Perfect, Ultimate House Way to end all problems

What would the Perfect, Ultimate House way be in Pai Gow Poker?
We have discussed a plethora of problems (oh, that word again) about the Pai Gow house way and any lack of standardization, but some requirements come to mind:

1. Short and Easy to Deal and play
2. In Plain English - unambiguous language, the meaning known every time.
3. Short - Very short, nothing convoluted.
4. Strong and powerful for it's length; accurate cut-off points.
5. Supports customer conventions (A-5 wheel straight, players may set to any legal hand, etc.

So I came up with this (mathematically proven) house way. A few things look off, but are actually spot on mathematically; it's just because of the conventions that we're used to playing.

Let me be the first to say: Nice work, and thank you.

Quote: clamchowder

Let me be the first to say: Nice work, and thank you.

Clamchowder, thank you.
I used a power ranking (hand rating chart) of Pai Gow hands.
The mathematician who ran millions of simulated hands is Charles R. Mousseau, very fine.

Quote: Paigowdan

What would the Perfect, Ultimate House way be in Pai Gow Poker?

1. Short and Easy to Deal and play
2. In Plain English - unambiguous language, the meaning known every time.
3. Short - Very short, nothing convoluted.
4. Strong and powerful for it's length; accurate cut-off points.
5. Supports customer conventions (A-5 wheel straight, players may set to any legal hand, etc.

1 and 3 seem about the same to me. I'd say "short but not too short". Various footnotes and exceptions do add to length and complexity but you should be able to cover the important parts in a straightforward manner in clear bold type.

Think of it as one of those free gambling lessons the casinos offer. They are not at the Ph. D. level. Its a straightforward presentation. The placarded houseway should be both visually and textually simple and straightforward. Its not as if those casinos send their dealers to Pai Gow School for six months or something.

Not the Ultimate, but clears up some of the varieties of certain hands with a decending order for the testing.

Pai Gow Poker House Decisions

References to the "front" or "front hand" indicate the 2-card hand.

1.) Five Aces: Split AAA behind AA.

2.) 6 or 7 card Royal Straight-Flush: Play a Straight-Flush in back with Ace-other in front
UNLESS a pair can play as the 2-card hand while maintaining a hand ranked at least King-High
Flush in back.

3.) Four of a Kind with Three of a Kind: Always play the highest Pair to the front.

4.) Paired Four of a Kind: Always play the pair in front.

5.) Four of a kind: Play according to the rank of the four of a kind as listed below.
2222, 3333, 4444, 5555: No Split.
6666, 7777, 8888, 9999: King-3 or better plays in front, else split.
10-10-10-10, J J J J, QQQQ: Ace-3 or better plays in front, else split.
KKKK & AAAA: Always Split
EXCEPT play KKKK with AJ or AQ in front.
EXCEPT play AAA with AK in front

6.) Full house with extra pair: Play the Triple and Low Pair behind the High Pair.

7.) Full house: Split Triple in back with Pair in front,
EXCEPT if A-K or A-Q is present, and the pair is 2-2, then play the A-K (A-Q) in front.

8.) Straights, Flushes, and Straight-Flushes with Three Pairs: Play as Three Pairs, see below.

9.)Straights, Flushes, and Straight-Flushes with Two Pair: Play as Two Pairs, see below.
EXCEPT If the high pair is AA, play as "Straights, Flushes, or Straight-Flushes" below.

10.)Straights, Flushes, and Straight-Flushes (all others): Order of Play top to bottom;
Straight-Flush + Pair in front
Straight-Flush + Ace in front
Flush + Pair in front
Flush + Ace in front
Straight + Pair in front
Straight + Ace in front
Straight or better with best two other cards to front.

11.)Two Three of a Kinds: The higher pair goes to the front hand..

12.)Three of a Kind: Play the Triple in back with best two remaining cards in front,
EXCEPT Always break up three Aces as AA in back of an Ace with best other card.
EXCEPT break up three Kings as KK in back if the highest remaining rank is Jack or less.

13.)Three Pairs: play the highest pair in the front hand

14.)Two pairs: Ranked by the highest pair
AA or KK high: always split
If the Low Pair is 10-10 or higher always split.
QQ JJ or 10-10 high: Ace-10 or better plays to front, else split
99 or 88 high: Ace-3 or better plays to front, else split
77 or 66 high: King-3 or better plays to front, else split
55 high or less: Q-7 (Lucky-Lady) or better plays to front, else split

15.)One pair: Place the pair in back and the two highest remaining cards in the front.

16.)No pair: The 2nd and 3rd highest cards play to the front hand: remaining cards in back.

