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## Division chart

I made this division chart to help my spouse practice division for 6 deck game, anyone finds it helpful can use it to aid your division ability.

Left and right are running counts
Top and bottom are remaining decks

I floor to the nearest half deck
All the integer remaining decks are omitted cause they are too easy to calculate. For example, 16/2=8, 17/3=between 5 & 6
All the running counts below 11 are omitted cause they are too easy
I don't use any index numbers above 8, so all the quotients above 8 are written as Duo, with the same background color as 8.

In the middle:
bolded numbers are integer TCs
numbers with a + sign are TCs with decimals
Quotients in the very left row go down to running count of 26, cause it's impossible to have a running count of 27 with 5.5 decks left

I try to make the division chart as little information as possible
The picture size fits perfectly on iPhone 6s
We take turn test each other all the quotient numbers on the edges to be more efficient

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The back ground color selection is reasonably bad, I tried so many combinations, just can't make it beautiful..

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hi lo ? it's like memorization after you done enough . Speed is important but i don't work on speed any more as long as i get by. these days.

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Originally Posted by stopgambling
hi lo ? it's like memorization after you done enough . Speed is important but i don't work on speed any more as long as i get by. these days.
It's a simple division chart, not deviation chart.

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I made this division chart to help my spouse practice division for 6 deck game, anyone finds it helpful can use it to aid your division ability.

If she is better at multiplying than dividing, use the following method for indices play:

1. Multiply the indice by the number of unseen decks.
2. If your running count is equal or greater than that figure, you must stand or double or split, if less then you must hit and not double or split.

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Folks, division at this level is fourth grade math! If you can't multiply and divide then you have a fundamental obstacle to learning to play advantage blackjack. You are making this harder than it needs to be.

Time better spent learning to accurately estimate remaining decks.

One deck resolution at 6 and 8 deck. Perhaps more granular at deep penetrations.

Half deck resolution at 2 deck. Determine true count by multiplying running count by 2 (# half decks in a deck) and divide by number of half decks remaining.

Quarter deck resolution at one deck. Determine true count by multiplying running count by 4 (# quarter decks in a deck) and divide by number of quarter decks remaining.

The hard and risky part is determining an accurate number of decks remaining not the math.

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Try changing the problem to a graphics problem rather than division. Memorize the multiples of each deck estimate you will be using.

You probably don't need the half deck accuracy for estimates until approaching mid-shoe for the 6-deck shoe. The RC would need to be quite large to make a difference and that doesn't happen very often early in the shoe. Example: at 5.5 deck estimation as your divisor rather than 6 the TC would differ at RC +11, +22 and+23, +33 thru +35, and +44 thru +47, etc. How often do you see those specific RCs with less than a deck dealt? Practically never. Now if you look at the 4.5 divisor versus a 5 divisor RCs +9, +14, +18 and +19, +23 and +24, +27 thru +29, etc. For a level 1 count you won't see these RCs much in the between decks 4.5 seen and 4 decks seen out of the 6 deck shoe. For a level 2 count you might want to think about knowing when 4.5 is a necessary divisor and when it is not. You get the idea. As you have smaller divisors and higher level counts the frequency that being accurate to a half deck early in the shoe becomes higher. Early in the shoe it is a waste of energy to try to be that accurate. But as the divisor gets smaller the number of RCs where there is a difference increases and gets closer to neutral counts while the RC frequency range increases. The point where you want to increase deck estimation accuracy to half deck accuracy becomes obvious, but it is still a judgement call.

So, back to the original point, you now have divisors 6, 5, 4, 3.5, 3, 2.5, 2, 1.5, 1, 0.75, and 0.5. You should already know the multiples of the divisor integers and the other factor (the number to multiply the divisor with to get the increments in the multiple sequence) that gets the product (RC barriers) from 4th grade math:
6 multiples: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66...
5 multiples: 0, 5, 10, 15, 20...
etc
You don't need to do math. You just need to know where the RC fits in the sequence of RCs and use the multiple that corresponds to your rounding technique. Like with a RC of +13 and a divisor of 5 decks you know that 10 is the second multiple of 5 so you have a TC of +2.

For the .5 decimals (non-integer divisors) add a pip in-between numbers in the sequence of double the divisor. Like for 2.5 decks remaining you would do the sequence of 5 multiples with pips in-between:
2.5 multiples (use multiples of 5 with pips in-between): 0, *, 5, *, 10, *, 15, *, 20...

The even multiples are the integers in the series and the odd multiples are the pips. So if the RC is +13 it is closer to the 6th multiple than the 4th multiple, so flooring would have you use the 5th multiple for positive RCs (TC +5) and the 6th multiple for negative RCs (RC -13 is TC -6).

You will never do math again at the table. With enough practice you just know the TC for any RC and divisor instantly without even thinking about it. The best part is you probably already know all the multiples without even thinking about it because every elementary school graduate learned them so they didn't even have to think about it. You just need to get used to doing it and then the TC is instantaneously known for any divisor and any RC. What you have done is changed the problem from a math problem to a graphics problem. Since all the multiples needed to come up with the TC are automatic the graphics are already in your head. You just need to get used to using them.

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You certainly have a knack for taking the simple and rendering it unspeakably complicated.

Don

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Since doing this change I have just instantaneously known the TC without thinking for almost every decision. The money gained through increased game speed heads-up is significant, especially when you factor in finishing a big advantage shoe before the ploppies could jump in. I think my record is an 8 deck shoe with less than a deck cut off in 5 minutes. Of course you need a really fast dealer to do that. Before that 8 minutes was my record.
Originally Posted by DSchles
You certainly have a knack for taking the simple and rendering it unspeakably complicated.

Don
I just wanted to make it clear. What I wrote was not complicated. It was thorough. He now should understand that he doesn't need non-integer divisors early in the shoe and exactly what RCs it would make a minuscule difference. The truth is early in the shoe you should be more conservative about TC than late in the shoe for betting. And any play, early in the shoe, that turns on the difference in true count from using 1/2 deck divisor accuracy is basically a coin flip decision that has no significant difference in EV.

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This chart is for testing purpose. Most of them like 11/5=2 is easy, I should delete those easy ones.
My goal is to divide every possible combination in 6 deck game within 0.5 second.
For beginner APs, I think it's hard to effortlessly know the answer for 17/3.5. I'd rather remember this kind of division cold like remember the basic strategy, rather than calculate them when they show up in real play.

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