Errors in this Lucky Ladies Analysis

dacium said:

Can someone see any errors here? I believe TC +7 is the norm

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dacium said:

So +4 on high/low is correct then?

thats cool I thought I had some major problems because I heard it was +7 but if its +7 zen then awesome! looks like its correct to me.


This side bet is AWESOME pitty it doesnt exist in Australia :-(

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OregonRick said:

I read some where that it wasn't profitable to make the lucky ladies side bet until the high/low count was at +6.5! Do I really only need +4 on my high/low count for that side bet to be profitable. That would definately be a lot better.

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dacium said:

Can someone see any errors here? I believe TC +7 is the norm:

'Lucky Ladies Analysis'

The luck ladies side bet pays when your first two cards are tens:
Any 20: 4 to 1
or if Suited 20: 9 to 1
or if Matched (both player and dealer have Ten-Ten hands): 19 to 1
or if Queen of hearts pair: 125 to 1
or if Queen of hearts pair and dealer has blackjack : 1000 to 1


6 decks is 312 cards. 96 cards are tens, 24 are aces, 6 are Queen of hearts.


Firstly probabilities of winning:
1000:1 Player Has QQh and dealer has blackjack
Qh then Qh then Ten Then Ace:
6H6/312*5H6/311*94H96/310*24H24/309
Qh then Qh then Ace Then Ten:
6H6/312*5H6/311*24H24/310*94H96/309

125:1 Player has QQh and dealer doesnt have blackjack
QhQh then not ace nor ten:
6H6/312*5H6/311*(310-94-24)NH/310
QhQh then Ace then not ten:
6H6/312*5H6/311*24H24/310*(309-94)NT/309
QhQh then Ten then not ace:
6H6/312*5H6/311*94H96/310*(309-24)NA/309

19:1 Player has TT which isn't QQh and dealer has TT
Not QH then QH then ten then ten
90H90/312*6H6/311*94H96/310*93H96/309
QH then not QH then ten then ten
6H6/312*90H90/311*94H96/310*93H96/309
Not QH then Not QH then ten then ten
90H90/312*89H90/311*94H96/310*93H96/309

9:1 Player has suited TT that isn't QQh and the dealer doesn't have TT:
Hearts Ten not QH then QH then ten then not ten
18H18/312*6H6/311*94H96/310*(309-93)NT/309
Hearts Ten not QH then QH then not ten
18H18/312*6H6/311*(310-94)NT/310
QH then Hearts Ten not QH then ten then not ten
6H6/312*18H18/311*94H96/310*(309-93)NT/309
QH then hearts Ten not QH then not ten
6H6/312*18H18/311*(310-94)NT/310
Hearts ten not QH then Hearts Ten Not QH then ten then not ten
18H18/312*17H18/311*94H96/310*(309-93)NT/309
Hearts ten not QH then Hearts Ten Not QH then not ten
18H18/312*17H18/311*(310-94)NT/310
Not Hearts ten then suited ten then ten then not ten
72H72/312*23H24/311*94H96/310*(309-93)NT/309
Not hearts ten then suited ten then not ten
72H72/312*23H24/311*(310-94)NT/310

4:1 Player has TT that isn't suited (inherently isn't QQh then) and the dealer doesnt have TT:
Ten, then ten not suited, then ten, then not ten
96H96/312*72H72/311*94H96/310*(309-93)NT/309
Ten, then ten not suited, then not ten
96H96/312*72H72/311*(310-94)NT/310

Where the following adjustments are made to include the count (each True Count is a fraction of 20 (20 high/lows per deck):

H6 = (1+(C/20*6/120) specific high card
H90 = (1+(C/20*90/120) any ten excluding a specific one
H96 = (1+(C/20*96/120) any ten
H24 = (1+(C/20*24/120) specific high card
H72 = (1+(C/20*72/120) ten of 3 suits (3 high cards)
H18 = (1+(C/20*18/120) ten of a certain suit and not of 1 certain rank
H1 = (1+(C/20*1/5) high card
H2 = (1+(C/20*2/5) two high cards
H3 = (1+(C/20*3/5)
H4 = (1+(C/20*4/5)
H5 = (1+(C/20*5/5)
L1 = (1-(C/20*1/5) low card
L2 = (1-(C/20*2/5) two low cards
L3 = (1-(C/20*3/5)
L4 = (1-(C/20*4/5) 4 high cards (any ten card)
L5 = (1-(C/20*5/5)
N = (1) netural
NT = (1-(C/20*4/9) not ten
NA = (1-(C/20*1/12) not ace
NH = (1-(C/20*5/8) not high

Where C is the true count.


