Pai Gow cost of strategy errors

Does anyone know of a study of the cost of strategy errors in Pai Gow? Usually people will ask the dealer for the 'house way' in no obvious cases, but i also know people will play three of a kind wrong and not think anything of it, or other cases as well (small two pairs). I am curious how much this increases the house edge.

Cheers!

If you're talking about Pai Gow Poker, then Yes. I did this with my mathematician while developing EZ Pai Gow. I would have to dig this up. It can add up to about 0.5%+ over a poor house way or strategy.

If your talking about Pai Gow tiles, see this.

Basically for PKP, the most important plays:
1. Properly playing two pairs;
Basically, best two pair strategy shortened down and excapsulized is:
* Always split Ace-high two pairs;
* Always split Jacks and 7's or better, except when having exactly AK for the top, then keep all two pairs together with an AK top.
* Keep low two pairs (6's and less) together with a king or better, else split.
* Always split all other two pairs except when having an Ace.

2. Straight and/or flushes with no pairs:
* Straight and flush together: Play the one with best top, except when both tops are J or less, then play the stronger flush.

3. Straight and/or flush with one pair;
* Play as one pair if a face-card pair can be played with an Ace and a face top, AND IF the straight or flush has a Queen or less top. Always Play the straight or Flush if it has at least a King or better top.

4. Straight or flush with two pairs: play as two pairs except if a straight or flush can be played with an AQ/AK top; else always play as two pairs.

5. Three of a kind: split 3 Aces, keep all lower trips together.

6. Full house: Always split, unless pair is 5's or less and an AK top can be played, 4's or less with an AQ top.

6. Four of a kind:
a. Always split four Aces 2 & 2, unless there’s a pair of 4’s or better for the top.
b. Keep all 4-faces (K, Q, J) with an Ace-Jack or better, else go to next step, c.
c. Split four K’s or Q’s 3 & 1 with an Ace-low (for an AK/AQ top), else split 2&2.
d. Keep 10’s or Jacks together with any ace or pair for the top, else split 2 & 2.
e. Keep 7’s through 9’s together with any King or Ace top, else split 2 & 2.
f. Keep 6’s and lower with a Queen or better top, else split 2 & 2.

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

12. Five aces: Always play a pair of aces up. Don't worry about the hand Five Aces and two Kings.

This is what we got with an optimal Pai Gow Poker strategy that can be fit onto one page.

Most important is properly playing two pair hands well, then straights and flushes.

For an exhaustive strategy, see or buy the book "Optimal Play for Pai Gow Poker" by Stanford Wong.

I would like to add

If your Straight, Flush, or Straight-Flush is also THREE Pairs, to play the hand as three pairs. (NOTE: one of the pairs is Ace-Joker)

Three Pairs: Play the highest pair as the 2-card hand. (This is a very strong hand)

Pai Gow Poker has some unusual hands like two triples (Play the high pair as 2-card hand), Quads with a Triple, Three Pairs, Two Pairs that are also a Straight, Flush, or Str-Fl, Triples and Full Houses that are also Str, Fl, or Str-Fl. The Odd-Ball stuff can throw you off if not careful, but the cost of such errors is minimal due to their rarity.

Its tuff to distill this "cat and mouse game" to one page, but Dan's work is the best I've seen at one page.

My way... which is close to Dan's ... arrived at independently

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

Quad + Triple: Play the high Pair in front.

Quad + Pair: The Pair plays in front.

Quads: TTTT = Four Tens, split = Pair + Pair
1.) 2222, 3333, 4444, 5555: do not split.
2.) 6666, 7777, 8888, 9999: King or Ace with best non-quad plays to front, else split.
3.) TTTT, J J J J, QQQQ: Ace with best non-quad plays to front, else split.
4.) KKKK or AAAA: Split, EXCEPT play KKK + AK, OR play AAA + AK.

[Str-Fl, FL, or Str] containing one Pair or better: Best [choice] 5-card hand + Pair.

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

Full House or Two Triples: Play Low Triple + Pair,
EXCEPT Play Ace-Face in front of any Full House with a Pair ranked 4-4 or less.

[Str-Fl, FL, or Str] that is also Three Pairs: Play as Three Pairs (see below).

[Str-Fl, FL, Str] that is also Two Pairs: Play as Two Pairs (see below)

[Str-Fl, FL, or Str]: Play the [choice] 5-card hand + best two cards.

Triples: Best two non-triples play to front, EXCEPT AAA plays as AA + Ace-best.

Three Pairs: Play the highest Pair to front.

Two Pairs: split = High Pair with others + Low Pair
1.) High Pair AA or KK: Always split.
2.) Low Pair 10-10 or better: Always split.
3.) High Pair 88 through QQ: Play Ace with best non-pair to front, else split.
4.) High Pair 33 through 77: Play King or Ace with best non-pair to front, else split.

One Pair: Play the Pair and three lowest ranks as the 5-card hand.

High Card (Pai Gow): Play the 2nd and 3rd highest ranks to front.

Quote: Paigowdan

excapsulized

Why is this thing that only looks like a word in bold?

Otherwise, your answer seems very thorough.

Quote: Paigowdan

If you're talking about Pai Gow Poker, then Yes. I did this with my mathematician while developing EZ Pai Gow. I would have to dig this up. It can add up to about 0.5%+ over a poor house way or strategy..

