At what count does "Field Gold 21" sidebet become advantageous?

[Claza]

After a recent visit to my local Casino (Spirit Mountain, in Oregon), I was relieved to notice that the "Field Gold 21" tables are just regular old blackjack tables that allow for a sidebet, not some weird incarnation of Blackjack (such as Spanish 21 that plays without 10s).

Here are some links to the Field Gold 21 rules: http://www.progressivegaming.net/pages/games/fieldgold.html (Archive copy)
(Dead link: http://www.wsgc.wa.gov/docs/game_rules/non_tribal/field_gold_21.pdf)

Could anybody tell me at what true count I should start making this sidebet?

Or should I just stay away from this sidebet altogether?

 

[dacium]

Need more information. What exactally does it pay? Seems it would be good to make the bet on negetive counts. May help reduce the house edge when negetive enough.

 

[Claza]

Need more information. What exactally does it pay? Seems it would be good to make the bet on negetive counts. May help reduce the house edge when negetive enough.

At Spirit Mountain all tables are Hit Soft 17, Split 4 times, Aces split once, Double on anything, Double for less, Insurance Yes, Surrender No, Midshoe entry Yes, Dealer peeks under Aces.

I don't recall if they offer this sidebet on any double decks.

The payout schedule is like this:
Ace-Jack Suited.… 25 to 1
Two Aces ........... 10 to 1
3 or 4 ...................3 to 1
9 or 10..................2 to 1
11 or 12 ............….1 to 1
Any Blackjack...…....3 to 2

 

[dacium]

I have seen bets like this before but still need very specific info:

How many decks? I assume 6
Is 3:2 blackjack part of the bet, what does it normally pay? I assume it pays 1:1 normally
Does the 3, 4, 9, 10, 11, 12 count with soft hands? I assume it does.



Ace-Jack Suited.… 25 to 1
48/312*24/311 = 0.011872372

Two Aces ........... 10 to 1
24/312*23/311 = 0.005688845

3 or 4 ...................3 to 1
A2, A3 are 48/312*24/311 = 0.011872372 * 2 = 0.023744744
22 is 24/312 * 23/311 = 0.005688845
total = 0.029433589


9 or 10..................2 to 1
A8 27 36 45 A9 28 37 46 all at 48/312*24/311 = 0.094978976
55 at 24/312 * 23/311 = 0.005688845
total = 0.100667821


11 or 12 ............….1 to 1
29 38 47 56 93 84 75 all at 48/312 * 24/311 = 0.083106604
66 at 24/312*23/311 = 0.005688845
[T2] at 96/312 * 24/311 = 0.023744744
[2T] at 24/312 * 96/311 = 0.023744744
total = 0.136284937


Any Blackjack...…....3 to 2
Can't use 4 suited cards
[ATns] 24/312 * 92/311=0.02275538
[TnsA] 96/311 * 20/311=0.019850911
total = 0.042606291

So...
25:1 pays at 0.011872372
10:1 pays at 0.005688845
3:1 pays at 0.029433589
2:1 pays at 0.100667821
1:1 pays at 0.136284937
3:2 pays at 0.042606291

Thats a player edge of about 17% so obviously something is badly wrong here. :0( still need more info.

 

[Claza]

...How many decks? I assume 6

6 decks is correct. Typical penetration: 65-75%.

...Is 3:2 blackjack part of the bet, what does it normally pay? I assume it pays 1:1 normally

Blackjack pays 3:2 in normal play, and it pays an additional 3:2 if you made the sidebet.

...Does the 3, 4, 9, 10, 11, 12 count with soft hands? I assume it does.

Yes: 2, 3, 4, 9, 10, 11, and 12 do count with soft hands.

...Thats a player edge of about 17% so obviously something is badly wrong here. :0( still need more info.

??!! Does anybody need directions to Spirit Mountain? They advertise their hotel rooms at $69 on weekdays.


Yes, when something sounds too good to be true, it usually isn't. But assuming that there is no catch, assuming that they do play fair, should I start making the sidebet at a moderately negative number when I aim for 4, 9, 10, 11, or 12?

