November 20th, 2015 at 4:27:08 PM
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In trying to get the simplest strategy, using the EV to switch values between hand sides, I come up with this, which I think closely aligns overall with each EV:

1. set two pat hands as high as possible, favoring the three-card side if 19 or better with 18 or better, or a 21 with 17 (granted 20 + 19 is best flipped favoring the two-card as an exception, but overall this general rule gives best EV; The rule also works best for hands like AK864, a 21+18, 20+19, and 19+19, where 21/18 can be set either two cards high or three cards high, with the three card 21 best as A64/K8. AK863 can be set 21+17 with only the two-card 21. The house dealer will have to set K8/A63, still a very good hand set.)

2. Else favor the two-card side if 18/17 or 19/17 and flip-able.

3. Never set 17+17 if you can set a two-card 19 or better with a fouled three-card side (e.g., K7962 = 762/K9)

4. If you can make only one hand side, set a good two-card side

Remember, I have to fit this on a rack card, and also not scare the players (convincing them the game is very easy to play fairly well).

Note that the entire detailed strategy can fit on a small strategy grid, like Basic strategy, but if four easy rules can do it well for a rack card, we're good. We'll leave the full strategy matrix to the big game writers.

1. set two pat hands as high as possible, favoring the three-card side if 19 or better with 18 or better, or a 21 with 17 (granted 20 + 19 is best flipped favoring the two-card as an exception, but overall this general rule gives best EV; The rule also works best for hands like AK864, a 21+18, 20+19, and 19+19, where 21/18 can be set either two cards high or three cards high, with the three card 21 best as A64/K8. AK863 can be set 21+17 with only the two-card 21. The house dealer will have to set K8/A63, still a very good hand set.)

2. Else favor the two-card side if 18/17 or 19/17 and flip-able.

3. Never set 17+17 if you can set a two-card 19 or better with a fouled three-card side (e.g., K7962 = 762/K9)

4. If you can make only one hand side, set a good two-card side

Remember, I have to fit this on a rack card, and also not scare the players (convincing them the game is very easy to play fairly well).

Note that the entire detailed strategy can fit on a small strategy grid, like Basic strategy, but if four easy rules can do it well for a rack card, we're good. We'll leave the full strategy matrix to the big game writers.

Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.

November 20th, 2015 at 6:57:06 PM
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Here is a list of the "either/or" sets that I found (i.e. where A/B is better than C/D in some cases and C/D is better than A/B in other):

I still get that the house is expected to win 3.03626% of the total amount bet, using perfect strategy, and with the "half of the 2-card bet" double-21 bonus.

As usual, I list the 3-card hands first

Also, when "K" appears, it can be any 10-card (so, for example, AKK88 can also be AQJ88)

There are only eight sets:

1. 17/Foul or Foul/19

Always play 17/Foul unless it's A6222

2. Foul/18 or 20/Foul

Play Foul/18 unless it's A722 and any of A,2,4,5,6,7

3. 17/20 or 19/18

Play 17/20 unless it's AKK88

4. 17/20 or 20/17

Play 17/20 with:

KK755

KK773

A9665

KK764

A9863

A9845

Play 20/17 with:

AA988

AAK96

A9962

AKK97

KK872

A9872

5. 17/21 or 20/18

Play 17/21 if it's AK854; play 20/18 if it's AA88K

6. 19/17 or 18/18

Play 18/18 with:

A7666

AA996

99855

A7765

99864

A9763

K9872

K9863

K9854

K8765

Play 19/17 with:

AAA76

A9998

99882

AA987

K8774

K8873

99873

A8764

7. 20/18 or 18/20

Play 20/18 unless it's A9774

8. 20/19 or 19/20

Play 20/19 if the hand has any 10-cards, and 19/20 if it does not

Also, when "K" appears, it can be any 10-card (so, for example, AKK88 can also be AQJ88)

There are only eight sets:

1. 17/Foul or Foul/19

Always play 17/Foul unless it's A6222

2. Foul/18 or 20/Foul

Play Foul/18 unless it's A722 and any of A,2,4,5,6,7

3. 17/20 or 19/18

Play 17/20 unless it's AKK88

4. 17/20 or 20/17

Play 17/20 with:

KK755

KK773

A9665

KK764

A9863

A9845

Play 20/17 with:

AA988

AAK96

A9962

AKK97

KK872

A9872

5. 17/21 or 20/18

Play 17/21 if it's AK854; play 20/18 if it's AA88K

6. 19/17 or 18/18

Play 18/18 with:

A7666

AA996

99855

A7765

99864

A9763

K9872

K9863

K9854

K8765

Play 19/17 with:

AAA76

A9998

99882

AA987

K8774

K8873

99873

A8764

7. 20/18 or 18/20

Play 20/18 unless it's A9774

8. 20/19 or 19/20

Play 20/19 if the hand has any 10-cards, and 19/20 if it does not

I still get that the house is expected to win 3.03626% of the total amount bet, using perfect strategy, and with the "half of the 2-card bet" double-21 bonus.

