baccarat math statistical probability

Would either this forum or the Wizard of Odds calculate and provide a table of probabilities?

What is the statistical probability that the banker's wins exceed the player's wins by one and through 20 hands?

Conversely, what is the statistical probability that the player's wins exceed the banker's wins by one through 20 hands?

I am new to the forum, but after reviewing some of its threads, I can see that some mathematically inclined members here have the ability to solve this question, but I also understand it is a lot to ask. If the forum cannot, how would I ask the Wizard if he would help me with this? I appreciate any help you can provide.

Let's break it down! Start with some data from the Wizard's site, the part about baccarat.

Probability of a banker win = 0.458597
Probability of a player win = 0.446247
Probability of a tie = 0.095156

Now over 20 hands, there are 10 combinations of events that fit your description, banker winning 1 more hand than the player:

1 banker win, 0 player wins, 19 ties.
2 banker wins, 1 player win, 17 ties.
3 banker wins, 2 player wins, 15 ties.
4 banker wins, 3 player wins, 13 ties.
5 banker wins, 4 player wins, 11 ties.
6 banker wins, 5 player wins, 9 ties.
7 banker wins, 6 player wins, 7 ties.
8 banker wins, 7 player wins, 5 ties.
9 banker wins, 8 player wins, 3 ties.
10 banker wins, 9 player wins, 1 tie.

So you want to calculate the probability of each of those combinations of events and add them all together. Ready for that?