Zen TC frequencies

UncrownedKing

Well-Known Member
#3
Let's say 6d h17 DAS RSA No Surrender.

I'm looking more for frequencies than EVs, basicly any 6d h17 or 8d. I'm not too particular about rules. I'm more or less trying to build a formula for SD for any number of hands, h, frequencies, and any bet, b. I'm trying to make this as generic as possible so it can be as useful as possible. I will post what I come up with to help others using Zen and hopefully get some ideas from other people on the board.


Moderators can move this to the math and theory section if they feel its better suited for that section. I didn't realize what I was getting into before I posted this thread.
 

bjcount

Well-Known Member
#4
UncrownedKing said:
Let's say 6d h17 DAS RSA No Surrender.

I'm looking more for frequencies than EVs, basicly any 6d h17 or 8d. I'm not too particular about rules. I'm more or less trying to build a formula for SD for any number of hands, h, frequencies, and any bet, b. I'm trying to make this as generic as possible so it can be as useful as possible. I will post what I come up with to help others using Zen and hopefully get some ideas from other people on the board.


Moderators can move this to the math and theory section if they feel its better suited for that section. I didn't realize what I was getting into before I posted this thread.
4.5/ 6d h17 das nls

BJC
 

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UncrownedKing

Well-Known Member
#5
Thanks! Now let me do some more thinking and I'll post my formula.

I would like some feed back on it. Whether it makes sense or not and why or why not it makes sense.
 

UncrownedKing

Well-Known Member
#6
General Formula for Standard Deviation

Warning, I have spend a good while preparing this post. It is fairly long and fairly heavy in algebra, but my hope is that everyone can learn from my thinking and hopefully I can get a formula to find Standard Deviation for any betting style, counting system, or anyone.

Ok. Here it goes. I've tried to make a generic formula to calculate Standard Deviation for entire playing sessions based on TC frequencies, for any given bet ramp or playing style.

First, I'm going to define my variables:

b = bet (This will change with each TC.
Where b*b simply means b squared, I didn't care to try to write the superscript 2.)



v = (1.33 + (n-1)*0.5)*n (With n = the number simultaneous hands of one bet, b. I am assuming that the simultaneous hands will be the same bet i.e. 2 hands of 6 units, 3 hands 4 units. Both simultaneous hands will have the exact same bet. You must calculate v before plugging it into the formula. Also, note that if you don't spread to two hands than v = 1.33.)

h = hands played (If you want to use hours simply multiply hours by an average of 100 hands per hour. I think the general consensus is that 100 hands per hour is an accurate estimate.)

fc = the frequencies of c, where c = the actual true count (Here is where it gets tricky. This number will represent the percentage of hands play at a certain TC for your count. Since you are betting according to the TC and every TC will have a different bet out, you want the correct bet to be attached to the correct frequency. Also, since most negative counts will be played with 1 unit, you can simply add all of the negative count frequencies together and use the total negative count frequency as the coefficient. If you don't get this now, I'll explain it again after the entire formula is presented.)

Now that all of the variables have stated here is the actual formula:

Total Session Standard Deviation = (f <=-3 * sqrt( b * b * v *h)) + (f-2 * sqrt( b*b*v*h)) + (f-1 * sqrt(b*b*v*h)) + (f0 *sqrt(b*b*v*h)) + (f1 * sqrt(b*b*v*h)) + (f2 * sqrt(b*b*v*h)) + (f3 * sqrt(b*b*v*h)) + (f4 * sqrt(b*b*v*h))+ (f5 * sqrt(b*b*v*h)) + (f6 * sqrt(b*b*v*h)) + (f7 * sqrt(b*b*v*h)) + (f >=8 * sqrt(b*b*v*h))

So, if I wanted to calculate the Total Standard Deviation for 10 hands of flat betting 1 unit, simply plug in:

b = 1
v = 1.33 (since we won't ever be spreading to two hands its simply 1.33)
h = 10
f = 100% (since 100% of the hands will have the same bet, 1 unit.)

