Standardizing Pai Gow Poker House ways

This is a topic whose time has come.

For eons, Pai Gow poker house ways have varied from casino to casino, causing confusion, gripes, and even altercations among players and dealers, and among dealers and other casino personnel. The amount of lost time, money, and good will is considerable, and some think that it would just be better if one standard, reliable, and accurate Pai Gow Poker house way finally became adopted as an industry standard, or at least within one operator. Pretty much static, stable, and reliable for the game, like a full house always beating a flush in Hold 'em poker, or the Baccarat drawing method never changing on the players or dealers.

Last night I played Pai Gow Poker at the Cannery, and got a doozy of a hand an hour into play, - the infamous full house with a straight/flush, upon which bad advice was heaped profusely by all. The hand was this: As (*joker) Qs Qh Qd 7s 2s.

The best play is to play the Ace-high flush with a pair of Queens on top, but everyone said "You gotta play the full house with a pair of aces up." No, I don't. The pair of queens up is about as strong as a pair of aces up, but the Ace-high flush is way stronger than trips. Funny thing, the dealer had a 6-high straight with no top, and the correct setting was the only way I could have won. ($50 bet, and $5 each bonus and insurance). A rare situation, but you see it if you play often. The Ace-high flush with Queens on top is 90% EV, and the full house is 82%, a big difference. NO ONE could figure out that the flush with queens was the stronger combo, it was like a mystery to them.

And so the development of Pai Gow poker house ways is a mystery among industry personnel; there's a running joke that house ways either come from some guy in a raincoat in the parking lot of Palace station, or from a shift manager's dart board. And there's a ton of truth to this. Ask anyone in the industry where their house way came from or how it was developed, and they wouldn't have a clue or an honest answer. No one in the industry analyzes house ways, they just fax them from one house to another, saying, "Here...try this one." Seriously. And it's ridiculous, and it has got to stop.

When I developed EZ Pai Gow, I also developed a house way that was actually designed to be mathematically accurate and efficient, to be included with the product as a best practices recommendation, as well as readable and sensible to dealers and players. But most houses simply said "nah, screw that, I don't want to retrain the dealers if it isn't necessary, even if we lose a little house edge here and there with what we got. Besides, any new house way has to come down to us from the corporate table games guy, high above us, like manna from heaven when it appears - not that they know what's going on either."

This is what I heard, both as a dealer and as a game designer afterwards. In any case, I did sit down with an accurate Pai Gow poker EV table of the two-card sides and five-card sides and some data, and discussed some points on Pai Gow Poker house way development with my mathematician, and kept all the notes that lead to two house ways (an "Easy, Plain English" one that's very deal-able, and a more detailed one for online and computer apps).

I did focus on the house way being strong and accurate for the house, but then, the players will also follow it, as the way the play is the house way they're exposed to. I also learned some interesting things about optimizing it, and the areas of efficiency in operating Pai Gow poker games:

1. In the casino, what is not known to them, but should be practiced, is selecting less aggressive and less volatile house ways that have the same EV strength, as it is better to push more hands and collect on a few wins, than to have wins and loses that just cancel each other out; as such it is just useless chip mucking. This is particularly true for commission-free Pai Gow poker games like EZ Pai Gow, because no commission is made on churning wins against loses. Simply put, it is better for the dealer to push four hands and win two, than to win four hands and lose two hands back - for the SAME net two wins. In one case, the dealer goes to the rack six times for two wins, and the other case, the dealer goes to the rack two times for the two wins.

2. The other area is that the dealer wins hand copies, and for this reason the house ways should explicitly mention and favor AK/AQ tops instead of splitting close hands based on whether the top is any ace or not. The deliberate use of fostering two-card side copies is a house technique in designing Pai Gow poker house ways, and yeah, it is used in some house ways.

3. In return, what is discarded here is the dealer "protecting" his high-card Pai Gow hands, by playing the 2nd & 4th cards up as disallowed or verboten; this move is particularly blatant and off-putting, and makes the casino house seems overtly stingy and greedy on the game, while the more accurate settings on high hands of two pairs and better are deemed fair and discreet for dealer and player alike to use.

4. More accurate game logic. If you truly examined and analyzed such things as four of a kind handling, you'd see some REALLY bad math represented in the hand cut-over break points. You should keep four jacks or 10's together with ANY ace-low, and four 7's to 9's with any King top, etc. Also noticeable is the lack of accurate handling in straights and flushes, aside to say "play the best two-card side" (generally correct), and "if you have two pairs, then always play as a two-pair hand" (quite often incorrect, but just sloughed off here and inserted into the house way). The addition of two simple clauses to the two-pair handling makes the two-pair logic immensely stronger: keeping all two pair hands with AK, and keeping low two pair with a King top.

Anyway, below is the best two house ways I have developed at this point, (the second one coming later to avoid overload), and it has gone a LONG way above the typical casino house way in both accuracy and in addressing the elimination of "churned wins-against-loses," etc.:
---------------------------
Pai Gow: Highest card in five card hand, 2nd and 3rd strongest on two card side.

One pair: Always play pair in five card side, with next two strongest cards up

Two pairs:
a. Always split Ace-high two pairs.
b. Always split jacks and 7�s or better, except when having an AK for the top.
c. Always keep two-pairs 6�s and less with any King or better top, else split.
d. Split all other two pairs without an ace, but keep together with an ace.

Three pairs: always play the highest pair in the two-card side

Three of a kind, simple (no flush or straight with it):
a. Three Aces always split 2-and-1, as a pair of aces for the five-card side.
b. All other three of a kinds (Kings and less) never break up.

Two three of a kinds: split off a pair from the higher group for the top.

Straights and/or flushes:
a. Straight or flush with one pair: If the pair is Jacks or better, and the top is Ace-face or better, play as one pair if the straight or flush has a queen or less top. (In other words, play the damn straight or flush with the King up, - if you only have a one pair hand with it.)
b. Straight or flush with two pairs: Always play the straight or flush if it has an AQ or better top, else use two-pair rule
c. Straight with Flush: play the one with the highest two-card side.
d. Straight or flush with three of a kind: always play it as a straight or flush with pair or ace up. (Play 9888765 as 98765/88, and AA*2459=A2*45/A9)
e. Straight or flush with full house: Play as flush or straight if it has 8�s or better for the top or the pair is better than the full house pair, else treat as full house, below.

Straight flush or Royal Flush: Always handle as straight and/or flush, above.

Full house:
a. If you have a full house with an extra pair, then play the higher pair up;
b. If your full house�s pair is 5�s or less, keep with AK, else split.

