gordonm888
Joined: Feb 18, 2015
• Posts: 2602
Thanks for this post from:
December 19th, 2019 at 7:21:31 PM permalink
Quote: Gialmere

Any speculation as to a simple strategy, one that would (hopefully) keep the element of risk at or below .5%? You don't often see a number that low and it would be worth making a special stop just to play it.

First decision: Bet 2X (otherwise Check) with
33 pair or higher (always)
A-x-x High Card or higher with a flush or straight draw
K-9 High Card or higher with a flush and straight draw

2nd Decision: Bet 1X (otherwise fold)
In general, you must have about a K-Q-x or higher to Bet 1X
Exceptions:
A-Q-T or higher when an A is the common card.
K-Q-T or higher when a K or Q is the common card.

Note edited.
Last edited by: gordonm888 on Dec 20, 2019
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2135
December 20th, 2019 at 1:04:24 PM permalink
Quote: gordonm888

First decision: Bet 2X (otherwise Check) with
33 pair or higher (always)
A-x-x High Card or higher with a flush or straight draw
K-9 High Card or higher with a flush and straight draw

2nd Decision: Bet 1X (otherwise fold)
In general, you must have about a K-Q-x or higher to Bet 1X
Exceptions:
A-Q-T or higher when an A is the common card.
K-Q-T or higher when a K or Q is the common card.

Note edited.

Assuming your breakdown, which seems a good idea, I agree with your optimal cutoff points except I get slight differences in thinking (i) it's marginally better to double with K8x or higher with flush and straight draw, and (ii) call KJ9 in general (-1.052%).

However in the calling decision it doesn't cost that much to simplify it to only playing Axx (-1.090%). i.e. fold all K-high hands.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2135
Thanks for this post from:
December 21st, 2019 at 6:55:30 AM permalink
^ Further to above I've had a little play since I think it's quite important to get the Doubling strategy correct, even at the expense of calling mistakes.
Flush Draw
1-way Str Draw
2-way Str Draw
Hand required
No
-
-
Pair of 3's
No
YES
-
A T 9+
YES
-
-
A x x+
YES
YES
-
K T 8+
YES
-
YES
K 5 4+

If you use this with your strategy (AQT,KQQT,KJ9) it gets -0.936%
However if you're happy to only CALL with Axx (or AQT vs A) it gets -0.975%.

Thus if you can only remember one, It seems better to remember more details on the Doubling than worrying about which Kxx's you call.

Personally the easiest to remember, with a minor loss of HE is
Double No Flush Draw {p(3), AT+*} (0, any way to make straight)
Double Flush Draw {A+*, KT+, Kx+} (0, 1, 2 ways to make straight),
* note this includes p(2)
Call {Axx+ (or AQTvsA) } is -0.988%.
gordonm888
Joined: Feb 18, 2015
• Posts: 2602
December 21st, 2019 at 7:03:48 PM permalink
Quote: charliepatrick

^ Further to above I've had a little play since I think it's quite important to get the Doubling strategy correct, even at the expense of calling mistakes.

Flush Draw
1-way Str Draw
2-way Str Draw
Hand required
No
-
-
Pair of 3's
No
YES
-
A T 9+
YES
-
-
A x x+
YES
YES
-
K T 8+
YES
-
YES
K 5 4+

If you use this with your strategy (AQT,KQQT,KJ9) it gets -0.936%
However if you're happy to only CALL with Axx (or AQT vs A) it gets -0.975%.

Thus if you can only remember one, It seems better to remember more details on the Doubling than worrying about which Kxx's you call.

Personally the easiest to remember, with a minor loss of HE is
Double No Flush Draw {p(3), AT+*} (0, any way to make straight)
Double Flush Draw {A+*, KT+, Kx+} (0, 1, 2 ways to make straight),
* note this includes p(2)
Call {Axx+ (or AQTvsA) } is -0.988%.

In the brief approximate strategy I offered to Gialmere, I never defined "straight draw"; I was intending 2-way straight draw. I intended that strategy to be a basic starting strategy for a new player, very approximate, 'like "hit to 16, stand on 17, double on 10, 11 and split 88 and AA."

Charlie, you continue to do good work. However, I note that your proposed strategy does not address hands like: As 8h 7d which have no flush draws but should be Bet 2X anyway because they have a 2-way straight draw. Your table should have an extra row like this:

Flush Draw
1-way Str Draw
2-way Str Draw
Hand required
No
-
-
Pair of 3's
No
YES
-
A T 9+
NO
-
YES
A x x+
YES
-
-
A x x+
YES
YES
-
K T 8+
YES
-
YES
K 5 4+

BTW, you refer to the Bet 2X as a "Double" when it is actually a Triple.

