Vega$ 3 Poker

Vega$ 3 Poker has begun a field trial at Harrah's. It's basically Three Card Poker with a dash of Four Card and Hold'em.

Play free demo at AGS.

Really nice to see the no forced secondary bet like UTH. This looks good.

I've only had a quick look at this so haven't checked my figures at all (I suspect the player should fold more often than I've got, especially with a hand such as 8 5 2 offsuit). I get a House Edge approaching 5% and the Dealer not qualifying over 38% (although it's nice you get paid on the raise part which might be 2x). Also changing it so the dealer qualifies with any Ace-x-x only puts the House Edge down a little bit, so I'm wondering why they didn't do that. The only reason I can see is that with AQx you rarely fold, so it doesn't cost too much to play everything. btw making it Kxx turns it to the player's advantage.

My guestimate on x2 strategy seems a reasonable approach (for Axx qualifying you play some lower pairs):
(i) Any pat hand (Trips, Stright, Flush)
(ii) Any pair of Aces or Kings
(iii) Any pair Queens or Jacks with either straight flush, straight or flush draw
(iv) Pair of 10s or 9s with Straight Flush draw (except fold 997).
(v) Also x2 with TTA, TTK, 889 with (Straight) Flush draw.

I'm busy tomorrow but will have a closer look sometime at my folding logic once you know the community card.

Can anyone explain how a “must hit by” works on a card game? Is it a random chance for anyone in the progressive or is it based on a hand

Quote: GBAM

Can anyone explain how a “must hit by” works on a card game? Is it a random chance for anyone in the progressive or is it based on a hand

As you surmise, it's random chance for any player on the STAX system. So you'll have the progressives associated with the game you're playing and simultaneously be entered in a mini lottery.

Quote: Gialmere

Vega$ 3 Poker has begun a field trial at Harrah's. It's basically Three Card Poker with a dash of Four Card and Hold'em.

Play free demo at AGS.

You would think AGS would goose the demo to generate interest, but I lost 8 hands in a row, then quit.

Okay for the fold decision I have only analyzed the cases where the common card is an Ace.

If the common card is an Ace, FOLD an AQ9 or lower.

Exception: When the common card is an Ace, an AQ9-2 or AQ9-3 should be BET 1X if one of your 3 initial cards is the same suit as the common card.

The reason for the exception is that a 2 or 3 in your hand partially blocks the dealer making a straight with the common card Ace, and a card in your hand that is the same suit as the common card Ace partially blocks the dealer making a flush with the common card Ace. The combination of these two effects just barely increases the EV enough so that it is favorable to BET1X rather than fold.

Examples:

1. Player: Qh-9s-2c Common card = As EV of BET 1X =-0.985487974
but changing the 2 to a 4:
2. Player: Qh-9s-4c Common card = As EV of BET 1X =-1.004625347

and, changing the suit of the 9 in Case #1:
3. Player: Qh-9d-2c Common card = As EV of BET 1X =-1.015148011

I just did this quickly, so there may (as always) be errors.

If the common card is a 2, FOLD a K87 or lower.

Exception: With a K87, BET 1X if one of your three original cards(K,8,or 7) is the same suit as the common card 2.

There could be other exceptions, I have not analyzed every possible hand.

Obviously, the threshold for the BET 1X/FOLD decision is quite dependent upon the rank of the common card.

Quote: gordonm888

Obviously, the threshold for the BET 1X/FOLD decision is quite dependent upon the rank of the common card.

It'll be interesting to see what the threshold is to make the X2 play bet.

Quote: Gialmere

Vega$ 3 Poker has begun a field trial at Harrah's. It's basically Three Card Poker with a dash of Four Card and Hold'em.

Hi Gialmere,

Below is my Three Card Poker, (Casino Hold'em® 2+1® Three-Cards out of Four-Cards Hold'em) ©2010, ​Patented.
Math by Cynthial Liu, House-Edge 3.17%.