Four of a kind with a pair:
a. Split four Aces or Kings 2 & 2 with a pair of 3�s or 2�s, to play Aces or Kings on top, else keep all other four of a kind hands together with any pair for the top.

Four of a Kind with no pair:
a. Always split four Aces 2 & 2.
b. Keep ALL four of a kinds together with an AJ, AQ or AK top, including 4 Kings.
c. Always split four Kings or Queens with an A-10 or less.
d. Keep four Jacks or 10�s with any Ace top, else split 2 & 2.
e. Keep 7�s through 9�s together with any King or better top, else split 2 & 2.
f. Keep 6�s and lower with a Queen or better top, else split 2 & 2.

For four of a kind with a three of a kind, split a pair from the higher group for top.

Five aces: Always play a pair of aces up.

Suggestion:

Five aces: Keep five aces down when you can play KK up.

Quote: Deucekies

Suggestion:

Five aces: Keep five aces down when you can play KK up.

Yes, true, but I purposely omitted it as a personal gripe of mine, because it is just SOOOO rare, and would return so little in terms of real-world difference, I wished to exclude that hand. In house way design, unless you can pick up 0.1% or better when the house way is only off 0.4% or so, then less is really more. This change would pick up 0.00001% or so.

I have an image in my mind's eye of a dealer looking at the house way and palm-slapping her forehead.

I have other improvements in a slightly more detailed house way (still one page) that I'll add;

I also have a player non-banking strategy that addresses house copies against you. Not all that much can be done against a good house way, but some tricks work.

True story about less being more.

A thought I had. I think it's true at most casinos that when a player needs help setting a hand, dealers are only allowed to quote houseway. To that end, it seems to me you don't want a houseway that's TOO optimal because that's how most players are going to be playing.

(I feel like a bad person when I have to tell a player with 6655732 that "Houseway is 7-3, sir." Yes, that's actually our houseway. Never split two pair 6s or lower.)

Quote: Deucekies

True story about less being more.

A thought I had. I think it's true at most casinos that when a player needs help setting a hand, dealers are only allowed to quote houseway. To that end, it seems to me you don't want a houseway that's TOO optimal because that's how most players are going to be playing.

Good point! This is why I had to take out the Pai Gow high-card maneuver of protecting the dealer's Pai Gow hand, it was just SOOOO greedy and cheap-ass and bad-will in nature for the extra tenth of a percent, it HAD to go. I mean, the player would be playing at the table, and get stuck with an Ace-high Pai Gow, - and the dealer would try to openly beat him by manipulating his OWN Pai Gow to sleaze-out a win. For a dealer to protect his Pai Gow hand is just too shameless.

Quote: Deucekies

(I feel like a bad person when I have to tell a player with 6655732 that "Houseway is 7-3, sir." Yes, that's actually our houseway. Never split two pair 6s or lower.)

And you're right - the split 6's and 5's will beat a number of dealer hands while the topless two pairs will only push or lose. I once coached a player who had a flush with a straight (that had an AJ top), and playable also as Aces and jacks. He asked me how I'd play it, and I said AJ top with King-high straight, in case I get two low pairs, trips, a lower straight, or a full house with a higher pair. Sure enough, I got Ax/5522x and he won and tipped me well. Surveillance called down to the pit and said I was coaching players, and I went to the shift office for a warning.

I'd like to share a top-down ranking. I well know the suits won't go for it, but the Players may see the value in this to simplifiy their own decisions. This has been gleaned from a lot of the work done by JB, the Wiz, and open discussions here with Dan.

The House Way: "Front hand" or "front" is the 2-card hand. "Back" or "in back"� is the 5-card hand.
....a.) Decisions are made top to bottom. If a decision fails, move to the next-lower decision.
....b.) If the decision matches, then the EXCEPTIONS and/or STEPS are tested.
....c.) A Royal-Straight-Flush is a Straight-Flush in these tests.
....d.) Ace-Face refers to Ace-Jack, Ace-Queen, and Ace-King only.

1.) Five Aces: A Pair of Aces plays to the front hand.

2.) Quad + Triple: Play the high Pair in front.

3.) Quad + Pair: The Pair plays in front

4.) [Straight-Flush, Flush, or Straight]: Play these STEPS as follows from top to bottom;
....a.) Play best [choice] with a pair in front
....b.) Play as Three Pairs (see 9. below)
....c.) Play a Straight-Flush with Ace-Face in front
....d.) Play as Two Pair (see 10. below)
....e.) Play best [choice] with Ace-other in front
....f .) Play as One Pair TT or better with Ace-Face in front
....g.) Play the best two non-choice cards in front

5.) Quads: TTTT = Four Tens, split = Pair + Pair. Play these STEPS as follows from top to bottom;
....a.) AAAA KKKK QQQQ : Always split.
....b.) J J J J TTTT 9999: Ace with best non-quad plays to front, else split.
....c.) 8888 7777 6666: King or Ace with best non-quad plays to front, else split.
....d.) 5555 4444 3333 2222: DO NOT SPLIT, play the best two non-quads in front.

6.) Full House + Pair: Higher of the two Pairs plays to front hand.

7.) Full House or Two Triples: Play as low Triple in back, the remaining Pair in front,
....EXCEPT Play Ace-Face in front of any Full House having the Pair ranked 22 or 33.

8.) One Triple: Best two non-triples play to front,
....EXCEPT AAA splits as Ace with best non-triple in front of AA with remainders.

9.) Three Pairs: Play the highest Pair to front.

10.) Two Pairs: Split = High pair in back, Low pair in front. Play these STEPS as follows from top to bottom;
....a.) High Pair QQ KK AA: Always split.
....b.) High Pair 99 TT J J: Play Ace to front, else split
....c.) High Pair 66 77 88: Play King or Ace in front, else split.
....d.) High Pair 55 or less: Play Queen or better in front, else split.

11.) One Pair: Play best two non-pair to front hand.

12.) High Card (Pai Gow): Play the 2nd and 3rd highest ranks in front, all other cards in back.

I think both perspectives have their value, and opportunities. The Cat & Mouse aspect of the game remains intact either way.

*** EDIT... PLAYER as BANKER EXCEPTIONS Below ***

EXCEPTIONS for PLAYER as BANKER listed by Rule Above

3.) If the Quad is 8 ranks or more higher than the Pair, then split the Quad.