If a true count of +3 is high enough for Insurance, is that good enough for Field Gold 21 when I aim for Blackjack or two aces?

What are the exact magic numbers?

 

[EasyRhino]

Normally, I just glaze my eyes over with the math, so pardon me if I smoke a little dope:

Ace-Jack Suited.… 25 to 1
48/312*24/311 = 0.011872372

I would say the odds of an Ace (any suit), would be 24/312. Odds of same-suit Jack would be 6/311. This drops the odds to 0.001484. If this number is correct, then that adjustment at 25:1 helps the house by 25%?

11 or 12 ............….1 to 1
29 38 47 56 93 84 75 all at 48/312 * 24/311 = 0.083106604
66 at 24/312*23/311 = 0.005688845
[T2] at 96/312 * 24/311 = 0.023744744
[2T] at 24/312 * 96/311 = 0.023744744
total = 0.136284937

Would this double-count the ten/2 pair? If so, that would be another 2.3% back to the house.

 

[dacium]

The T2 both ways is correct

But the AJ is an error.

The first card can be any ace or jack, which is 48/312. Then there are only 6 cards (either the ace or the jack depending on the first) so thats 6/311,
so it should be 48/312*6/311= 0.00296.

Thats much better, then it works out to house edge of 6.1% (-6% to player).

Figuring out what count is a little harder... so give me a while ;-)

 

[dacium]

Ok the formula for house edge is:


(25*48/312*6/311) +
(10*24/312*23/311) +
(3*48/312*24/311*2) +
(3*24/312*23/311) +
(2*48/312*24/311*8) +
(2*24/312*23/311) +
(1*48/312*24/311*7) +
(1*24/312*23/311) +
(1*96/312*24/311) +
(1*24/312*96/311) +
(1.5*24/312*92/311)+
(1.5*96/312*20/311)
+(-1*(1-(
((48/312*6/311) +
(24/312*23/311) +
(48/312*24/311*2) +
(24/312*23/311) +
(48/312*24/311*8) +
(24/312*23/311) +
(48/312*24/311*7) +
(24/312*23/311) +
(96/312*24/311) +
(24/312*96/311) +
(24/312*92/311)+
(96/312*20/311)
)))) = -0.06159

I have to further seperate the equation to seperate the high cards (T through Ace) from the low cards (2 through 6) and the middle cards (7 through 9). Then I can adjust the 312 and 311 values based on the true count to figure out the new edge for that true count. I don't have time to do that tonight, maybe tomorrow

 

[dacium]

Edit Due To Errors

 

[Claza]

Ok the formula for house edge is:
...
I have to further seperate the equation to seperate the high cards (T through Ace) from the low cards (2 through 6) and the middle cards (7 through 9). Then I can adjust the 312 and 311 values based on the true count to figure out the new edge for that true count. I don't have time to do that tonight, maybe tomorrow

I truly appreciate the effort you put into this, Dacium.

I can hardly wait to see what you come up with, when you get the time to finish calculating it. Thank you.

 

[dacium]

OK I think I have the complete solution now.
I seperate each way to win by high and low cards:

AJ SUITED:
AJ suited both high cards:
(48H2/(312)*6HS/(311))

AA:
Two aces (both high)
(24H1/(312)*23H1/(311))

3 or 4:
Ace then 2 (high then low)
(24H1/(312)*24L1/(311))
2 then Ace (low then high)
(24H1/(312)*24L1/(311))
Ace then 3 (high then low)
(24H1/(312)*24L1/(311))
3 then Ace (low then high)
(24L1/(312)*24H1/(311))
22 (both low)
(24L1/(312)*23L1/(311))

