Braun's 100,000 hand simulation

Hey guys, just for funzies I decided to try to recreate Julian Braun's Chart B21 simulation, as published in Lawrence Revere's book "Playing Blackjack as a Business," presumably Braun's source code is lost to the masses, he probably wrote it in Fortran, but who knows. So with my code, I just ran 15,000,000,000 simulations of 100,000 hands each, and in a lot of places I match Braun's result, but also in a lot, I don't. With reference to the attached image, the white results match Braun's where the red results do not. The simulation as published by Revere is to show how many times a player will be dealt every two card total versus each dealer's up card. Player's two card dealt hand are shown down the left, dealer's up card is across the top. I don't really want to show Braun's results from the book, because it's copywrited, but google has the page scanned on google books, if anyone's interested enough to look. Had fun writing this simulation, was surprised to see so many differences from Braun's result, although since he was using a 1960s ALU whereas mine is modern, that would doubtless account for the minor differences, but some of the differences are significant.

vishnu,

The Totals don't seem to agree with the numbers shown.

For example, every row from A,A to 9,9 adds to 450 (8*36 + 144 + 18 = 450), but none of the row totals says 450.

At a quick glance, at least some of the column totals are off as well.

Can you explain how you got the Totals shown?

Dog Hand

A few other comments:

1. This is single-deck, right?

2. Wong's page 294 of Pro BJ is a similar chart. You can check your work against that.

3. You can also check the cumulative totals in my Appendix D charts. They're the most accurate in print.

4. Many of your red boxes differ from Braun by a single number. It wasn't worth it to make them red when, clearly, they are just rounding errors.

Hey guys, thanks for the comments! Yes the totals are just for the final round (so they are not averaged), I only put them in to make sure that each round was 100,000 hands, I should probably have taken them out since Braun's sim (as published in the Revere book) doesn't have them.

Don, yes this is single deck dealt to the last card, I had no idea that both you and Stanford had run this sim too, I'll have a look. For what it's worth, I just had my sim flag every number that didn't match Braun's exactly, but yes I know that my numbers differ from his by minus 1 in a lot of the cases, for example for the pairs where Braun published 145 for the case of the dealer's 10 whereas I got 144 each time. In some of the cases though my numbers are significantly different than Braun's, which surprised me.

Thanks again for the comments! 😁

EDIT: Also for what it's worth, I think the number published in the Revere book for player's hard 17 vs. dealer's 7 is just a typo, I'm pretty sure the number Braun got was in fact 386 but the typesetter just screwed up and put in 396, oops! 😆