The basic nature of this game is that it offers many ways to improve a three card hand. Any three card hand with both a flush draw and 2-way straight draw offers 25 outs (out of 49 cards) to make a pair or better. The fact that this is 25 outs and 24 'misses' is what makes the math on the doubling decision so fascinating. And a large fraction (about 70% ???) of all unpaired 3-card hands offer at least a flush draw or some kind of straight draw or both. So, the Bet 2X decision is complicated.

But, I also find the Calling Decision fascinating because of the amount of information that you have. You have your entire hand defined, as well as one of the four dealer cards -and thus you know the most likely ways of Dealer pairing, flushing or straightening (which involve the common card) and which cards in your hand can reduce and increase those probabilities. You criticize me for my call rules yet I used only one more rule than you for the Call decision and I did a clumsy job of it, at that and still got you almost 40% of the remaining gap to the computer perfect house edge. Look, Bet 1X or fold decisions are "wager 2 units OR automatically lose 1 unit." Bet2X decisions are almost always "wager 3 units OR wager 2 units" because of the quality of the hands, so there is only one incremental unit of wager affected by the BET 2X decision. I see no grounds for asserting that Bet2X decisions are inherently more important than Bet 1X vs Fold decision.s

Here is the current "advanced strategy" as I currently understand it based on everyone's work. We should continue to update this as we refine it.

Requirement to Bet 2X (otherwise check)
Pair of threes or higher; Always
Pair of twos: Any flush or straight draw (includes 1-way straight draw)
AT8, AJ3, AJ9, AQx-AKx high card: Always
Other Axx: Either a flush or 2-way straight draw
KT+ high card: with a flush draw and any straight draw
K98, K87, K76, K65 high card: with any Flush draw
K97, K54 high card: with K-high Flush draw

Requirement to Bet 1X (otherwise FOLD)
Common Card
Minimum to Bet 1X
A
A Q T
K
K Q 9
Q
any A Q
J
K J 9
T
K J T
4 - 9
any K Q
3
any K T
2
any K 9

The above table for Bet 1X leaves out a lot of additional possible rules about suit distribution and kickers. I plan to develop that table and publish it as a computer perfect strategy at some point in time. But why suggest that when a 2 is the common card, that a player should fold all KQ, KJ, KT and K9 high? That is mis-playing >10% of all possible high card hands when 2 is the common card.

Quote: charliepatrick

Personally the easiest to remember, with a minor loss of HE is
Double No Flush Draw {p(3), AT+*} (0, any way to make straight)
Double Flush Draw {A+*, KT+, Kx+} (0, 1, 2 ways to make straight),
* note this includes p(2)
Call {Axx+ (or AQTvsA) } is -0.988%.

It took me quite a while to unfold your 'vector arithmetic' way of displaying a strategy. I suggest you should revise your proposed strategy to include 2 way straights with no flushes as follows:
Bet2X No Flush Draw {p(3)+, AT+*, Ax+*} (0, 1, 2 ways to make straight)
Bet2X Flush Draw {Ax+*, KT+, Kx+} (0, 1, 2 ways to make straight),
* note this includes p(2)
Bet1X {Axx+ (or AQTvsA) }

The house edge is reported as -0.88%, you quote the above as -0.988%. It could be much closer to -0.9% if you used

Bet 1X {(AQT vs A); (A vs T-K); (KQ vs 4-9),(KT vs 2,3)}
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2135
December 21st, 2019 at 11:11:13 PM permalink
The complexity of the various decisions in this game has similar problems to Pai Gow Tiles. There are various ways to try and create a simple strategy but the challenge is how much detail to include to get a compromise between simplicity and ease to remember against the cost in House Edge. Here's another way to look at a Double strategy - it gets -0.921% (without adding your calling vs 3/2 rule).

Interestingly if you can remember the No Flush Draw cutoffs, having a Flush draw means you can call with each card exactly one rank lower.

Straight Draw
No Flush Draw
Flush Draw
(0 ways) None
Pair of 3s
A x x+
(1 way) Inside
A J 9+
K T 8+
(2 ways) Outside
A 6 5+
K 5 4+

Note: There must be a small bug in my spreadsheet as it has a difference whether you play AJ9 or AT9 as 1-way inside, in theory this shouldn't make a difference. So I'm not yet 100% sure of the cutoff points.
gordonm888
Joined: Feb 18, 2015
• Posts: 2602
December 22nd, 2019 at 2:22:23 PM permalink
I have already checked many of the cutoffs we've listed but had not checked this cutoff before.

