Probability of dealer bust blackjack

Hello everyone,

I am trying to recreate the probabilities found here: /games/blackjack/side-bets/buster-blackjack/
Mostly, I'm interested in the bust probabilities with 4,5,6,7 or 8 cards for an 8 deck game with dealer standing on soft 17.
I tried to program this in VBA as follows. Every probability for a given arrangement of cards is stored in a 10-dimensional array. The first index represents the number of aces, the second the number of 2's, third numers of 3's, etc... By looping through all arrangement for n number of cards, I hope to generate the arangements for n+1 cards by induction. I also consider the fact that cards are drawn without replacement. For example: the probability to have arrangement A,5,6 by drawing a 6 when the dealer has an A and a 5 would be ARRAY(1,0,0,0,1,1,0,0,0,0) = number of 5s / (416-2) * ARRAY(1,0,0,0,1,0,0,0,0,0). The probability to have arrangement 2,3,3,4,3 by drawing a 3 when the dealer has a 2, two 3's and a 4 would be ARRAY(0,1,3,1,0,0,0,0,0,0) = (number of 3s - 2) / (416-4) * ARRAY(0,1,2,1,0,0,0,0,0,0). Then, after looping over all arrangements for n to generate the arrangements for n+1, I have a method to check which hands keep drawing cards because they have value <17 and discard the rest before looping over the arrangements for n+1 to generate n+2 etc..
This does not work well. The answer I get (~0,080877) for 4 card bust is close but not exact (~0.087163). What could be the problem here? Also, should the wizard read this, first of all thank you for your great site(s). I love them. Second, how did you program and/or calculate these probabilities?

Thank you for any responses or ideas for improvement!
Best.

Welcome to the forum.

https://wizardofodds.com/games/blackjack/side-bets/buster-blackjack/

Blessing the link for the filter, and the convenience of all.
Enjoy the day!