November 20th, 2015 at 7:18:16 PM
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The house wins 3% of ONE betting unit, or about 1.5% of the total amount bet.

The composition dependent strategy is very interesting.

The composition dependent strategy is very interesting.

Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.

November 20th, 2015 at 10:22:06 PM
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But is it AP proof?

♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪

November 20th, 2015 at 10:37:19 PM
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Quote:AxelWolfBut is it AP proof?

Some game protection steps were taken, namely using one deal per shuffle (machine shuffle) instead of a shoe dealt version.

As we have seen, there are some composition-dependent plays, but those exceptions are generally on close play decisions, don't effect HE (as HE was calculated against optimal play), and don't necessarily point to collusion vulnerability.

So I also don't think it is particularly vulnerable to collusion. Steve How isn't coming out of retirement to analyze this game I would say. I think in the game protection area it is at least as safe as High Card Flush or Pai Gow Poker, and that AP is a non-issue with this game. So far it looks robust.

Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.

November 21st, 2015 at 5:58:22 AM
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Here is a fairly simple strategy - House Edge = 3.267%.

(A) Find the value of the highest hand that leaves you with two valid hands;

-- (i) If you have a choice (e.g. 21-19 or 19-21) make the best 3-card hand.

(B) Check whether to play one really good hand, also sometimes instead of playing two average ones;

-- (i) Make 2-card 21 and bust the 3-card hand, also if you cannot better 19+other;

-- (ii) Make 2-card 20, otherwise 3-card 21, also if you cannot better 18+other.

(C) With one valid hand, unless (B) applies, make best 2-card hand rather than a 3-card hand;

-- (i) Exception make 3-card 20 rather than 2-card 17.

This only costs .146% in errors.

You need to add the last exception as this saves .24%.

(A) Find the value of the highest hand that leaves you with two valid hands;

-- (i) If you have a choice (e.g. 21-19 or 19-21) make the best 3-card hand.

(B) Check whether to play one really good hand, also sometimes instead of playing two average ones;

-- (i) Make 2-card 21 and bust the 3-card hand, also if you cannot better 19+other;

-- (ii) Make 2-card 20, otherwise 3-card 21, also if you cannot better 18+other.

(C) With one valid hand, unless (B) applies, make best 2-card hand rather than a 3-card hand;

-- (i) Exception make 3-card 20 rather than 2-card 17.

This only costs .146% in errors.

You need to add the last exception as this saves .24%.

November 21st, 2015 at 2:57:37 PM
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Charlie,

This is excellent, the game has a good "Poker Eye effect," where the hands are easy to see and the strategy very accessible. For a few good rules to get a player within 0.146% of optimal is a good thing.Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.

This is excellent, the game has a good "Poker Eye effect," where the hands are easy to see and the strategy very accessible. For a few good rules to get a player within 0.146% of optimal is a good thing.

November 21st, 2015 at 5:05:03 PM
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Okay, the best I can do for a player's strategy:

1. Find the value of the highest hand that leaves you with two valid hands 17 to 21;

• If you have a choice and hand is strong (two 19’s or better), balance towards highest 3-card side.

• If you have a choice and hand is weak (19 with 18 or less), balance towards highest 2-card side.

• Exception on weak hands: if you can make a 2-card 21, then make a 2-card 21 with a fouled 3-card side. If best hand is 18 and you can make a 2-card 20, then make a 2-card 20 side. (*)

2. If you can make only one hand side, make the best 2-card side, unless the 3-card side is three points higher (20 versus 17, 21 versus 18) or best three-card is a 21 and best 2-card would be 19.

...for the exception, the hand K8765 is best played as two 18's, as the three-card 21 with a foul is weak, when a two-card 21 with a foul is strong, but cannot be made here.

Also, the Positive EV Hand zone starts at two 19's, to include playing it better as a 20 and 18, or 21 and 17. The Negative EV hand zone is 19 with 18 or less, better played as one good two-card 21.Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.

1. Find the value of the highest hand that leaves you with two valid hands 17 to 21;

• If you have a choice and hand is strong (two 19’s or better), balance towards highest 3-card side.

• If you have a choice and hand is weak (19 with 18 or less), balance towards highest 2-card side.

• Exception on weak hands: if you can make a 2-card 21, then make a 2-card 21 with a fouled 3-card side. If best hand is 18 and you can make a 2-card 20, then make a 2-card 20 side. (*)

2. If you can make only one hand side, make the best 2-card side, unless the 3-card side is three points higher (20 versus 17, 21 versus 18) or best three-card is a 21 and best 2-card would be 19.

...for the exception, the hand K8765 is best played as two 18's, as the three-card 21 with a foul is weak, when a two-card 21 with a foul is strong, but cannot be made here.

Also, the Positive EV Hand zone starts at two 19's, to include playing it better as a 20 and 18, or 21 and 17. The Negative EV hand zone is 19 with 18 or less, better played as one good two-card 21.

November 21st, 2015 at 8:44:18 PM
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Wizard

Dissect this game like a surgeon.

Dissect this game like a surgeon.

I belong to an elite group called the "Zombie Outbreak Response Team."