5.) QUADS are rewritten
....a.) AAAA Always Split
....b.) KKKK QQQQ JJJJ: Play Ace-Other Face to front, else split
....c.) TTTT 9999: Play Ace to front, else split
....d.) 8888 7777: Play King or Ace to front, else split
....e.) 6666 5555: Play Queen or better to front, else split
....f .) 4444 3333 2222: DO NOT SPLIT, play best two remainders to front

8.) Add the following rule as 8b.):
....Split KKK as above in 8a.) UNLESS an Ace or Queen can play to front

10.) Use Poker Hand ranking for the two pairs and determine as follows;
....a.) QQ77 to AAKK: Always Split
....b.) JJ66 to QQ66: Play Ace-Face to front, else split
....c.) 8855 to JJ55: Play Ace-other to front, else split
....d.) 5544 to 8844: Play King or Ace to front, else split
....e.) 5533 or less: Play Queen or better to front, else split

12.) EXCEPTIONS to Ace-High Pai Gow: Protect a bad hand
....a.) If the the 3 highest ranks in the 7-card hand are AKQ, play the 2nd and 4th high ranks to front.
....b.) If the 2nd high rank in the 7-card hand is a 9 or 8, play the 3rd and 4th high rank to front.
....c.) Play the 2nd and 4th highest ranks to maintain an 8 or better in the 5-card hand.

Quote: Paigowdan

Good point! This is why I had to take out the Pai Gow high-card maneuver of protecting the dealer's Pai Gow hand, it was just SOOOO greedy and cheap-ass and bad-will in nature for the extra tenth of a percent, it HAD to go. I mean, the player would be playing at the table, and get stuck with an Ace-high Pai Gow, - and the dealer would try to openly beat him by manipulating his OWN Pai Gow to sleaze-out a win. For a dealer to protect his Pai Gow hand is just too shameless.

Incidentally, in what situations is playing the 2nd and 4th card up as a player mathematically better than playing the 2nd and 3rd card up? Have you quantified it? Are there ever times where playing 3rd and 4th would be better? A876432 as the lowest ace-high?

Quote: Deucekies

Incidentally, in what situations is playing the 2nd and 4th card up as a player mathematically better than playing the 2nd and 3rd card up? Have you quantified it? Are there ever times where playing 3rd and 4th would be better? A876432 as the lowest ace-high?

Yes, this has been quantified by many; in cases where the Pai Gow hand has a large gap between the 3rd and 4th highest card, it is better to play the hand as 2nd and 4th in the low hand, putting the 3rd highest card in the 5-card side to protect it in case the dealer also has a Pai Gow hand. The hand AKJ6432 is better plated as K6/AJ432 than KJ/A6432, because the A6432 five-card side would be clobbered when facing another Ace-high Pai Gow, whereas the AJ432 setting would most likely provide a saving push or surprise win IF facing another Pai Gow. If a casino house decides to fine-tune playing to protect Ace-high Pai Gow hands, players would revolt.

Quote: 98Clubs

I'd like to share a top-down ranking. I well know the suits won't go for it, but the Players may see the value in this to simplifiy their own decisions. This has been gleaned from a lot of the work done by JB, the Wiz, and open discussions here with Dan.

The House Way: "Front hand" or "front" is the 2-card hand. �Back� or �in back� is the 5-card hand.
....a.) Decisions are made top to bottom. If a decision fails, move to the next-lower decision.
....b.) If the decision matches, then the EXCEPTIONS and/or STEPS are tested.
....c.) A Royal-Straight-Flush is a Straight-Flush in these tests.
....d.) Ace-Face refers to Ace-Jack, Ace-Queen, and Ace-King only.

1.) Five Aces: A Pair of Aces plays to the front hand.

2.) Quad + Triple: Play the high Pair in front.
....[going down to Pai Gow hands]
.....

The top-down way is good for programming a PGP simulator, but is slow and cumbersome for human play. The suits just have to be 100% satisfied, in order to accept and adopt a house way, and in the order from weakest to strongest.

Quote: Deucekies

Incidentally, in what situations is playing the 2nd and 4th card up as a player mathematically better than playing the 2nd and 3rd card up? Have you quantified it? Are there ever times where playing 3rd and 4th would be better? A876432 as the lowest ace-high?

There are many situations where you don't play the 2nd & 3rd highest cards in the low hand. Trying to describe this aspect of PGP strategy accurately would be very difficult, but here are some example hands (against the Foxwoods house way, when the dealer is banking):

Cards in Low Hand	Example Hand	Low Hand
2nd and 4th	A♠ K♦ 10♥ 9♦ 7♣ 3♣ 2♣	K♦ 9♦
2nd and 5th	A♦ K♠ 8♠ 6♥ 4♣ 3♦ 2♣	K♠ 4♣
2nd and 6th	A♦ Q♠ 9♥ 8♥ 6♦ 5♣ 2♣	Q♠ 5♣
2nd and 7th	A♦ J♦ 7♥ 6♦ 4♣ 3♣ 2♣	J♦ 2♣
3rd and 4th	A♦ 10♥ 8♣ 6♦ 4♣ 3♣ 2♣	8♣ 6♦
3rd and 5th	A♥ 9♥ 7♦ 6♣ 4♣ 3♣ 2♣	7♦ 4♣
3rd and 6th	A♥ 9♦ 8♥ 6♦ 5♥ 3♦ 2♣	8♥ 3♦
4th and 5th	A♦ 9♥ 8♦ 6♣ 4♣ 3♣ 2♣	6♣ 4♣
4th and 6th	A♥ 9♥ 8♣ 7♦ 5♣ 4♣ 2♣	7♦ 4♣

Thanks, both of you, for posting your House Ways. From your lips to Corporate's ear...lol

Quote: JB

There are many situations where you don't play the 2nd & 3rd highest cards in the low hand. Trying to describe this aspect of PGP strategy accurately would be very difficult, but here are some example hands (against the Foxwoods house way, when the dealer is banking):

Cards in Low Hand	Example Hand	Low Hand
2nd and 4th	A♠ K♦ 10♥ 9♦ 7♣ 3♣ 2♣	K♦ 9♦
2nd and 5th	A♦ K♠ 8♠ 6♥ 4♣ 3♦ 2♣	K♠ 4♣
2nd and 6th	A♦ Q♠ 9♥ 8♥ 6♦ 5♣ 2♣	Q♠ 5♣
2nd and 7th	A♦ J♦ 7♥ 6♦ 4♣ 3♣ 2♣	J♦ 2♣
3rd and 4th	A♦ 10♥ 8♣ 6♦ 4♣ 3♣ 2♣	8♣ 6♦
3rd and 5th	A♥ 9♥ 7♦ 6♣ 4♣ 3♣ 2♣	7♦ 4♣
3rd and 6th	A♥ 9♦ 8♥ 6♦ 5♥ 3♦ 2♣	8♥ 3♦
4th and 5th	A♦ 9♥ 8♦ 6♣ 4♣ 3♣ 2♣	6♣ 4♣
4th and 6th	A♥ 9♥ 8♣ 7♦ 5♣ 4♣ 2♣	7♦ 4♣

Wow. That's incredible.