9 or 10:
A then 8 (high then netural)
(24H1/(312)*24N/(311))
8 then A (netural then high)
(24N/(312)*24H1/(311))
2 then 7 (low then neutral)
(24L1/(312)*24N/(311))
7 then 2 (neutral then low)
(24N/(312)*24L1/(311))
36 / 63 (both low, so order doesnt matter)
(48L2/(312)*24L1/(312))
45 / 54 (both low so order doesnt matter)
(48L2/(312)*24L1/(312))
A then 9 (high then netural
(24H1/(312)*24N/(311))
9 then A (net then high)
(24N/312*24H1/(311))
2 then 8 (low then neutral)
(24L1/(312)*24N/(311))
8 then 2 (neutral then low)
(24N/(312)*24L1/(311))
3 then 7 (low then neutral)
(24L1/(312)*24N/(311))
7 then 3 (neutral then low)
(24N/(312)*24L1/(311))
46 / 64 (both low order doesnt matter)
(48L2/(312)*24L1/(311))
55 (both low same card)
(24L1/(312)*23L1/(311))

11 or 12:
2 then 9 (low then net)
(24L1/(312)*24N/(311))
9 then 2 (net then low)
(24N/(312)*24L1/(311))
3 then 8 (low then net)
(24L1/(312)*24N/(311))
8 then 3 (net then low)
(24N/(312)*24L1/(311))
4 then 7 (low then net)
(24L1/(312)*24N/(311))
7 then 4 (net then low)
(24N/(312)*24L1/(311))
56 / 65 (both low order doesnt matter)
(48L2/(312)*24L1/(311))
3 then 9 (low then net)
(24L1/(312)*24N/(311))
9 then 3 (net then low)
(24N/(312)*24L1/(311))
4 then 8 (low then net)
(24L1/(312)*24N/(311))
8 then 4 (net then low)
(24N/(312)*24L1/(311))
5 then 7 (low then net)
(24L1/(312)*24N/(311))
7 then 5 (net then low)
(24N/(312)*24L1/(311))
66 (both low same card)
(24L1/(312)*23L1/(311))
T then 2 (high then low)
(96H4/(312)*24L1/(311))
2 then T (low then high)
(24L1/(312)*96H4/(311))

Any Blackjack (both high), not suited blackjack
A then T not suited:
(24H1/(312) * 92H4/(311))
T then A not suited:
(96H4/(312) * 20H1/(311))

Where:
HS = (1+(C/20*1/5/4)
H1 = (1+(C/20*1/5)
H2 = (1+(C/20*2/5)
H3 = (1+(C/20*3/5)
H4 = (1+(C/20*4/5)
H5 = (1+(C/20*5/5)
L1 = (1-(C/20*1/5)
L1 = (1-(C/20*2/5)
L1 = (1-(C/20*3/5)
L1 = (1-(C/20*4/5)
L1 = (1-(C/20*5/5)
N = (1)

Where C is the True Count.