Not hard, but not easy either, Pai Gow Poker has some unusual hands. I didn't want to play "Stump the Dealer".
This House Way is rather strong in comparison, but it all washes in the end.

98Clubs

98 clubs - looks very good, but disagree with two pair and straights/flushes. This is because of the "copy factor," where AK copies about 7% of the time for the win, and AQ somewhat less but still considerable. This is why in borderline hands in two pairs, straights/flushes, play QQJJAK4 as AK/QQJJ4 instead of JJ/QQAK4;

Also, a casino operator had implemented a new house way company wide, the One Pair rule, where the dealer must play a straight or a flush with a pair of tens or better with an ace up, if the straight or flush does not have an ace for the top. They may have done this to be compatible with Shufflemaster's I-deal machine.
The hand Ad-Kc-10d-10s-4d-3d-2d is MUCH better played as K-10/Ad-10d-4d-3d-2d than AK/1010432. The Ace-high flush with a K-10 top has an EV of about 33%, but the 10's with AK top has about a 13% EV. The rule should be : "Play a straight or a flush as one pair IF a pair of Jacks with an Ace and FACE can be played WHEN the straight or flush has a queen or less for the top." But this might be too compliacted for I-deal to implement at this point. (The I-deal shuffler machine remembers the cards dealt, and so can recommend the best house way to the dealer - or to a player who is uncertain as to play his hand.)

I AGREE with playing KKK 10-9-4-2 as K-10/KK942 for a player's position! Trip kings with a 10 top can ONLY push or lose, but K-10/KKxxx beats a LOT of pai gows and one pair hands. I did not use it becuase it is very "churny," where a dealer's house way (specifically) needs to push through such hands, instead of winning and losing many hands for the same net income, - as it causes hands per hour loses. In this regard, it is BETTER to win two hands and push four hands, than win 4 hands and lose two back, as for the same net 2 wins, you have SIX tansactions instead TWO transactions!

A Player do not have to worry about how long it takes the dealer to process his hand. A casino operator has to consider how long it takes for its dealer to process six hands at a full table.

98 clubs - where did your house way come from?
It would be great to get a mathematician to make a call for the industry.

Thanks for the kind words:

"The hand Ad-Kc-10d-10s-4d-3d-2d is MUCH better played as K-10/Ad-10d-4d-3d-2d than AK/1010432." Yes,, especially since it does not make a STR or STR-FL.

"KKK 10-9-4-2 as K-10/KK942 for a player's position!" Yup, K-J + KKxyz rather marginal, but strong. Flipped it around for the House.

Most of this is a mish-mash of several concepts from "Strong 2-card" to Wong's Analysis. By making a decision-ladder for the STR, FLUSH, STR-FL's the better 2-card hand plays given multiple choice failure of the ladder. The 2-pair that is also a STR/FL/STR-FL with AA high was put there to get a strong front hand... hopefully AA + straight or better. This is where Pai Gow gets complex, especially with the Joker. Thats why there are several decisions based upon having a STR/FL/STR-FL, and a bucket Just In Case.

Two pair is over-simplified but generally traditional, though JJ + QQxyz is about 60/40 on the 5-card (As a Player, I hate 2-pair QQ ups, Any Ace in the 2-card hand is almost as good as the QQxyz in the 5-card hand: thus QQ99z can play behind A-10 (also 60%) or better). Quads seem fairly routine for most House Ways: the exceptions are a bit unusual.

The Full House was altered in favor of AK/AQ with the 22 (99.7% + 70%). I gave serious consideration to Ace-Face plays up front at all times. The Player should also consider it, as straights and flushes by the Dealer can be overcome, with a strong 2-card hand. BUT, the Dealer splitting 2-pair is a certain push. Six or a half dozen, your choice. (When Player or Dealer has a flush/straight, usually the 2-card hand isn't strong, by breaking up the full house, the trips in the 5-card hand become somewhat vunerable, especially if the House way favors playing Str's or Fl's to the 5-card hand). My personal decision on Full House is play Ace-Face (AJ, AQ, AK) to the Front at all times.

IMHO: I have always found that PaiGow Poker is more of a game of Concepts rather than hard math, but I must state that hard math is needed.

EDIT: The only problem I have with my ladder and bucket is that I play putting all the "and Pairs" up top, and all the "and Ace" on the bottom. There are some serious flaws picking Flush + Ace over a Straight + Pair. I'm not a my way or the highway kind of player, Dealers might see the easy testing of either way

98Clubs

Is there an AP way to beat PGP? If there's not, why
would anybody be interested in playing it. I'm in a
casino to win, not to lose at a games HE.

None that I know of. Same goes for Craps.

