the same method to calculate the advantage that she/he used to calculate the player advantage for the '6' value card scenario because the probability of having an Ace follow by chance a card that appears four times as often (10) is greater?