Casino Hold'em® 2+1® 賭場德州撲克二加一™ (Casino Hold'em® FAMILY)
THE FIRST 3-Cards out of 4-Cards Casino Holdem® Invented by Stephen Au-Yeung in 2010.
P.S. It has been exposed on my website for many years.

RULES:

1. Each Player makes an Ante-bet, and an Optional Side-bet (AK Bonus).

2. Two cards are dealt Face-down to each Player and the Dealer, and One community-card are dealt Face-up.

3. Each Player examines his cards and must either Fold or Stay in the game by making a Call-bet, which is double his Ante-bet.

4. One more community-card is dealt, and the Dealer exposes his two cards.

5. Players and Dealer will make Their best 3-card Poker-hand by using (Their TWO Hole-cards plus ONE of the Community-cards) or (The TWO Community-cards Plus ONE of Their Hole-cards).
​
6. Dealer compares his 3-Card Poker-hand with each Player’s 3-Card Poker-hand.

The Dealer Qualify with Ace High or better.

​If the Dealer does not Qualify:
The Ante-bet will pay according to the AnteWin® Pay-table and the Call-bet will push.

If the Dealer Qualifies:
(a) Player beats the Dealer then his Ante-bet will win according to the AnteWin® Pay-table and his Call-bet will win 1-to-1.
(b) Dealer beats the Player then the Player will lose his Ante and Call-bets.
(c) Dealer and Player tie then the Ante and Call-bets will push.

For those that are interested Below is my Three Card Poker, (Casino Hold'em® Flop-3™ Three-Cards out of Five-Cards Hold'em) ©2007, ​Patented.
Math by Michael Shackleford (The Wizard of Odds) House-Edge 3.46%.: http://bit.ly/2Z4dfSO

Casino Hold'em® Flop-3™ 德州三張牌™ (Casino Hold'em® FAMILY)
THE FIRST 3-Cards out of 5-Cards Casino Holdem® Invented by Stephen Au-Yeung in 2007.

RULES:

1. Each Player making an Ante-bet, and an Optional Side-bet (2+1® Bonus).
​
2. Each player and the dealer will receive two cards Face-down.
​The Dealer will also deal one community card Face-up.

3. Player has the choice to Fold or make a Call-bet.
The Call-bet must be two times the Ante-bet.
If the Player Fold he will lose his Ante-bet.

4. The Dealer will deal two more community cards, for a total of three.

5. Both Player and dealer will make the best 3-card Poker-hand using any combination of his own two cards and the three community cards.

The Dealer Qualify with a Pair of 7s or better.

​If the Dealer does not Qualify:
The Ante-bet will pay according to the AnteWin® Pay-table and the Call-bet will push.

If the Dealer Qualifies:
(a) Player beats the Dealer then his Ante-bet will win according to the AnteWin® Pay-table and his Call-bet will win 1-to-1.
(b) Dealer beats the Player then the Player will lose his Ante and Call-bets.
(c) Dealer and Player tie then the Ante and Call-bets will push.

Quote: gordonm888

...
1. Player: Qh-9s-2c Common card = As EV of BET 1X =-0.985487974
...
3. Player: Qh-9d-2c Common card = As EV of BET 1X =-1.015148011

From your post the last one of these (i.e. all four suits) represents -17558/17296, so we do agree on the denominator.

I do it slightly differently as I always have the highest card of the player as a Spade. So the hand I've got is Qs 9h 2d and then the common card can be any of the other 49 cards.
From that the Dealer's 3-cards can be any from the remaining 48 cards, so 48*47*46/6 = 17296 possibilities.
I get
Qs 9h 2d - As as -17405 (EV=-1.006302)
Qs 9h 2d - Ah as -17326 (EV=-1.001735)
Qs 9h 2d - Ad as -17354 (EV=-1.003353)
Qs 9h 2d - Ac as -17839 (EV=-1.031395) (DNQ 4543 W 785 T 209 L 11759)
and with Qs 9h 2d you only fold the upcard of an Ace for an initial EV = -0.673476 given an unknown community card.

