Hi, i'm reading BJA. Why the 7th & 8th column of these tables have different values? Shouldn't they be the same?
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To clarify, back in the day that John Gwynn did this, he had taken to writing "Per Hand Contr(ibution)" to mean what we would write today as e.v. (of that particular true count bin). So, the Units Won (or lost) for any given horizontal line of true count is simply the product of Units Bet and the e.v.
Don
Look at the link below:
https://www.blackjackincolor.com/truecount1.htm
You see the DD game's graph TC frequencies reduce on odd counts and go up on even counts. This is because using some divisors odd TC are impossible. For 6 deck the effect is too small a part of the sampling for any TC to cause this occulting effect, but at certain divisors it is there.
San Jose Bella,
Ahh... sorry for the confusion! I thought you were asking why Column 7 differed from Column 8 in each table. Instead, you want to know why Column 7 (and Column 8) is not exactly the same for each table.
The explanation is given on page 82: Column 7 equals Column 3 divided by Total Hands.
Table 6.17A is a segment of a simulation whose penetration is 5.00/6. As shown on the Summary Table 6.16 (page 86), for this penetration the Total Hands played is 436,923,359. Thus, the Per Hand Contr. for, say, the first row is found to be
100%*(-2,320,393.0)/(436,923,359) = -0.53108...
Table 6.21A is a segment of a simulation whose penetration is 5.50/6. As shown on the Summary Table 6.20 (page 87), for this penetration the Total Hands played is 480,070,015. Thus, the Per Hand Contr. for, say, the first row is found to be
100%*(-2,320,393.0)/(480,070,015) = -0.48334...
Hope this helps!
Dog Hand
He is talking about two sets of the same thing (.00 to 4.50 decks) in two different table (6.17A and 6.21A). Columns 1 thru 6 are identical in both tables with identical pen, but columns 7 and 8 inch table are different. I can't believe I am saying this but it looks like a mistake in Don's book, most likely in table 6.17A since 6.21 and 6.21A are identical but table 6.17A is different with all 3 tables having the same data for columns 1 to 6. All three are for penetration .00 to 4.50 decks according to their headers.
Thanks Dog Hand! your explanation is ultra clear. It's clearly written on page 81:
100 times column 3 divided by the total number of hands played (throughout the deck for all true counts).
The book has no problem at all.
Three, see page 81 rather than 82, I'm a slow English reader, forgot that sentence when I reached the chart pages.
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