Excellent, thank you PGD. By the way, yes I was talking about Pai Gow Poker, and also I really have enjoyed your "EZ Pai Gow", nice work on that one!

Dr. E = you're very welcome!

Quote: dwheatley

Quote: Paigowdan

excapsulized

Why is this thing that only looks like a word in bold?

Otherwise, your answer seems very thorough.

Consider these things Rice Wine related..... "condensed" or "in a nutshell" didn't have the juice in a word I was looking for.....

Quote: 98clubs

4.) KKKK or AAAA: Split, EXCEPT play KKK + AK, OR play AAA + AK.

Very Fine way to play quads King with an ace-low, or Four aces with a King. About the same EV, but balances the hand nicely. I am always happy to play trips+ on the bottom with an AK or better top. It's having just a single pair on the five-card side that really bothers me, even if AA or KK, as a single-pair five-card side in Pai Gow Poker is not that strong, really. Edit: actually, Four queens with an ace-low is also better as AQ/QQQxx. But...AJJJJ72 is better as A7/JJJJ2.

Several weeks ago I was dealing Pai Gow (usually I'm on craps) and a lady had the hand KKK222A; she asked me how to play it. I told her the house way is KK/222AK, but to play it as AK/222KK as a lark, because nothing burns me more than pushing a dealer's flush or straight if I could have found a strategy way to win, and the full house down just ain't gonna lose; it would also stomp the crap out of a typical hand I get away. I said "Try it, because I always seem to get the flush or straight with no top whenever a player has either three pairs or a split full house. Trust me, - Here's YOUR chance to throw a dart at Murphy's Law....." She loved that.

She played it AK/222KK.

I had A9/<heart flush>. She beat the house on this hand with my blessing and laughter.

And who said Paigowdan is a house pet??

That reminds me... One time in Foxwoods a few years ago a newbie sat next to me and was doing ok. But after I played my hand he turned to me and asked about this one AAAA22Q. My instinct was AA22Q/AA, getting the Aces into the 2-card hand. But AAA22/AQ aint bad either (considering he had 4 Aces) He went with what I have printed, actually, as AAAAQ/22, and promptly pushed a split 88/77 dealer hand.

Quote: 98Clubs

That reminds me... One time in Foxwoods a few years ago a newbie sat next to me and was doing ok. But after I played my hand he turned to me and asked about this one AAAA22Q. My instinct was AA22Q/AA, getting the Aces into the 2-card hand. But AAA22/AQ aint bad either (considering he had 4 Aces) He went with what I have printed, actually, as AAAAQ/22, and promptly pushed a split 88/77 dealer hand.

No. If you were going to do that, then 22/<four Aces> beats AQ/full house every day. AQ/AAA22 is weaker on both sides, why do it?
Pair/<Quads>, versus Ace/<Full house>?

As AQ/AAA22 he still would have won against a dealer's A10/88773 with that AQ/AAA22 setting, also a typical hand. Still a monster.

I would have gone with AA/AA22Q, then 22/AAAAQ, but never AQ/AAA22.
You notice the high four of a kind with a loose Ace; but Four of a kind with a pair is different, - always play some pair on top, one way or another.

Monster hands can blind.

My advice was AA22Q/AA or AAAAQ/22.

My reason for asking about the Full House/AQ was although the FH is weaker than Quads, percentage-wise I think its 1/2% weaker, and covers Straights and Flushes also. But that is one-sided thinking in a double-handed game. There was a good chance that two small pair would be split, spoiling the monster, but with the Joker still not seen, a Dealer Straight or Flush could not be excluded.

True; the thing is, when spliting a monster, getting an AK or AQ top with trips or better is generally superior to a pair top and a big pair of aces or kings on the bottom. This is the weakness of two-pair rules in PGP. A pair of aces is only 67% on the five-card side, and Kings more like 60%. Still good, but not a "stopper." This is the problem with splitting up for of a kinds to get a pair on the bottom. I once had to split the hand KQ77773 as 77/77KQ3 by the house way. KQ/77773 was the way to go.

Just about all facing Players splitting a full house, or splitting something like Jacks and 10's, or playing a three-pair hand, would cream the hand 66/77KQ3, - and so would also cream 77/77KQ3 when it would otherwise be unbeatable as quads, and win many hands with the "almost Ace" KQ top.

The full house on the five-card side is 99%, and quads or better is about 100% unsplit.

Splitting Quad Kings or Aces into Trip Kings or Aces still ives an 88% bottom, also a stopper, and a strong AK top, just great balanced hand. Even split four Queens with an Ace-low as AQ/QQQxx as best play. But play AK/QQQQx, and AJ/QQQQx.

If you can find an excuse to keep quads together (such as an ace top), or splitting for three-of-a-kind kings or aces, you'll be in better shape, as an AK top is about as strong on the two-card side as a pair of aces is on the five-card side, but the monster on the bottom gives the hand a lock.

Playing quads very well gives little to the player's percentage, (as four of a kinds are about 1 in 500 hands, or 0.2% of the time), but shows PGP acumen. Keeping quad jacks together with an Ace gives the best play, as does splitting 4 Kings with an loose ace as AK/KKKxx. With 8's or less, keep together with a King.

But it is always just slightly better (and immaterially so) to split 4 aces as 2 & 2, without a pair of 5's or better for the top. With 4's or less, the best play is really AA/AA44x, but by a tiny amount %.

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