The expected value is:
((1 - (
(48*(1+(C1/20*2/5))/(312)*6*(1+(C1/20*1/5/4))/(311))+
(24*(1+(C1/20*1/5))/(312)*23*(1+(C1/20*1/5))/(311))+
(24*(1+(C1/20*1/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1+(C1/20*1/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1+(C1/20*1/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24*(1+(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*23*(1-(C1/20*1/5))/(311))+
(24*(1+(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1+(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(48*(1-(C1/20*2/5))/(312)*24*(1-(C1/20*1/5))/(312))+
(48*(1-(C1/20*2/5))/(312)*24*(1-(C1/20*1/5))/(312))+
(24*(1+(C1/20*1/5))/(312)*24/(311))+
(24/312*24*(1+(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(48*(1-(C1/20*2/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*23*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(48*(1-(C1/20*2/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*24/(311))+
(24/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*23*(1-(C1/20*1/5))/(311))+
(96*(1+(C1/20*4/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(24*(1-(C1/20*1/5))/(312)*96*(1+(C1/20*4/5))/(311))+
(24*(1+(C1/20*1/5))/(312) * 92*(1+(C1/20*4/5))/(311))+
(96*(1+(C1/20*4/5))/(312) * 20*(1+(C1/20*1/5))/(311))
) * - 1) + (
(25*48*(1+(C1/20*2/5))/(312)*6*(1+(C1/20*1/5/4))/(311))+
(10*24*(1+(C1/20*1/5))/(312)*23*(1+(C1/20*1/5))/(311))+
(3*24*(1+(C1/20*1/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(3*24*(1+(C1/20*1/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(3*24*(1+(C1/20*1/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(3*24*(1-(C1/20*1/5))/(312)*24*(1+(C1/20*1/5))/(311))+
(3*24*(1-(C1/20*1/5))/(312)*23*(1-(C1/20*1/5))/(311))+
(2*24*(1+(C1/20*1/5))/(312)*24/(311))+
(2*24/(312)*24*(1+(C1/20*1/5))/(311))+
(2*24*(1-(C1/20*1/5))/(312)*24/(311))+
(2*24/(312)*24*(1-(C1/20*1/5))/(311))+
(2*48*(1-(C1/20*2/5))/(312)*24*(1-(C1/20*1/5))/(312))+
(2*48*(1-(C1/20*2/5))/(312)*24*(1-(C1/20*1/5))/(312))+
(2*24*(1+(C1/20*1/5))/(312)*24/(311))+
(2*24/312*24*(1+(C1/20*1/5))/(311))+
(2*24*(1-(C1/20*1/5))/(312)*24/(311))+
(2*24/(312)*24*(1-(C1/20*1/5))/(311))+
(2*24*(1-(C1/20*1/5))/(312)*24/(311))+
(2*24/(312)*24*(1-(C1/20*1/5))/(311))+
(2*48*(1-(C1/20*2/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(2*24*(1-(C1/20*1/5))/(312)*23*(1-(C1/20*1/5))/(311))+
(1*24*(1-(C1/20*1/5))/(312)*24/(311))+
(1*24/(312)*24*(1-(C1/20*1/5))/(311))+
(1*24*(1-(C1/20*1/5))/(312)*24/(311))+
(1*24/(312)*24*(1-(C1/20*1/5))/(311))+
(1*24*(1-(C1/20*1/5))/(312)*24/(311))+
(1*24/(312)*24*(1-(C1/20*1/5))/(311))+
(1*48*(1-(C1/20*2/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(1*24*(1-(C1/20*1/5))/(312)*24/(311))+
(1*24/(312)*24*(1-(C1/20*1/5))/(311))+
(1*24*(1-(C1/20*1/5))/(312)*24/(311))+
(1*24/(312)*24*(1-(C1/20*1/5))/(311))+
(1*24*(1-(C1/20*1/5))/(312)*24/(311))+
(1*24/(312)*24*(1-(C1/20*1/5))/(311))+
(1*24*(1-(C1/20*1/5))/(312)*23*(1-(C1/20*1/5))/(311))+
(1*96*(1+(C1/20*4/5))/(312)*24*(1-(C1/20*1/5))/(311))+
(1*24*(1-(C1/20*1/5))/(312)*96*(1+(C1/20*4/5))/(311))+
(1.5*24*(1+(C1/20*1/5))/(312) * 92*(1+(C1/20*4/5))/(311))+
(1.5*96*(1+(C1/20*4/5))/(312) * 20*(1+(C1/20*1/5))/(311))
)

The results are:
Count EV
-14 -11.68
-13 -11.34
-12 -10.99
-11 -10.62
-10 -10.26
-9 -9.88
-8 -9.50
-7 -9.11
-6 -8.71
-5 -8.31
-4 -7.90
-3 -7.48
-2 -7.05
-1 -6.62
0 -6.18
1 -5.73
2 -5.28
3 -4.82
4 -4.35
5 -3.87
6 -3.39
7 -2.90
8 -2.40
9 -1.89
10 -1.38
11 -0.86
12 -0.33
13 +0.20
14 +0.75

So it is essentially not beatable with standard high/low count. Thats pretty much what I expected because the payouts favour to many small cards (all the 9 10 11 12 payouts etc).

 

[dacium]

My friend did a sim and confirmed +13 so this isnt beatable.

 

[Simon_BJUK]

Is Field Gold 21 still available?

I am planning a trip to Las Vegas and I would like to try my hand at this side bet while I'm there.

I tried signing up with Trackjack and Blackjack News, but they don't seem to mention the Field Gold side bet.