So when I look online for this everything wants to talk about just BlackJacks themselves but I want to find the probability of any player getting $21$ after having hitting $N$-times when playing vs a casino with $X$-deck shoes. For simplicity I only need to know the values with $n$ is $1, 2$, or $3$ and when $X$ is $6, 7$ or $8$. But a generalized formula would be great.
For a baseline we can assume just the player vs dealer but if having more players affects the odds of any player getting this I would be intrigued to know how to account for that. Max players of $7$.
If this is easier to do with code instead of formulas that works for me as well.
Thanks for any help you can provide.