Hi,all
This is a long shot but maybe Eric or someone like that can help me...
I've been writing a program to calculate 'perfect play'using combinatorics. I started off with ENHC and 1 deck to keep things simple.
I've been using the calculator on Wizard of Odds site: https://wizardofodds.com/games/blackjack/hand-calculator/
as well as this one: http://www.bjstrat.net/cgi-bin/cdca.cgi
to check my answers as I go along.
My program gives correct EV if the player STANDS on his first two cards in all situations.
My program also gets correct EV results if the player HITS his first two cards for 10,10 vs. any dealer card down through 10,6 vs. any dealer card.
The problem starts at 10,5 vs certain dealer's cards.
My program is correct for 10,5 vs. 10, but my program is incorrect if the player HITS 10,5 vs. a dealer 9 (my EV is more negative by 0.0007 than the online calculators) or a dealer 8 (more negative by 0.0041)or a dealer 7 (more negative by 0.0036). Specifically, for 10,5 vs.9, my program calculates EV = -0.4760 while the online calculators show -0.4753.
But, my program is correct for 10,5 vs dealer 6 or dealer 5 or dealer 4 or dealer 3 or dealer 2.
My program is also incorrect for 9,6 vs. 9, 8 or 7 and 8,7 vs. 9,8, or 7 but correct for 9,6 and 8,7 vs. all else.
So, the problem only shows up with a player 15 vs. a dealer 9,8 or 7.
I thought I could isolate the problem further by using the online calculators to check each constituent part of my calculations. So, I used the Wizard of Odd's calculator to give me the EV for a 10,5,10 vs. 9 and 10,5,9 vs. 9 and so on. Then, I took those EV's and multiplied them by the probability that such a hand could occur and added them all up for a total EV if you HIT 10,5 vs. dealer 9 as follows:
105vs9HIT.jpg
So, using the online calculators' EV numbers for each individual possible hand when you hit 10,5 vs. 9, I get a number that exactly matches MY program's number when you ask it for EV for hitting 10,5 vs. 9 but doesn't match both of the online calculators when you ask them for EV for hitting 10,5 vs. 9.
As a further check, I used the same technique as shown in the table above for 10,5 vs. 10 (where my program agrees with the online calculators.) The technique above works for this scenario and gives me the same answers as the online programs and my program (EV for Hit= -0.5418).
I'm sure there is something wrong with my approach because the online calculators both agree, but I just can't see it. Am I missing something?
Thanks for any help and best of luck to all!
SiMi
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