Is there a rule of thumb you would use to decide when to make this play in practice (without using a calculator)?

Some one else mentioned "a big stretch" between the Ace and the next highest card. I would say if you're not holding at least A-10 in the high hand when placing 2-3 in the low, the 2nd and 4th should be played. Exception: if you "happen to" know where the other aces are, play normally.

Quote: Deucekies

Is there a rule of thumb you would use to decide when to make this play in practice (without using a calculator)?

Verbal "easy" rule of thumb/general practice when done = Maintain a 9 or 10 card in the Ace-high Pai Gow 5-card high side, if possible. (e.g., play AK106432 as K6/A10432, not K10/A6432).

Earlier I said there are some other defensive player action in PGP, aside from protecting Pai Gow hands.


Other non-banking player defensive moves against a dealer is:
1. Split 10's with 7's, 8's, or 9's when holding a weak Ace (Ace-low, less than AJ);
2. split 6's with 5's or 4's, and 5's with 4's, when holding a weak King for the top.
3. Ignore AQ top with a straight or flush (when with two pairs), if you can play two pairs A's and Q's.

Quote: Paigowdan

Earlier I said there are some other defensive player action in PGP, aside from protecting Pai Gow hands.


Other non-banking player defensive moves against a dealer is:
1. Split 10's with 7's, 8's, or 9's when holding a weak Ace (Ace-low, less than AJ);
2. split 6's with 5's or 4's, and 5's with 4's, when holding a weak King for the top.
3. Ignore AQ top with a straight or flush (when with two pairs), if you can play two pairs A's and Q's.

How about the Ballys AC exception rule:
If you have a straight that has a Joker and an Ace, play the pair of Aces with the next two highest cards on top.

Quote: bw

How about the Ballys AC exception rule:
If you have a straight that has a Joker and an Ace, play the pair of Aces with the next two highest cards on top.

That rules sounds weird, but it is to play Aces with a King-face up instead of a straight with no top. (A * KQ1032 as KQ/AAxxx instead of 32/AKQ*10.)

It's actually a weak and volatile rule that wrecks many hands: It also produces a lot of cancelled wins, and it loses like the dickens to two low pairs or better with any weak ace top. It also blows hands like AK*J1098 - which should be played as AK/*J1098, not KJ/A*1098! (however, if you have the wheel straight, it'll still gives the straight: A * 98542 = 98/A2*45).

Yes, thats the rule at Ballys AC, just the way you describe it. They call it the exception, as normally they need two pairs to break up a straight, no other exceptions there. Actually it seems to net them more than a straight with a very low top, which basically can only push or lose to a flush. Remember one ace and a joker are already out of play for any players as they are in the dealers hand.

Quote: Paigowdan

3. Ignore AQ top with a straight or flush (when with two pairs), if you can play two pairs A's and Q's.

This brings me to my next question. If a straight/AQ or flush/AQ contains two pair, how can it not be Aces and Queens? If it's always Aces and Queens, how can the houseway justify not splitting those, even if you're just trying to defend one side?

Queens up top are worth 97.8758% to the dealer.
A broadway straight down is only worth 96.6111% to the dealer.
An ace-high flush down is worth 99.7366% to the dealer, so this I'll buy.

To my eyes, the AQ rule is good for flushes but not necessarily straights. What am I missing here?

bw,
True, but the house way should state "With a joker and an Ace, play a pair of Aces with a K-face top if you cannot play a straight or flush with at least a King top." Because often you can. House ways are the neglected red-headed step child of the casino pit. It's either the raincoat guy or the office dart board in terms of finding or updating a house way.

NO casino operator as of yet has really got it together scientifically, although I hear a very large operator is going to standardize on a mathematically sound, clear and plain English sensible house way.

A question that came up at the table the other day, which gets a different answer depending on which dealer or floor person asked is in places where A, 2, 3, 4, 5 is the second highest straight, does that mean that A, 2, 3, 4, 5 of the same suit is therefore the second highest straight flush? I would guess so.

Quote: Paigowdan

1. In the casino, what is not known to them, but should be practiced, is selecting less aggressive and less volatile house ways that have the same EV strength, as it is better to push more hands and collect on a few wins, than to have wins and loses that just cancel each other out; as such it is just useless chip mucking. This is particularly true for commission-free Pai Gow poker games like EZ Pai Gow, because no commission is made on churning wins against loses. Simply put, it is better for the dealer to push four hands and win two, than to win four hands and lose two hands back - for the SAME net two wins. In one case, the dealer goes to the rack six times for two wins, and the other case, the dealer goes to the rack two times for the two wins.

Dan, is this the reason in general the house way seems to attempt to minimize volatility, even at the expense of some EV? I would think with the (essentially) unlimited bankroll you would sacrifice all for every fraction of a percentage point of EV.

Quote: Deucekies

This brings me to my next question. If a straight/AQ or flush/AQ contains two pair, how can it not be Aces and Queens? If it's always Aces and Queens, how can the houseway justify not splitting those, even if you're just trying to defend one side?

Queens up top are worth 97.8758% to the dealer.
A broadway straight down is only worth 96.6111% to the dealer.
An ace-high flush down is worth 99.7366% to the dealer, so this I'll buy.

To my eyes, the AQ rule is good for flushes but not necessarily straights. What am I missing here?

-- QQ/AAxxx is a tiny bit better than AQ/AKQJ10, as the "boundary point case." You're missing that on average it is very strong and sound, and that a house way cannot be multiple pages or overly complex with multiple clauses, so it was better to include AQ+ than to Limit it to AK only. I am aware of the AQ + straight is borderline (as opposed to AQ + flush or AK + straight OR flush)

I had it "AK with straight or flush, or AQ with the flush only, if [yada yada yada]" but on top of all the clauses in the house way it was too cumbersome for the dealer. (Too much Boolean logic in English....I may put it back in, though).

In house way design, you CANNOT lose the dealer, which is why I also excluded formulas from the house way, although they can be made to give better two-pair handling. When it began to read like "If the sum of the two pairs is greater than or equal to..." - I could NOT imagine an exhausted dealer dealing with the house way except to say, "what am I doing, - taking an SAT test over here...." - although it is quite easy for the mathematically literate. you have got to realize again that less is more, and in getting accurate cut-over points, there may be the tiniest bit of boundary run-over that is better to keep than to let the house way get too unclear or anal in excessive detail.