I get for A-T-8(rainbow) : Check: -0.39118 Bet 2X: -0.39926; so I see that's off the list. And I calculate that A-J-2 (rainbow) is a Check and A-J-9 is a Bet2X.

Quote:

Note: There must be a small bug in my spreadsheet as it has a difference whether you play AJ9 or AT9 as 1-way inside, in theory this shouldn't make a difference. So I'm not yet 100% sure of the cutoff points.

Its spooky, but I may understand what you're saying and may be able to explain it.

If you have AT9 and get a Jack -so that you have AJT9 - it's easier than you might think for the Dealer to beat your JT9 straight. Dealer only needs to get KQ in the other three cards to make a KQJ straight, and there's a lot of ways to do that.

But if you have AJ9 and get a Ten - thus giving you an AJT9 - then the most probable way for the dealer to beat your JT9 straight is to get QJ in his other three cards and make a QJT straight. But, because there are only 3 jacks left in the deck, its easier for dealer to beat an AJT9 that started as an AJ9 than one that started as a AT9. Its a "common card effect."
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
gordonm888
Joined: Feb 18, 2015
• Posts: 2602
December 22nd, 2019 at 2:25:48 PM permalink
Another way to describe the 2X or fold decision:

Bet 2X (otherwise fold)

Always: with 33 pair or better
With Flush draw: KJ high or better
With 1-way straight draw: AJ9 or better
With 2-way straight draw: A65 or better
With flush draw and 2-way Str Draw: K54 or better
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2135
December 22nd, 2019 at 3:18:55 PM permalink
Quote: gordonm888

I have already checked many of the cutoffs we've listed but had not checked this cutoff before.

I get for A-T-8(rainbow) : Check: -0.39118 Bet 2X: -0.39926; so I see that's off the list. And I calculate that A-J-2 (rainbow) is a Check and A-J-9 is a Bet2X....

I agree with the decisions but still get slightly different numbers.
AT8 rainbow As Th 8d -.399 710 -.408 612

I think how we describe the summary will always be a matter of style but one idea is similar to your first idea
Simple Strategy
(i) Always Pair 3s
(ii) Flush or 2-way Straight - Axx or P(2)
(iii) Flush and 2-way Straight - Kxx
Intermediate You still need Axx or Kxx (as per above) but If your second card is 10 or higher, then you only need a 1-way straight.
gordonm888
Joined: Feb 18, 2015
• Posts: 2602
December 22nd, 2019 at 4:55:41 PM permalink
I agree with Simple Strategy.

Simple Strategy

Bet 2X
(i) Always Pair 3s or better
(ii) Flush or 2-way Straight - Axx or better
(iii) Flush and 2-way Straight - Kxx or better

Bet 1x
(i) Axx or better
(ii) except, AQT or better when common card = A

***************
Working on debug. Found that AQ7 probabilities were always zeroed out. Still working.
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
gordonm888
Joined: Feb 18, 2015
• Posts: 2602
December 23rd, 2019 at 12:13:12 PM permalink
Charlie, these are from cases you previously posted for comparison.

P: Qs 8h 3d C: Kc V: 2513 DNQW: 5311 DNQT: 155 DNQL: 515 W: 0 T: 0 L: 11315 F: n/a EV: -1.031104 EVD: n/a Pm: 24 Z:

I now calculate EV = -1.031105458 Disagreement of 1 in 7th significant digit, hopefully its nothing.

P: Qs 8h 3d C: Kd V: 2513 DNQW: 5493 DNQT: 158 DNQL: 523 W: 0 T: 0 L: 11122 F: n/a EV: -0.998727 EVD: n/a Pm: 24 Z:

I now calculate EV = -0.99872803 Again, difference of 1 in 7th digit. DNQW=5493 DNQT=158 DNQL=523 L=111222

Just curious, what is definition of V?
************************************************
For A-T-8 (three different suits) you reported : AT8 rainbow As Th 8d -.399 710 -.408 612
I am getting Check = -0.400087787 Bet2X = -0.409683022. Help!

As Th 8d
For Common = 9s (T98 straight) I get Check= 1.322675763 Bet2X=2.195420907
For Common = 5d (AT8 hi) I get Check = -0.806891767 Bet2X = -1.024629972
For common = 8c (88-A) I get Check = 0.097074468 Bet2X = 0.363089732

Would you be willing to give me your numbers for comparison? Thx.
Last edited by: gordonm888 on Dec 23, 2019
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.