Total Session Standard Deviation = 1 * sqrt(1*1*1.33*10)

Total Session Standard Deviation = 3.6469 units.

If I wanted to calculate a 1-10 bet spread for Zen after playing 10 hours, betting 1 unit at a TC of <=1, 2 units at TC of 2, 3 units at TC of 3, 4 units at TC 4, 5 units at TC 5, and spreading to two hands of 5 units at TC >= 6 (I know this isn't an optimal/realistic spread I'm just using it as an example). I'm using the frequencies provided by bjcount above. The formula would look like this:

b = bet at each TC. So in this example, we will be betting 1 unit 74.17% of the time, 2 units 7.58% of the time, 3 units 4.65% of the time, 4 units 3.97% of the time, 5 units 2.42% of the time, and 2 hands of 5 units 7.19% of the time (the frequencies add up to 99.98% of hands due to rounding error, but I'm ok with that for the example). Now we want to make sure each bet corresponds with each frequency.

v = 1.33 (Except when we spread to two hands shown below, we also want to make sure that the right variance will be corresponding with each frequency.)

For the 7.19% of hands we play two hands of 5 units, we calculate v like this:

v = 1.33 + (n-1)*0.5
Since we only spread to two hands, n = 2:

v= (1.33 + (2-1)*0.5) * 2
v= (1.33 + (1)*0.5) * 2
v= (1.83) *2
v= 3.66
Remember v only equals 1.83 for when f = .0719

h = 10 hours * 100 hands per hour
h= 1000 hands

Now f = the frequency (in decimal form) of each bet.

So our formula looks like this:

Total Session Standard Deviation = (.7417*sqrt(1*1*1.33*1000)) + (.0758*sqrt(2*2*1.33*1000)) + (.0465*sqrt(3*3*1.33*1000)) + (.0397*sqrt(4*4*1.33*1000)) + (.0242*sqrt(5*5*1.33*1000)) + (.0719*sqrt(5*5*3.66*1000))

Which gives you:

Total Session Standard Deviation = 69.618 units


You simply add as many functions as needed i.e. (fc*sqrt(b*b*v*h))+


Please let me know if my thinking is flawed or if I have any arithmetic issues. If my thinking is flawed please tell me how so I can learn from my mistakes. Also note that I have spent several hours coming up with this logic, it has been well thought out and not just slapped together.
 

psyduck

Well-Known Member
#7
My own sim showed that complete Zen is no better than Hi Lo for 6 deck game

Here is what I did:

I used my simulator to generate indices for Hi Lo. Then I compared my own Hi Lo indices to the complete Zen included in the simulator in a 6-deck game using flat betting (to compare the combined effect of PE and IC). The result was complete Zen was no better than my Hi Lo under these conditions.
 

UncrownedKing

Well-Known Member
#8
Something in your sim is wrong or off because zen is slot more powerful than hi-lo.

I know it should be posted in the math and thoery section, but the point of the thread is to get feedback on my equation/logic.
 

kewljason

Well-Known Member
#9
psyduck said:
Here is what I did:

I used my simulator to generate indices for Hi Lo. Then I compared my own Hi Lo indices to the complete Zen included in the simulator in a 6-deck game using flat betting (to compare the combined effect of PE and IC). The result was complete Zen was no better than my Hi Lo under these conditions.
I don't doubt that for a second. I raised this very issue a while back. Even though Zen is a level two count, it has a betting correlation of .96 slightly less than the .97 of hi-lo. Since betting correlation is so much more important in 6 and 8 deck games, I didn't (and still don't) see how zen outpermorms hi low in these particluar games. The answer I received was that Zens strength was partially due to it's many indices. Well to me that's like comparing apples to oranges. If you are going to compare the two systems, you compare them both using a fixed number of indices. Whether you use the I18 or use 150, just as long as you use that number for both.
 
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