EV=
((1-
(
(6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*94*(1+(C/20*96/120))/310*24*(1+(C/20*24/120))/309)+
(6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*24*(1+(C/20*24/120))/310*94*(1+(C/20*96/120))/309)+
(6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*(310-94-24)*(1+(C/20*5/8))/310)+
(6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*24*(1+(C/20*24/120))/310*(309-94)*(1+(C/20*4/9))/309)+
(6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*94*(1+(C/20*96/120))/310*(309-24)*(1+(C/20*1/12))/309)+
(90*(1+(C/20*90/120))/312*6*(1+(C/20*6/120))/311*94*(1+(C/20*96/120))/310*93*(1+(C/20*96/120))/309)+
(6*(1+(C/20*6/120))/312*90*(1+(C/20*90/120))/311*94*(1+(C/20*96/120))/310*93*(1+(C/20*96/120))/309)+
(90*(1+(C/20*90/120))/312*89*(1+(C/20*90/120))/311*94*(1+(C/20*96/120))/310*93*(1+(C/20*96/120))/309)+
(18*(1+(C/20*18/120))/312*6*(1+(C/20*6/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(18*(1+(C/20*18/120))/312*6*(1+(C/20*6/120))/311*(310-94)*(1+(C/20*4/9))/310)+
(6*(1+(C/20*6/120))/312*18*(1+(C/20*18/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(6*(1+(C/20*6/120))/312*18*(1+(C/20*18/120))/311*(310-94)*(1+(C/20*4/9))/310)+
(18*(1+(C/20*18/120))/312*17*(1+(C/20*18/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(18*(1+(C/20*18/120))/312*17*(1+(C/20*18/120))/311*(310-94)*(1+(C/20*4/9))/310)+
(72*(1+(C/20*72/120))/312*23*(1+(C/20*24/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(72*(1+(C/20*72/120))/312*23*(1+(C/20*24/120))/311*(310-94)*(1+(C/20*4/9))/310)+
(96*(1+(C/20*96/120))/312*72*(1+(C/20*72/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(96*(1+(C/20*96/120))/312*72*(1+(C/20*72/120))/311*(310-94)*(1+(C/20*4/9))/310)
) * -1)) + (
(1000*6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*94*(1+(C/20*96/120))/310*24*(1+(C/20*24/120))/309)+
(1000*6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*24*(1+(C/20*24/120))/310*94*(1+(C/20*96/120))/309)+
(125*6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*(310-94-24)*(1+(C/20*5/8))/310)+
(125*6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*24*(1+(C/20*24/120))/310*(309-94)*(1+(C/20*4/9))/309)+
(125*6*(1+(C/20*6/120))/312*5*(1+(C/20*6/120))/311*94*(1+(C/20*96/120))/310*(309-24)*(1+(C/20*1/12))/309)+
(19*90*(1+(C/20*90/120))/312*6*(1+(C/20*6/120))/311*94*(1+(C/20*96/120))/310*93*(1+(C/20*96/120))/309)+
(19*6*(1+(C/20*6/120))/312*90*(1+(C/20*90/120))/311*94*(1+(C/20*96/120))/310*93*(1+(C/20*96/120))/309)+
(19*90*(1+(C/20*90/120))/312*89*(1+(C/20*90/120))/311*94*(1+(C/20*96/120))/310*93*(1+(C/20*96/120))/309)+
(9*18*(1+(C/20*18/120))/312*6*(1+(C/20*6/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(9*18*(1+(C/20*18/120))/312*6*(1+(C/20*6/120))/311*(310-94)*(1+(C/20*4/9))/310)+
(9*6*(1+(C/20*6/120))/312*18*(1+(C/20*18/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(9*6*(1+(C/20*6/120))/312*18*(1+(C/20*18/120))/311*(310-94)*(1+(C/20*4/9))/310)+
(9*18*(1+(C/20*18/120))/312*17*(1+(C/20*18/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(9*18*(1+(C/20*18/120))/312*17*(1+(C/20*18/120))/311*(310-94)*(1+(C/20*4/9))/310)+
(9*72*(1+(C/20*72/120))/312*23*(1+(C/20*24/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(9*72*(1+(C/20*72/120))/312*23*(1+(C/20*24/120))/311*(310-94)*(1+(C/20*4/9))/310)+
(4*96*(1+(C/20*96/120))/312*72*(1+(C/20*72/120))/311*94*(1+(C/20*96/120))/310*(309-93)*(1+(C/20*4/9))/309)+
(4*96*(1+(C/20*96/120))/312*72*(1+(C/20*72/120))/311*(310-94)*(1+(C/20*4/9))/310)
)

The results are:
Count: EV:
-14 -84.87%
-13 -82.73%
-12 -80.38%
-11 -77.77%
-10 -74.88%
-9 -71.68%
-8 -68.16%
-7 -64.29%
-6 -60.03%
-5 -55.38%
-4 -50.28%
-3 -44.73%
-2 -38.67%
-1 -32.10%
0 -24.98%
1 -17.24%
2 -8.90%
3 +0.11%
4 +9.8%
5 +20.26%
6 +31.47%
7 +43.49%
8 +56.37%
9 +70.14%
10 +84.85%
11 +100.54%
12 +117.26%
13 +135.05%
14 +153.95%


I am fairly sure the error is in the count adjustment section
"
H6 = (1+(C/20*6/120) specific high card
H90 = (1+(C/20*90/120) any ten excluding a specific one
"
etc.
because the house edge at count 0 is 24.96% which is the standard value that everyone agrees in I believe.

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