As an aside I get that you fold some higher hands, e.g. Ks Th 9d with the community card of Qc (but not other cards). By and large with bad hands (you're never going to win with King-high) the community card affects how likely the Dealer will qualify, so if it's less than 2/3 you might as well play.

Stephen, sorry that your game got poached! Technically there are some slight differences in the math of the decisions. Can you provide a link to a WOO page on your Casino Hold'em 2+1 game? I can't find one.

Quote: charliepatrick

From your post the last one of these (i.e. all four suits) represents -17558/17296, so we do agree on the denominator.

I do it slightly differently as I always have the highest card of the player as a Spade. So the hand I've got is Qs 9h 2d and then the common card can be any of the other 49 cards.
From that the Dealer's 3-cards can be any from the remaining 48 cards, so 48*47*46/6 = 17296 possibilities.
I get
Qs 9h 2d - As as -17405 (EV=-1.006302)
Qs 9h 2d - Ah as -17326 (EV=-1.001735)
Qs 9h 2d - Ad as -17354 (EV=-1.003353)
Qs 9h 2d - Ac as -17839 (EV=-1.031395) (DNQ 4543 W 785 T 209 L 11759)
and with Qs 9h 2d you only fold the upcard of an Ace for an initial EV = -0.673476 given an unknown community card.

As an aside I get that you fold some higher hands, e.g. Ks Th 9d with the community card of Qc (but not other cards). By and large with bad hands (you're never going to win with King-high) the community card affects how likely the Dealer will qualify, so if it's less than 2/3 you might as well play.

Charlie, when I play the AGS demo, I observed that when the Dealer Does Not Qualify the Ante Bet is pushed but the Play Wager is still determined by highest hand - so that player's "Ks Th 9d with the community card of Qc" would still win the play bet when faced by a lower Dealer hand.

Also, what assumption are you making about ties? I model as a push on both ante and play.

I had assumed that the raise (I.e. the x2 or x1) gets paid regardless of the Dealer’s hand if they don’t qualify. However if you have Q9x and the community card is A then you beat the Dealer (AQ9) if they don’t qualify. I hadn’t noticed when you get paid or didn’t. That’s why they picked AQx as it then doesn’t cost too much calling when you shouldn’t and it’s not that often when you should fold. I also assumed ties were a standoff- essentially the dealer needs Q9x without three being suited or two being same suit as the common card.

Quote: gordonm888

Stephen, sorry that your game got poached! Technically there are some slight differences in the math of the decisions. Can you provide a link to a WOO page on your Casino Hold'em 2+1 game? I can't find one.

Thanks Gordonm888,

Casino Hold'em® 2+1® is not in WOO.
As it has not been installed in any casinos yet., but It has been Exposed on my website: NewTableGames.com for many years as (2Plus1Holdem.com) or (1Plus2Holdem.com).
Also it was Exposed at Linkedin (2 Months Ago): http://bit.ly/35tLh6J

P.S. When I added Casino Hold'em® 2+1® to my website, I already know games like this (or Variations) will come out soon or later, maybe by coincidence.
I just like to point out the fact that I am THE FIRST to Invented (3-Card out of 4-Cards Hold'em Game/s) not to be accused of copy others.

If you are interested in the FULL Math-Report of Casino Hold'em® 2+1® Here is a link to it. http://bit.ly/2rjlcbq

Quote: MrCasinoGames

...games like this (or Variations) will come out soon or later, maybe by coincidence...3-Card out of 4-Cards...

Yes even I've got some ideas in this area, but not Hold Em. I also think there was, it might have been yours, a variant in the Broadway several years ago.

Interesting in your game that you used Axx for the qualifying hand. My quick calcs with Vega$3P is you would fold more often (Axx 25%) than when it's AQx (4%).

