Peter Griffin vs. The Wiz

Chapter 6 in The Theory of Blackjack contains the (virtually) complete set of Effects Of Removal for a 1D, S17, No DAS game. Griffin also offers 2 additional pages for the H17 version of this game when the dealer has an Ace or a 6 showing. The difference between the H17 and S17 EORs is small except for these two dealer upcards.

Griffin's method for optimal play is to add all the EORs for your particular hand and multiply by 51/(52-n) (n=cards seen) then add that total to the 11th line in the table. This 11th line is the difference in expectation between taking exactly one more card and standing. If the resulting number is positive then hit... if negative, stand. EORs for relevant doubles and splits are given as well and the method is the same.

When I apply this method, the results differ slightly from the Wizard's Blackjack Hand Calculator. It seems the more cards removed, the greater the difference between the Wiz's calculator and the Griffin method...with 10 cards removed the difference could be about .8 percent or so.

Practically speaking that difference won't change many decisions and even when it does, the loss for making the wrong play is very small. But... small mistakes can add up.

Griffin admits in the chapter that his EORs and method are a best approximation. He also didn't have the computing advantages that we enjoy today.

So what method does the calculator use? Does the Wiz have an EOR table that is preferable to Griffin's that he can publish?

Thank You.

LOL...Never thought of that.

I have algorithms (very long algebraic expressions) that will calculate the dealer's chances of getting a 17, 18, 19 20, 21 or Bust as a function of the the dealer's upcard and the number of cards of each rank that remain in the deck.

I use those algorithms in a spreadsheet that will calculate the EV for hit, stand , double and split for player's relevant decisions.

I am not sure what method the Wizard's calculator uses.

You can find another composition-dependent BJ calculator at BJstrat.com. It's calculated probabilities agree with the Wizard's calculator but there are some different outputs and inputs.

The problem with Peter Griffin's method is that the EORs are linear coefficients for a single variation, and in reality the effect of removing very cards can include non-linear coupled effects. Still, its not a bad method.

Interesting. It appears you've done quite an in depth study. Logic suggests one wouldn't need a spreadsheet to determine that a 2 will only get the player or dealer from 12 to 14, or best case scenario 15 to 17, 16 to 18. Therefore, I question the EOR that Peter Griffins worked on years ago without todays technology. In contrast, the 5 will get the player or the dealer from 12 to 17, 13 to 18, 14 to 19, 15 to 20, and 16 to 21.

Therefore, I've never understood the logic in giving the 5 the same value as the 2 and the 7 no tag value. I'm curious, what tag values did you determine were best based on your algorithms method on a spreadsheet?

Hey Gordon:
Im currently trying to program a script that will accomplish the same as the spreadsheets that you have. I'm basing my code on Griffin's Theory of Blackjack Book Page 158 (1996) algorithm. I am having a hard time understanding some of the steps in the algorithm. I would like to ask if you can provide any pertinent references that will ease / clarify the process, perhaps some materials that helped you when putting the spreadsheets together?
Thanks in advance!