Quote: gts4ever

Dan, is this the reason in general the house way seems to attempt to minimize volatility, even at the expense of some EV? I would think with the (essentially) unlimited bankroll you would sacrifice all for every fraction of a percentage point of EV.

No, you get as close as you can to it within reason (say 0.3% or 1 in 300 hands - for a tiny bit of EV) - without reducing any hands-per-hour performance or increasing volatility or causing dealer acceptance/ability-to-deal issues; also realize that casinos have been operating on an "Ach!! It's good enough! I can't organize all the math and all this English Language logic crap, so this is good enough! Just Deal it! Get a house way from the man in the Raincoat, dammit!" basis because they didn't know how to mathematically analyze and logically organize the document. Many house ways simply stink, simply because pit bosses and table games directors are NOT mathematicians, and the corporate office should have made a formal GLI type lab project and got it done. Instead, game designers mathematicians are starting to do it, and doing it better than floor supervisors or shift managers.

Quote: Paigowdan

-- QQ/AAxxx is a tiny bit better than AQ/AKQJ10, as the "boundary point case."

I certainly don't profess to know more on this than you do. You've clearly put a LOT of man-hours into this, and I think it's fascinating and awesome. There's nothing I hate more than a non-sensical houseway, after all.

That said, I get 69.136% vs 63.519%, a difference of over 5.6%. For AK/AKQJT, I get 70.725% vs 70.129% for KK/AAxxx, only a 0.404% improvement. Are those similar to your numbers?

I absolutely agree on keeping the houseway as simple as possible. That's why I think I'd skip the AQ rule altogether and go directly to the two-pair rule.

Quote: Deucekies

I certainly don't profess to know more on this than you do. You've clearly put a LOT of man-hours into this, and I think it's fascinating and awesome. There's nothing I hate more than a non-sensical houseway, after all.

That said, I get 69.136% vs 63.519%, a difference of over 5.6%. For AK/AKQJT, I get 70.725% vs 70.129% for KK/AAxxx, only a 0.404% improvement. Are those similar to your numbers?

No, I get 62% for AK + Broadway straight, up to 66.7% with AK+ Royal , versus 59.98 for KK/AAxxx two pairs split. With AK top, even the straight is always better. Are you adding in the much greater copy ratios for AK/AQ two-card sides?

Quote: Deuckies

I absolutely agree on keeping the houseway as simple as possible. That's why I think I'd skip the AQ rule altogether and go directly to the two-pair rule.

I feel it's simple and very deal-able while fairly complete with it. You also get the copy advantage of the AQ/AK and the "push-and-win" versus win churning. The advantages of this house way over a generic/aggregate "simple" house way is considerable, especially for commission-free play. A Generic "textbook" typical Nevada house way to be considered is:
------------------
Generic/Composite House Way:
� No pair: Place the highest card in the high hand and the next two highest cards in the low hand.

� One pair: Place the pair in high hand and the next two highest cards in the low hand.

� Two pair:
o Ace and any other pair - always split.
o Face card pair and pair 7's or higher - always split
o With any other 2 pair, split unless the hand contains an ace - then play the ace in the 2 card hand

� Three pair: Always play highest pair in low hand.

� Three of a kind:
o Always play three of a kind in high hand except break up three aces.
o Two three of a kinds - play the low 3 of a kind as the high hand and split the higher 3 of a kind

� Straight:
o 6 card straight - use the highest card in the low hand.
o 5 or 6 card straight with a pair - use the pair as the low hand.
o Straight with 2 pair - play the 2 pair rule.
o Straight with a pair of 10�s or better and an Ace � play as one pair with Ace top unless straight has an Ace top.

� Flush or Straight Flush
o 6 card flush - use the highest card in the low hand.
o 5 or 6 card flush with a pair - use the pair as the low hand.
o Flush with 2 pair - play the 2 pair rule.
o Flush with a pair of 10�s or better and an Ace � play as one pair with Ace top unless flush has an Ace top.

� Straight and a Flush: A flush and a straight with no pair - play the combination that results in the highest 2 card hand.

� Full house: Split except with pair of 2's and an ace/king can be played in low hand.

� Four of a kind: Play according to the rank of the four of a kind:
o 2 through 6: Always keep together.
o 7 through 10: Split unless a pair or Ace can be played in the low hand.
o Jack through king: Split unless hand also contains a pair of 10's or higher.
o Aces: Split unless a pair of 7's or higher can be played in low hand.

� Straight Flush:
o Same as Straight or Flush, above

� Royal Flush:
o Keep as the high hand.
o Royal flush with a pair - play the pair in the low hand.
o Royal flush with 2 pair - play the 2 pair rule.
o Split the royal flush if an ace, king or a pair can be played in the low hand while retaining a straight or flush in the high hand.

� Five aces: Split unless pair of kings can be played in low hand.

Quote: Paigowdan

No, I get 62% for AK + Broadway straight, up to 66.7% with AK+ Royal , versus 59.98 for KK/AAxxx two pairs split. With AK top, even the straight is always better. Are you adding in the much greater copy ratios for AK/AQ two-card sides?

I'm using Wizard's banker Power Ratings. I'm not considering royal flushes, and maybe that's where the math skews.

AQ: 0.703037
AK: 0.77876
QQ: 0.978758
KK: 0.989071

AAxxx: 0.749273
AKQJT: 0.966111
A-high flush: 0.997366

Quote: Deucekies

I'm using Wizard's banker Power Ratings. I'm not considering royal flushes, and maybe that's where the math skews.

AQ: 0.703037
AK: 0.77876
QQ: 0.978758
KK: 0.989071

AAxxx: 0.749273
AKQJT: 0.966111
A-high flush: 0.997366

1. I am using non-banking side PRs.
2. Also, PRs are house way dependent.

What would reveal the house way's strength is a run against the generic and benchmark house way, where they play heads-up against each other.

What would also be important in the simulation run is the tally of each one's "cancelled wins versus net wins per round" as dealer against 6 players, representing a full table from the operator's Point of View.

I would say the optimized house way would have a 0.2%+ edge over the old generic/typical house way.
How important is this? Well, let's say it improves the hold by 2% between the house way's improved accuracy, and quicker game play/hand-per-hour; it hold 29% instead of 27%.

Now, if a table drops $200,000 a month plus (more in a busy Barona type Casino, or a Heavy-duty Atlantic City casino), 2% of that drop is $4,000 a month or $48,000 a year additional per table. It holds $58,000 a month, instead of $54,000 a month. If a small operator drops $10M a year from all its PGP tables, that 2% adds up to $200,000 a year; if a bigger operator drops $50M a year, it earns an additional $1M a year, and so on. This isn't chump change. It's so important that just about every Blackjack table now has side bets, to get away from the 0.5% BJ house edge that yields a 9% table hold instead of a 22% table hold.