Quote: charliepatrick

Yes even I've got some ideas in this area, but not Hold Em. I also think there was, it might have been yours, a variant in the Broadway several years ago.

Interesting in your game that you used Axx for the qualifying hand. My quick calcs with Vega$3P is you would fold more often (Axx 25%) than when it's AQx (4%).

Hi Charliepatrick,

Thanks for the input.

Yes, The One in Broadway Casino UK, several years ago was my, but it is a different 3-Card Poker-Game.

Quote: Ayecarumba

You would think AGS would goose the demo to generate interest, but I lost 8 hands in a row, then quit.

It's a longshot but has anyone been to Harrah's to play "Vega$ 3 Poker" live? Like Ayecarumba, the demo game just eats me up and spits me out on the virtual felt. I know, I know, it could easily be random chance, but you can only watch the dealer get so many flushes in a row before you have to wonder.

Sorry for the late arrival. I just asked my contact at AGS for the math report, which I believe he will provide. Stay tuned for more information.

I was playing the demo game and my Q-J-10 straight lost to the dealer's A-2-3 straight. I suspect this is a bug in the demo game.

I just got the GLI math report for the game, kindly provided by AGS. It states the house edge (relative to the Ante bet) is 0.88%. The average total wager is 2.1262 units, making the Element of Risk equal to 0.41%.

The report does not indicate any information on player strategy.

Please be the first to see my new page on Vega$ 3 Poker. I hope to add more information on the analysis. I'm still waiting on the original math report, as opposed to the GLI one, which doesn't provide much detail.

I see there are some posts about strategy. If anyone would care to provide a concise strategy for the game, I would be happy to add it to the page, giving full credit to the author, or course.

Now I've got the handle over the Play bet is always compared to the dealer's hand and the Play bet (if you x2, the DNQ and you win) gets paid, I get very close...
House Edge = -0.877 268%
Average bets made = 2.124 650
Element of Risk = -0.412 921%

Double	460 796	42.552%
Call	296 292	27.361%
Fold	325 812	30.087%

Double strategy
(i) Any pat hands (Trips, Stright, Flush)
(ii) Pairs : Aces thru Threes
(iii) Pair of Twos with Flush or any Straight draw
(iv) AJ+ with Flush or any Staight draw
(v) Ax with Flush or easy/outside Straight draw
(vi) KT8+ with Flush draw (these all have Straight draws as well)
(vii) K98 with Flush draw
(viii) K97(a), K87, K76, K65, K54(a) with Flush draw ( a = unless lower two cards are suited)

Call/Fold strategy
Note I haven't checked this as there's a long list of hands to be folded, so as far as I can tell...
(i) Call any hand KQT or greater regardless of upcard.
(ii) Fold any hand Q7x or lower that misses.

Quote: Wizard

Sorry for the late arrival. I just asked my contact at AGS for the math report, which I believe he will provide. Stay tuned for more information.

I was playing the demo game and my Q-J-10 straight lost to the dealer's A-2-3 straight. I suspect this is a bug in the demo game.

I just had the same experience with the demo game: my 7-6-5 straight lost to the dealer's A-2-3 straight. Shades of Pai Gow Poker! Has anyone determined (via the math report or by actually playing the game in a casino) how the A-2-3 straight is ranked?

Quote: gordonm888

...Has anyone determined (via the math report or by actually playing the game in a casino) how the A-2-3 straight is ranked?

You would get a slightly better House Edge, as you can double more often, if A23 is the second best straight. (-0.849 619%, Dbl 463148, Call 293940, Fold 325812). This is because a straight from mixed suit AJ3 and AJ2 has been doubled. This slightly increases the average bet size is 2.126822.

So the House Edge (as -0.8496% is different from -0.8773%) and (Element of Risk: -0.3995% vs -0.4129%) might suggest A23 is not supposed to be the second highest straight, whereas the Average Bet size (2.1268 vs 2.1247) isn't so clear.

Edit: Added more details to compare results.