And I also think a 1.5% advantage isn't much to write home about either unless the following occurs
8hrs a day at 75 rounds/hr for 300 days a year times 50 years at $100/hand ave.
Thats 13.5 million based on a 2400 hour work-year from age 21 to 71.
Is anyone doing this at Blackjack? or does there still have to be a LARGE variance of wager and/or a LARGE minimum bet?

98Clubs

Well, there is an "anti-banker/anti-house strategy" that considers the copy effect of the two card side.
Because of the two-card copy factor (where the house wins copies or "matches" on the two-card side), - for all borderline hands that could be reasonably played either way (such as KK55Q2 as 55/KKAQ2 or AQ/KK552), the house picks up a couple of points advantage on these particular hands because of the copy effect, and the player loses if a couple of points if putting up a "copyable hand.

On average, the two card side copies about 2% - 2.5% of the time but on one-half of the full hand; However, certain hands copy FAR more frequency, because with the remaining pool of cards to form the two-card side is about 5 cards in length of average, so the two-card side gravitates to high cards, causing them to copy far more frequently.

The list of copy-able two-card side hands - and the differences in power rankings between dealer/Banker or player for these two-side hands are:
AK Dealer wins 69.3%, player 64.6%
AQ Dealer wins 62.4%, player 59.3
AJ Dealer wins 57.7%, player 55.6%
KQ Dealer wins 47.0%, player wins 44.2%
KJ Dealer wins 39.8%, player wins 38.3%
This is from Wong's stats. Mike Shackelford's stats can be determined from Mike Shackleford's Pai Gow power rankings. Notice the negligible difference between player and banker with a Q-6 or Q-7 top, versus an Ace-face or Face-face top.

In other words, the best way for the banker or dealer to play the hand QQJJAK7 is as AK/QQJJ7, as the AK top copies very often for the dealer/banker advantage, making it essentially a three pair hand, as ONLY a pair on top can beat the AK. But a player (who doesn't receive the copy benefit) is better off playing it as JJ/QQAK7 instead. A non-banking player's AK top facing an opponent's AK top (a common occurence) will lose instead of win in this case.

A player's strategy that accounts for their weakened Ace-face or Face-face top where a split hand become stronger for the player's position is considered.

Lotsa good stuff there Dan. I would presume its in the best interest to put a pair in the two-card hand as Player, but take advantage of the favorable copy rules as Banker.

What happens when the House decides that playing a pair to the 2-card hand (non-fouled) is the House Way ? Does this "pair to 2-card Strategy" cause too much churn or push?

Thanks
98Clubs

Quote: 98Clubs

...What happens when the House decides that playing a pair to the 2-card hand (non-fouled) is the House Way ? Does this "pair to 2-card Strategy" cause too much churn or push?

The house would loose the extra H.E. built into its use of the copy advantage, - and as a result would play weaker. Hands like QQ44AK7 would be a lot weaker for the house dealer when played as 44/QQAK7 instead of AK/QQ447, because it would now lose to hands like 77/KKxxx, 55/AAxxx instead of pushing, and would now push instead of win against player hands like AK/66223, K7/55332, QJ/KK964 or AK/AA632 - all fairly common. And it would still lose to full houses (which often have higher pair than a low pair up), and very often lose to three pair hands, which always have the highest pair up, when it would otherwise push with a stronger two pair on the bottom if kept together. When you consider that a casino adds about an extra percentage point in table hold for each tenth of a point in H.E., it adds up to a REAL lot. The difference between a 2.2% H.E and a 2.7% house edge is the difference between a table hold of 22% versus a table hold for 27%. On a table drop of $100,000 a month, that's thousands. The down side is that a player may feel a little bit like he's playing against a tournament player instead of a diluted and weak house way on his visit to the casino. You expect your buy-in to last a long time when playing casino Pai Gow, it's one of the game's "good reps" as a casino game.

Using the copy advantage to your favor when you have it (like in the house's case or when banking) increases hand strength, and losing this strong advantage can only weaken play if you don't utilize it when you have it in your favor.

It is ONLY the non-banking player who can fight against the dealer's copy advantage by promoting his own hand splitting somewhat - since he never had the copy advantage to use for his advantage in the first place, and so would have to guard against it being used against him.

Players would be better off playing AAKKQJ10 as KK/AAQJ10, but banking players and house dealers would be better of playing AK/AKQJ10, picking up a hand or two with that may copy with an AK top also. Granted, the hand is very strong either way, but the points really add up to a lot when adjusted accurately for all the "player versus banker" cases that occur for all the Pai Gow hands a casino pumps out - or a player faces from the casino.