A lot of that extra hold on PGO would be earned by quicker play (less churning play) resulting in higher turnover - more people jumping on to play, and each lasting just a little less long on the tables, times a gazillion player buy-ins over a year's time over all the tables. A player's buy-in lasts 2-1/2 hours instead of 3 hours, let's say, but if the player hits, he takes his winnings. It's really slightly less time on the PGP table per player. And an individual social or recreational player wouldn't notice that 2% overtly. He goes to dinner 10 minutes earlier, times a lot of individual players.

Is it worth spending $10,000 let's say, from a fine mathematician or GLI, to compare "House Way A" versus "House way B" - to earn an additional $200,000 or $1M a year? I'd say. And I'd say specifying AK/AQ in a few places, preferring straights/flushes versus more volatile split pairs when equal or better, and better full house and four-of-a-kind handling would increase revenue by a few percent across many PGP tables, instead of using a "dart-board" house way. It adds up for a big operator.

I have updated my orig. post on Pg.1 to include a few "Player as Banker" Rules. They are not complete and not perfect, but they will help. Naturally, these are "hand-in-glove" to the House Way posted. Two of these IMHO are very important, the 8b.) rule for a set of Kings, and the 12a.) rule for A-Q Pai Gow. The latter wins against all House Way Ace-High Pai Gow's IN THE 5-CARD HAND. The trade-off for a bad hand. These rules are pretty much independently discovered, except JB's rule on Quad+Pair was re-written for simplicity (I used to split Quad A's or K's if the pair was 22 33 44, and QQQQ with 22). The redo of the two-pair rules are evidently unique, never seen anything like it, and it is close to the "Sum the Pairs" rules provided by JB, Wiz, et al. HTH

Quote: Paigowdan

This is a topic whose time has come.

For eons, Pai Gow poker house ways have varied from casino to casino, causing confusion, gripes, and even altercations among players and dealers, and among dealers and other casino personnel. The amount of lost time, money, and good will is considerable, and some think that it would just be better if one standard, reliable, and accurate Pai Gow Poker house way finally became adopted as an industry standard, or at least within one operator. Pretty much static, stable, and reliable for the game, like a full house always beating a flush in Hold 'em poker, or the Baccarat drawing method never changing on the players or dealers.

Last night I played Pai Gow Poker at the Cannery, and got a doozy of a hand an hour into play, - the infamous full house with a straight/flush, upon which bad advice was heaped profusely by all. The hand was this: As (*joker) Qs Qh Qd 7s 2s.

The best play is to play the Ace-high flush with a pair of Queens on top, but everyone said "You gotta play the full house with a pair of aces up." No, I don't. The pair of queens up is about as strong as a pair of aces up, but the Ace-high flush is way stronger than trips. Funny thing, the dealer had a 6-high straight with no top, and the correct setting was the only way I could have won. ($50 bet, and $5 each bonus and insurance). A rare situation, but you see it if you play often. The Ace-high flush with Queens on top is 90% EV, and the full house is 82%, a big difference. NO ONE could figure out that the flush with queens was the stronger combo, it was like a mystery to them.

Based on a conversation I had with a floor supervisor who knows Pai Gow (I don't deal it but have played it,) at my casino, we would have put the Aces in the low hand and played trips as the high hand. My casino apparently focuses on getting the best low hand possible, which kind of makes sense, seeing as how it will generate fewer player wins and the dealer wins tied hands. (Yes, I know my casino is run by cheap SOBs.) I probably would have done it your way - take the flush with the pair of Queens.

What gets me is this - the hand I got that crushed me at Belterra.

Joker-A-K-Q-10-6-2 (don't remember the suits, doesn't matter, no chance of a flush)

I thought about putting the 6-2 in the low hand, taking the straight, and playing for the push, but I ended up taking the Joker and Ace in the high hand, putting the KQ in the low hand, and crossing my fingers - and the dealer drew a damn full house, put a pair in the low hand, and wiped me out.

But then I ran that hand by my supervisor, who told me that our casino would have put AQ in the low hand and played Joker-K-10-6-2 in the high, which makes zero sense to me. I get that they want to build a god low hand, but the difference between KQ and AQ is negligible and the difference between Ace high in the high hand and a pair of Aces is pretty big. Of course, in another conversation here, I read that most casinos would do 6-2 as the low hand and play the straight, thereby almost guaranteeing a push.

Quote: hwccdealer

Based on a conversation I had with a floor supervisor who knows Pai Gow (I don't deal it but have played it,) at my casino, we would have put the Aces in the low hand and played trips as the high hand. My casino apparently focuses on getting the best low hand possible, which kind of makes sense, seeing as how it will generate fewer player wins and the dealer wins tied hands. (Yes, I know my casino is run by cheap SOBs.) I probably would have done it your way - take the flush with the pair of Queens.

What gets me is this - the hand I got that crushed me at Belterra.

Joker-A-K-Q-10-6-2 (don't remember the suits, doesn't matter, no chance of a flush)

I thought about putting the 6-2 in the low hand, taking the straight, and playing for the push, but I ended up taking the Joker and Ace in the high hand, putting the KQ in the low hand, and crossing my fingers - and the dealer drew a damn full house, put a pair in the low hand, and wiped me out.

This is the safest way (62/AKQJ10) to play it, in terms of the least losses, but KQ/AA1062 is technically stronger, but a volatile way to try for the win. Your choices are a safe push hand, versus a coin-flip hand to try for a win.

Quote: hwccdealer

But then I ran that hand by my supervisor, who told me that our casino would have put AQ in the low hand and played Joker-K-10-6-2 in the high, which makes zero sense to me.

You're right - it's a horrid way to play it. Convert a straight (or a pair of Aces) into a Pai Gow? No, absolutely absurd. The best play for the casino is to play 62/AKQJ10 and push through quickly to their next winning round of play. These situations are exactly what I'm talking about - What does it take for a casino operator to use a provably correct house way instead of just guessing - and guessing wrong? Yeow.

Quote: hwccdealer

Joker-A-K-Q-10-6-2 (don't remember the suits, doesn't matter, no chance of a flush)

I thought about putting the 6-2 in the low hand, taking the straight, and playing for the push, but I ended up taking the Joker and Ace in the high hand, putting the KQ in the low hand, and crossing my fingers - and the dealer drew a damn full house, put a pair in the low hand, and wiped me out.