Charlie has done a brilliant job of scoping out the strategy. I would like to supplement what he has done by offering this (approximate) strategy for the Bet1X or Fold Decision. I prefer to show that it varies with the rank of the common card.

Common Card	Min to Bet 1X
A	A Q T
K	K Q 9
Q	any A Q
J	K J 9
3 - T	any K Q
2	any K 9

The strategy is 'approximate' because many of these are razor-thin margins and can change slightly with suit distribution of your 3 cards relative to the common card and occasionally with the rank of the 4th card.

I've had a quick look and get the following based on your three cards (I've typed this in, so please accept any typos, but it agrees with your quick summary). As you say hands imbetween depend on the exact suits of your cards.

Common Card	Always Play	Always Fold
A	Q 9 3	Q 9 2
K	Q 9 3	Q 8 2
Q	K T 3	K 9 2
J	K 9 3	K 8 2
T	K J 3	K 9 2
9	K Q 3	K T 2
8	K Q 3	K J 2
7	K Q 3	K J 2
6	K Q 3	K J 9
5	K Q 9	K J 9
4	K Q T	K J T
3	K J T	K T 7
2	K 9 8	K 7 6

Quote: charliepatrick

I've had a quick look and get the following based on your three cards (I've typed this in, so please accept any typos, but it agrees with your quick summary). As you say hands imbetween depend on the exact suits of your cards.

Common Card	Always Play	Always Fold
A	Q 9 3	Q 9 2
K	Q 9 3	Q 8 2
Q	K T 3	K 9 2
J	K 9 3	K 8 2
T	K J 3	K 9 2
9	K Q 3	K T 2
8	K Q 3	K J 2
7	K Q 3	K J 2
6	K Q 3	K J 9
5	K Q 9	K J 9
4	K Q T	K J T
3	K J T	K T 7
2	K 9 8	K 7 6

Way cool. Thanks. In particular, I was wondering, based on your earlier comment, in which situation a Q-8 was playable. Now I see it is when the common card is K - and when one of your cards is the same suit as that king. I get that Common = Ks Player = Qh 8s 2d has an EV = -0.99219, which is indeed better than folding.

I see that at least of my rules appears to be slightly incorrect - when the common card is a 3. I didn't actually calculate that case, but did it by similarity with common card = 6 - 10 and was trying to state the rules in a concise way. "No short cut goes unpunished." I'll take another look at that,

Notice how much a common card = 2 significantly weakens the dealer! This is a game in which straights and flushes are a significant fraction of the dealer's equity and a common card = 2 gives the dealer fewer chances to make a straight.

Quote: gordonm888

...in which situation a Q-8 was playable. Now I see it is when the common card is K - and when one of your cards is the same suit as that king. I get that Common = Ks Player = Qh 8s 2d has an EV = -0.99219...

I get slightly different figures, are you including times the dealer beats you (e.g. KQ9) and takes your bet.
Your case corresponds to the Kh in my method so I get EV = ( 5454 - 523 - 2*11141 ) / 17296 = -17351 / 17296 (whereas your figure is -17161).

C = Internal value of the hand.
DNQW = Dealer Doesn't Qualify and you win, e.g. KJ63
DNQT = Dealer Doesn't Qualify and you tie, e.g KQ8x
DNQL = Dealer Doesn't Qualify but you still lose. in this case something like KQ9x
L = Dealer Qualifies and you lose two units.

