Confirmation on math for generating index plays?
July 11th, 2016 at 2:26:18 PM
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Hello all,
I've been reading "The Theory of Blackjack" lately. On my last trip to the tables I was dealt an extraordinary amount of 10,2 versus dealers 2. I decided to use it as a test run for generating index plays using the math formulas Griffin has in his book. Though I felt he sort of glossed over the methods and didn't give sufficient explanation for a math peasant such as myself. Still, you won't learn anything by not trying.
As I understand it, say in the example of a hard 12 versus the dealer's 2, we look at the table and see that there is a 4.49 advantage to hitting over standing. 10's increase this advantage while every other card reduces it. To determine when the count indicates it is time to stand rather than hit my understanding is we...
Average the sum of plus and zero cards
determine the average number of cards in which 4.49 is reduced to a negative.
multiply it by the average point count for cards.
multiply it by the percentage of cards removed from the deck
Round to the nearest whole number
That right???
Wong has 3 listed as the index play for HiLo and Halves for hard 12 versus dealer's deuce and that's what I got though barely if you are rounding to the nearest whole number thus I wanted to make sure I was doing it right. Is there an program or an app yet for generating index plays (apologies in advance if it's in plane sight and I didn't see it)?
I've been reading "The Theory of Blackjack" lately. On my last trip to the tables I was dealt an extraordinary amount of 10,2 versus dealers 2. I decided to use it as a test run for generating index plays using the math formulas Griffin has in his book. Though I felt he sort of glossed over the methods and didn't give sufficient explanation for a math peasant such as myself. Still, you won't learn anything by not trying.
As I understand it, say in the example of a hard 12 versus the dealer's 2, we look at the table and see that there is a 4.49 advantage to hitting over standing. 10's increase this advantage while every other card reduces it. To determine when the count indicates it is time to stand rather than hit my understanding is we...
Average the sum of plus and zero cards
determine the average number of cards in which 4.49 is reduced to a negative.
multiply it by the average point count for cards.
multiply it by the percentage of cards removed from the deck
Round to the nearest whole number
That right???
Wong has 3 listed as the index play for HiLo and Halves for hard 12 versus dealer's deuce and that's what I got though barely if you are rounding to the nearest whole number thus I wanted to make sure I was doing it right. Is there an program or an app yet for generating index plays (apologies in advance if it's in plane sight and I didn't see it)?
July 11th, 2016 at 3:42:36 PM
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I analyzed T,2 vs 2 many years ago, so my comments are based on memory.
I seem to remember being surprised to learn that removing a 9 from the deck actually improved the player's EV when hitting T,2 vs 2. This is because the absence of a 9 from the deck hurts the dealer's 2, in addition to hurting when the player hits a 12. I remember that the net effect was that the impact on the dealer's 2 was more important than the impact on the player's 12.
As another example, the absence of a Ten from the deck does make it less likely that you will bust when hitting a 12 - but it also makes it less likely that the dealer will bust when playing a 2. Bottom-line: you must consider how the absence of any card affects both the dealer's outcomes and the player's outcomes and then convolve the probability distributions.
I tried to verify this on the WOO Site Blackjack Calculator but I kept getting error messages when I removed any card from the deck and tried to calculate T,2 vs 2. Not sure what's going on.
I seem to remember being surprised to learn that removing a 9 from the deck actually improved the player's EV when hitting T,2 vs 2. This is because the absence of a 9 from the deck hurts the dealer's 2, in addition to hurting when the player hits a 12. I remember that the net effect was that the impact on the dealer's 2 was more important than the impact on the player's 12.
As another example, the absence of a Ten from the deck does make it less likely that you will bust when hitting a 12 - but it also makes it less likely that the dealer will bust when playing a 2. Bottom-line: you must consider how the absence of any card affects both the dealer's outcomes and the player's outcomes and then convolve the probability distributions.
I tried to verify this on the WOO Site Blackjack Calculator but I kept getting error messages when I removed any card from the deck and tried to calculate T,2 vs 2. Not sure what's going on.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
July 11th, 2016 at 8:42:58 PM
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Per the tables in "The Theory of Blackjack", basic strategy calls for hitting over standing but by a fairly small margin. Once Ten cards become more plentiful (such as at TC3 or higher for HiLo) you should stand however neither option is particularly advantageous.