You made the better play by far:

AKQWT/62 return = -0.023538
WAT62/KQ return = +0.254272

And for academic interest:

WKT62/AQ return = -0.172832

Quote: JB

You made the better play by far:

AKQWT/62 return = -0.023538
WAT62/KQ return = +0.254272

And for academic interest:

WKT62/AQ return = -0.172832

No. Using Shackleford's WOO PGP player side power rankings, Here are the basics:

KQ/AAxxx = wins 29.25%, lose 22.75%, EV=0.065 (6.5%) pushes 48% of the time. Five-card side = 65%, two-card side=45%. A VERY neutral hand that's just slightly positive and quite volatile. This is not a +25% hand, and NOT much better than playing the straight.

62/AKQJ10 = wins 1%, lose ~ 3%, EV= -0.03, or -3% (you have -2.35%, I ballparked), will push 96% of the time. Five Card side as Broadway straight wins 96% of the time.. Two-card side of 62 wins 1%, loses 99%. Overall it'll push 96%-97% of the time, lose 3%, and win 1%. An extremely stable push hand.

AQ/AK1062 = wins about 13% of the time (beats dog hands only), loses 30%, pushes 57% of the time. -17% is correct. A real dog hand setting.

Dan -

Your attempts to standardize are well intentioned, but I think you're fighting a vertical uphill battle - one which you should probably give up on.

You said yourself that you supplied a better house way with EZPG which got ignored. In this post from the recent Pai Gow dispute thread, Mike said that he had offered to write a new house way when he was working at the Venetian. If he, as the in-house math guy, couldn't get it done, what chance do you have?

Quote: DJTeddyBear

Dan -

Your attempts to standardize are well intentioned, but I think you're fighting a vertical uphill battle - one which you should probably give up on.

You said yourself that you supplied a better house way with EZPG which got ignored. In this post from the recent Pai Gow dispute thread, Mike said that he had offered to write a new house way when he was working at the Venetian. If he, as the in-house math guy, couldn't get it done, what chance do you have?

That said, if managers of new card rooms and casinos are on this site looking for a good house way, there it is for them.

Quote: DJTeddyBear

Dan -

Your attempts to standardize are well intentioned, but I think you're fighting a vertical uphill battle - one which you should probably give up on.

You said yourself that you supplied a better house way with EZPG which got ignored. In this post from the recent Pai Gow dispute thread, Mike said that he had offered to write a new house way when he was working at the Venetian. If he, as the in-house math guy, couldn't get it done, what chance do you have?

1. Mike wasn't the Table Games V.P. at LVS. He should have been, or he should have been given a lot more consideration and respect on these matters.

2. I am aware of both the politics and the resistance (better words to use: "Almost Insurmountable Inertia") concerning modernization of PGP and other game issues and matters, but there IS some new movement and effort - and at this V.P. level - at some operators to both standardize house ways, and to use mathematically sound house ways. (to read: simulations and analyses will be run on PGP house ways instead of using "Dart Boards and Raincoated Rendezvous' " to determine which are the strong and reliable house ways, which I and others have done.)

3. I've been in this [interesting and semi-functional] business a while, and don't undertake something unless it really does have some sort of a shot of not being in vain; I will say that I was already contacted by a big-operator V.P. for an easy-to-deal and mathematically sound house way, (as have others recently, I believe), and the earlier supplied house way herein is strong and accurate, and is expressed in straightforward "house way English." The V.P. who had called me for this is young, assertive, a true up-and-comer, and is very intelligent, and he sees the "dollar sense and savings" on a large scale if done right.

4. On certain game products that require house ways or dealer strategies, we supply "best recommendation" house ways for the products which are mathematically solid and fully reviewed, as well as reviewed for dealer usability. In one case the house way IS a gaming-submitted requirement, that is to say, the local pit boss can't take out a sharpie and say "Hmm.....lemme try something here, here goes...")

Quote: Paigowdan

No. Using Shackleford's WOO PGP player side power rankings, Here are the basics:

KQ/AAxxx = wins 29.25%, lose 22.75%, EV=0.065 (6.5%) pushes 48% of the time. Five-card side = 65%, two-card side=45%. A VERY neutral hand that's just slightly positive and quite volatile. This is not a +25% hand, and NOT much better than playing the straight.

62/AKQJ10 = wins 1%, lose ~ 3%, EV= -0.03, or -3% (you have -2.35%, I ballparked), will push 96% of the time. Five Card side as Broadway straight wins 96% of the time.. Two-card side of 62 wins 1%, loses 99%. Overall it'll push 96%-97% of the time, lose 3%, and win 1%. An extremely stable push hand.

AQ/AK1062 = wins about 13% of the time (beats dog hands only), loses 30%, pushes 57% of the time. -17% is correct. A real dog hand setting.

The EV figures I listed are the accurate results of an exact combinatorial analysis against the Foxwoods house way. Having a Joker-Ace pair is better than having a natural pair of Aces because it means the dealer doesn't have the Joker; this may explain much of the discrepancy. The power ratings on WoO are only a rough guideline since the interaction between the low and high hand isn't taken into consideration. So, sorry to disagree, but an exact combinatorial analysis is more accurate.

The example hand shape I used was: Joker/AK/Q/T62, with a slash separating different suits. The results are:

Split	Win	Lose	Push	EV
WAT62/KQ	21,439,842 (40.06%)	6,758,023 (12.63%)	25,326,815 (47.32%)	+0.254272
AKQWT/62	189,809 (0.35%)	1,440,163 (2.69%)	51,894,708 (96.95%)	-0.023538
WKT62/AQ	9,419,339 (17.60%)	18,199,166 (34.00%)	25,906,175 (48.40%)	-0.172832

Quote: JB

The EV figures I listed are the accurate results of an exact combinatorial analysis against the Foxwoods house way. Having a Joker-Ace pair is better than having a natural pair of Aces because it means the dealer doesn't have the Joker; this may explain much of the discrepancy. The power ratings on WoO are only a guideline since the interaction between low and high hands isn't taken into consideration.

True, having the joker is immense, not just in one's own hand strength, but in what it denies the opponent when you still can't do much with it. I can see playing Joker+Ace as KQ/AAxxx, but I cannot see splitting Joker+Ace into a Pai Gow hand, as all it can beat are lower Pai Gow hands; I'd play a pair of aces with a decent KQ top over a Pai Gow hand setting every time as a player, but as the dealer, I'd play the straight and push through to the next round.

The natural KQ/AAxxx is way below the wild KQ/AAxxx.

Quote: Paigowdan

True, having the joker is immense, not just in one's own hand strength, but in what it denies the opponent when you still can't do much with it.

Agreed.

Quote: Paigowdan

I can see playing Joker+Ace as KQ/AAxxx, but I cannot see splitting Joker+Ace into a Pai Gow hand

Me either, that would be pretty foolish even without knowing the math.