P: Qs 8h 3d C: Ks V: 2513 DNQW: 5381 DNQT: 178 DNQL: 586 W: 0 T: 0 L: 11151 F: n/a EV: -1.012198 EVD: n/a Pm: 24 Z:
P: Qs 8h 3d C: Kh V: 2513 DNQW: 5468 DNQT: 178 DNQL: 523 W: 0 T: 0 L: 11127 F: n/a EV: -1.000751 EVD: n/a Pm: 24 Z:
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:
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:

P: Qs 8h 2d C: Ks V: 2513 DNQW: 5367 DNQT: 178 DNQL: 586 W: 0 T: 0 L: 11165 F: n/a EV: -1.014627 EVD: n/a Pm: 24 Z:
P: Qs 8h 2d C: Kh V: 2513 DNQW: 5454 DNQT: 178 DNQL: 523 W: 0 T: 0 L: 11141 F: n/a EV: -1.003179 EVD: n/a Pm: 24 Z:
P: Qs 8h 2d C: Kd V: 2513 DNQW: 5484 DNQT: 158 DNQL: 523 W: 0 T: 0 L: 11131 F: n/a EV: -1.000288 EVD: n/a Pm: 24 Z:
P: Qs 8h 2d C: Kc V: 2513 DNQW: 5297 DNQT: 155 DNQL: 515 W: 0 T: 0 L: 11329 F: n/a EV: -1.033533 EVD: n/a Pm: 24 Z:

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.

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.

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.

^ 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%.

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.

Advanced Strategy

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)}

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.

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."

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

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.

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.

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.

P: As Th 8d C: 9s V: 130009 DNQW: 7313 DNQT: 0 DNQL: 0 W: 8748 T: 315 L: 920 F: n/a EV: 1.327994912118409 EVD: n/a Pm: 24 Z:
P: As Th 8d C: 5d V: 2681 DNQW: 6731 DNQT: 23 DNQL: 307 W: 0 T: 0 L: 10235 F: n/a EV: -0.812095282146161 EVD: n/a Pm: 24 Z:
P: As Th 8d C: 8c V: 40111 DNQW: 7523 DNQT: 0 DNQL: 0 W: 3362 T: 226 L: 6185 F: n/a EV: 0.10852220166512488 EVD: n/a Pm: 24 Z:
P: Qs 8h 3d C: Kc V: 2513 DNQW: 5311 DNQT: 155 DNQL: 515 W: 0 T: 0 L: 11315 F: n/a EV: -1.0311054579093433 EVD: n/a Pm: 24 Z:
P: Qs 8h 3d C: Kd V: 2513 DNQW: 5493 DNQT: 158 DNQL: 523 W: 0 T: 0 L: 11122 F: n/a EV: -0.9987280296022202 EVD: n/a Pm: 24 Z:
P: As Th 8d C: n/a V: n/a DNQW: 7943016 DNQT: 31656 DNQL: 174960 W: 2060184 T: 120984 L: 10009296 F: 0 EV: -0.39971138779286 EVD: -0.40861282070645094 Pm: 24 Z:

I've also had tried where A23 by the dealer would win and these don't marry up with your figures
( P: As Th 8d C: n/a V: n/a DNQW: 7943016 DNQT: 31656 DNQL: 174960 W: 2055864 T: 120984 L: 10013616 F: 0 EV: -0.40056 EVD: -0.409886 Pm: 24 Z:.)

I tried to round the figures to six decimals, but I guess the program didn't trunc as I expected so always went down, I've rerun the program so these are the full length numbers, which corresponds to yours.

V: Is the value of the hand
130009 is a straight where the 9th card (2 3 4 ... 10...) is the highest card in the straight.
4xxxx is a pair with 14*pair+odd card.
The others are 14*14*hi+14*mid+lo to produce rankings.

btw In my method the program keeps all the totals for the various possible common cards and then does the adding up. I'm wondering whether you're considered permutaions of the common card, e.g. with As Th 8h I only consider Spades, Hearts and Diamonds but then (hopefully) multiply Diamonds by 2, but this wouldn't apply to AT8 mixed (though you do need to consider something like 9s, 9h, 9d, 9c differently).

Charlie and Gordon,

Thank you for all your outstanding work on this game. I quoted a strategy Gordon kindly summarized for me, giving credit to both you of. I had to push my luck, but if you should put together an "advanced strategy," I would be honored to add it to my Vega$ 3 Poker page.

An interesting new game. Just played it at ags... no peek at strategy. Intuitively, it does look like outside straight AND flush draw gives enough outs for Ace and King High, and Pair or better looks like 2x. Now having seen the more expert advice, I am on the right track so far.

Has anyone thought of "number of outs" as a way of determining play? Is Deuces with K or A kicker as 3-card good enough for 2x raise?

Regards
Suited89

Quote: Suited89

...Has anyone thought of "number of outs" as a way of determining play? Is Deuces with K or A kicker as 3-card good enough for 2x raise?..

2s 2h As -.004 614 .189 452 2x
2s 2h Ad -.332 754-.302 428 2x
2s 2h Ks -.135 020 -.010 519 2x
2s 2h Kd -.466 672 -.507 489
A flush draw has 11 outs, which is why with a Pair of 2s or Axx you raise 2x. 22A has a straight draw, so you also raise 2x.

It's actually more complicated than outs since your cards can make a difference, where you don't draw anything you're probably comparing your high cards with the Dealer's, so there you are looking at how many hands the dealer can beat you. e.g. Ks 5h 4h or Js 10s 8h you don't raise until you know the UpCard even though you have lots of outs.

Quote: Wizard

Charlie and Gordon,

Thank you for all your outstanding work on this game. I quoted a strategy Gordon kindly summarized for me, giving credit to both you of. I had to push my luck, but if you should put together an "advanced strategy," I would be honored to add it to my Vega$ 3 Poker page.

Thanks - as you may have seen we've come up with a simple strategy assuming outside/easy straight using Axx and Kxx. The advantage is its simplicity and doesn't cost that much. However I can understand why you've looked at 1-way K9x as it's better by 0.05% than 2-way Kxx. Note it's a Pair of 2s OR Axx.

Our simple method (-1.041%) allows an "intermediate" strategy to add the condition about calling with an inside/hard straight with a high card (xTx -0.949%). I have a spreadhseet which can calculate the House Edge using different strategies, although I know there's a small bug I'm hoping it's consistent for comparisons, and it seems more important to get the initial raise right than the smaller raise.

This is the strategu I put forward earlier in the thread - I haven't double checked it against my latest figures but you can see there are simple cutoffs except at the lower end of Kxx with a Flush and 2-way Straight draw.

Quote: my post earlier in this thread

Double strategy
(i) Any pat hands (Trips, Stright, Flush)
(ii) Pairs : Aces thru Threes
(iii) Pair of Twos with Flush or any Straight draw
(iv) AJ+ with Flush or any Staight draw
(v) Ax with Flush or easy/outside Straight draw
(vi) KT8+ with Flush draw (these all have Straight draws as well)
(vii) K98 with Flush draw
(viii) K97(a), K87, K76, K65, K54(a) with Flush draw ( a = unless lower two cards are suited)

Christmas is slightly bigger in the UK so I'll be away for a while - so Happy Holidays everybody.

Quote: Wizard

Charlie and Gordon,

Thank you for all your outstanding work on this game. I quoted a strategy Gordon kindly summarized for me, giving credit to both you of. I had to push my luck, but if you should put together an "advanced strategy," I would be honored to add it to my Vega$ 3 Poker page.

Thank you, Wiz. If you scroll up, you can see that Charlie and have been working on just such an advanced strategy. We will try to hammer out the last details and get back to you with it.

Quote: gordonm888

Thank you, Wiz. If you scroll up, you can see that Charlie and have been working on just such an advanced strategy. We will try to hammer out the last details and get back to you with it.

Thank you! Much appreciated.

Quality check: My Vega$ 3 Poker calculator is now agreeing with Charliepatricks code to 9 digits on every output in every case. Thanks for the help, Charlie!

Super-Advanced Strategy for Bet 1x or Fold Decision

Below is a near-computer perfect strategy for the Bet1X or Fold decision, after you have seen the common card. I have a great memory and might possibly be able to handle this level of detail at the casino, but I realize this is way too much detail for any normal gambler. This is certainly too complex for a WOO page. However, its nice to report somewhere what the right strategy is, for those who want to know.