Quote: Paigowdan

as the dealer, I'd play the straight and push through to the next round

It is sometimes said that house ways are designed not to win the most, but to lose the least. Playing the Straight would be in line with that.

Quote: JB

It is sometimes said that house ways are designed not to win the most, but to lose the least. Playing the Straight would be in line with that.

This is so true, but is unpracticed/unaddressed. I see dealers play 6543322 as two split pairs, and win 3 and lose 3 for no gain, and take a TON of time just mucking the rack. Granted, the dealer might lose one (to a flush) with 32/65432, but not lose any to split pairs, trips, full houses split, etc. Cancelled out wins are actually very costly to PGP performance, better to push a full table than churn a full table.

Dan, here's something I didn't notice last time we discussed this.

Your houseway suggests keeping quad Kings or Queens when holding an AJ, AQ or AK, reverts to splitting quad Kings or Queens when holding a pair of 2s or 3s, then reverts BACK to keeping the quads with 4s or higher. What gives there? Is splitting the quads with the 2s or 3s important enough to not just say "Keep quad Kings and Queens when holding AJ or better"?

Quote: Deucekies

Dan, here's something I didn't notice last time we discussed this.

Your houseway suggests keeping quad Kings or Queens when holding an AJ, AQ or AK, reverts to splitting quad Kings or Queens when holding a pair of 2s or 3s, then reverts BACK to keeping the quads with 4s or higher. What gives there? Is splitting the quads with the 2s or 3s important enough to not just say "Keep quad Kings and Queens when holding AJ or better"?

It's very straightforward:
1. keep all quads together if it forms a monster that can sweep the table (Quads with an Ace-Face top or better is always the case), and
2. keep all quads together to prevent having a weak hand (such as playing it as two very low pairs split, but still okay to split if with a zero top).
3. With top high quads and a very low pair, it can be better to split into three pairs, highest pair on top. AAAA338 = AA/AA338, because the better top is a lock, and two pairs ace-high is very strong, too - but it really matters little here. Playing 33/AAAA8 is still a fantastic hand.

examples:
AK / JJJJ4 is better than JJ/JJAK4, as having a pair of Jacks on the 5-card side is only about 50% in strength. With the JJJJ quads, that's about 100% strength on the 5-card side, and the AK top is about a 70% winner. A very strong setting for a monster hand.

Q10 / 33332 is better than 33 / 33Q10 2. While the split will wins against pai gows (the pair of 3's is so weak it'll essentially beat only pai gow hands), the split will also lose to a lot of split two pair hands like (66/99xxx), full houses, flushes with a pair top, etc.

Basically, split quads into two pair hands only when it gets you a DECENT two pair hand, and when the quads have no decent top.
Split QQQQJ72 as QQ/QQJ72, 8888953 as 88/88953, KKKKQ42 as KK/KKQ42, etc.

It is because you often split quads, you may think that you should always split quads. No. You shouldn't split quads at all when you're handed a monster as is.

When it comes to Quads + Pair, I always used the following simple rule...
If the quad is 9 ranks or more than the pair, split the quad.

J J J J 22
QQQQ22 or 33
KKKK22 or 33 or 44
AAAA22 or 33 or 44 or 55

98clubs, this is very good; I get just K's and Aces with 2's or 3's, but quads with a low pair are so rare, and settings so close, it's fine to go.

Ok, Dan. I see your point about splitting the quads when you can have two pair down. That said, unless the edge is increased substantially for those two hands ( KKKK/22, KKKK/33), I think if I were in charge of allocating a houseway for a casino, I would rather just go ahead and keep those quads with the lower pair in the interest of simpler houseway. Because as you said...

Quote: Paigowdan

3. With top high quads and a very low pair, it can be better to split into three pairs, highest pair on top. AAAA338 = AA/AA338, because the better top is a lock, and two pairs ace-high is very strong, too - but it really matters little here. Playing 33/AAAA8 is still a fantastic hand.

In fact, you can consolidate your two Quads rules into one if you make that concession. This...

Quote:

Four of a kind with a pair:
a. Split four Aces or Kings 2 & 2 with a pair of 3�s or 2�s, to play Aces or Kings on top, else keep all other four of a kind hands together with any pair for the top.

Four of a Kind with no pair:
a. Always split four Aces 2 & 2.
b. Keep ALL four of a kinds together with an AJ, AQ or AK top, including 4 Kings.
c. Always split four Kings or Queens with an A-10 or less.
d. Keep four Jacks or 10�s with any Ace top, else split 2 & 2.
e. Keep 7�s through 9�s together with any King or better top, else split 2 & 2.
f. Keep 6�s and lower with a Queen or better top, else split 2 & 2.

...becomes this...

Quote:

Four of a Kind:
a. Twos through Sixes: Split unless holding any Queen, King, Ace or additional pair.
b. Sevens through Nines: Split unless holding any King, Ace or additional pair.
c. Jacks or Tens: Split unless holding any Ace or additional pair.
d. Queens or Kings: Split unless holding an AJ, AQ, AK or any additional pair.
e. Aces: Split unless holding an additional pair of Fours or higher.

deleted

Quote: Deucekies discussing...

This is simpler:
Four of a Kind:
a. Twos through Sixes: Split unless holding any Queen or better.
b. Sevens through Nines: Split unless holding any King or better.
c. Jacks or Tens: Split unless holding any Ace or better.
d. Queens or Kings: Split unless holding an AJ, AQ, AK or any additional pair.
e. Aces: Split unless holding an additional pair of Fours or higher.

Yeah, good and short.

Interesting notes:
1. The difference between 22/KKKKx and KK/KK22x is about 2% in EV, from about 76% to 74%, both monster hands. But since you'll see quad kings once in 6,500 hands where it'll make that 2% difference, - AND assuming a low pair present every time - this'll amount to making a difference once in 325,000, or 0.000308% if you had the extra 2's every time. The extra print and training is not worth inserting anything more complicated into a dealer's house way. What you pick up with Kings on top with the two-pair in the 5-card side (KK/KK22x) is equally lost by not picking up hands against someone with trips, a flush, or straight with no top against 22/KKKKx.

2. It is better to play KKKKA73 as AK/KKK73 (when you have quad kings with an Ace-low instead of an AJ/AQ where you keep the quads) than KK/KKA73. However, AAAAK73 is played as AA/AAK72, as an ace top facing you is unlikely, but a pair top facing you is more likely. Again, would it really matter in house edge effect if playing AK/KKK73 versus playing KK/KKA73? No.

3. The only thing that really matters with quads is the cut-off points for splitting 2+2 versus keeping quads. The above does it. Good job, Deucekies.