And the insights that are here! It helps to have a KQ or KJ high card hand, but the power of your high cards is not all that counts. It is also worth about 3% in EV if one of your three cards is the same suit as the common card - because that helps to block the ability of the dealer to make a 3-card flush using the common card. I call these suited cards "flush blockers", which is the terminology used in the poker world. When you have a "flush blocker" you sometimes will have a lower minimum hand for making the 1X Bet.

But also, it helps if you have one or more cards with a rank adjacent to or near the rank of the common card -because that helps to block the Dealer from making a 3-card straight with his common card. So, if the common card is a 6, you can sometimes make a 1X Bet on a lower hand if you have a 5, 7 or 8 in your hand. That's why I sometimes list the 4th card in the table below- the so-called 'kicker' to your 3 card poker hand - when it gives you a decisive edge by lowering the probability of the dealer beating you with a straight. It makes the table below a bit unwieldy, but I this does illuminate what may be a helpful insight..

On this table, "Minimum Hand" means to Bet1X with that hand and any better hand, given the common card rank shown at the beginning of the row. I also include "Also Hit" hands that are lower than the minimum hand but have kickers that reduce the dealers chance to make a straight.

High Card Hands for Making the 1X Bet

Common Card	Minimum Hand: No Flush Blocker	Also Hit, No Flush Blocker	Minimum Hand, With Flush Blocker	Also Hit, With Flush Blocker
A	A Q T		A Q T
K	K Q T		K Q 9
Q	A Q x		K Q T
J	K J T		K J 9
T	K J T		K J T
9	K Q T		K J 9
8	K Q 8-7		K J 8-6
7	A x x	KQ8, KQ7-6	K J 7-6
6	K Q T	KQ8, KQ7, KQ6-5	K J T	KJ8, KJ7, KJ6-5
5	K Q T	KQ7, KQ6, KQ5-4	K J T	KJ7, KJ6, KJ5-4
4	A x x	KQ5, KQ4-3	K Q x
3	K J T		K J x	KT5, KT4
2	K T x	K94, K93	K 8+

Again, this is not the strategy that I suggest you try to remember. I'll work with Charlie (who I imagine is going to hate this table, LOL), to come up with something that is digestible for the WOO Page.

Quote: gordonm888

Again, this is not the strategy that I suggest you try to remember. I'll work with Charlie (who I imagine is going to hate this table, LOL), to come up with something that is digestible for the WOO Page.

This stuff is less interesting than even EvenBob's life here, in agonizing minutia, and how he became that way, including those pictures of the uncooked stuff he claims to eat, homemade puke for cheapskates.

Ironic that the closet "warriors" of the world, who supposedly need nor want for anything, unite on dwindling internet forums to overcompensate for the result.

Casinos, and the old people who still cling to them are hopelessly passé. No wonder that the planet is already dead. Blame it on religion, I guess. Weren't they the ones who started the science kick?

Quote: G2

This stuff is less interesting than even EvenBob's life here, in agonizing minutia, and how he became that way, including those pictures of the uncooked stuff he claims to eat, homemade puke for cheapskates.

Ironic that the closet "warriors" of the world, who supposedly need nor want for anything, unite on dwindling internet forums to overcompensate for the result.

Casinos, and the old people who still cling to them are hopelessly passé. No wonder that the planet is already dead. Blame it on religion, I guess. Weren't they the ones who started the science kick?

Merry Christmas likely sock puppet.

Quote: unJon

Merry Christmas likely sock puppet.

Thanks. Same to you.

Better to soberly say once (or twice) in the right spot and time what's on your mind than to spend years on other forums trying to say the same things over and over to overcompensate for missed "opportunities" here. Be done with it, regardless the consequences.

MrV held this community with such high esteem, for years, but, left, on Groundhog Day, without so much as a goodbye? Something wrong there, too.