Pai Gow Tiles: Wizard Way Strategy
I count gongs as 10, wongs as 11, and mixed pairs as 12. So playing the 4/pair is worth a total of 16, whereas the 7/7 has a total value of 14.
In my practice playing the Wiz' simulator (Thanks Wiz!), there's one key rule that I've learned: Never split pairs. Yeah, maybe there are statistical exceptions, but certainly for a newbie, never split them.
Of course, one of the biggest problems I'm working on, is recognizing those few unmatched pairs, and excluding other unmatched tiles that look like they should be pairs, but aren't.
As for the mixed pairs, the 9's and 5's are easy because they only have an unmatched pair. I'd focus on the matched eights - the 4/4 "yun" tiles - and the matched sevens - the 1/6 "tit" tiles. The mixed pairs are the other eights and sevens.
Pair/4 = 83 + 40 = 123
7/7 = 31 + 81 = 122
Well, that didn't help my case. I think what JB would say is that the power ratings don't consider the effect of removal of the other two tiles. With a teen and day removed, it is more unlikely the dealer will make a wong or gong, depressing the value of the pair. It only needs to be lowered by 2 points to make 7/7 the better play. I'll alert JB to this thread. I think he once spoke about this exact hand to me, but I don't remember what he said. However, I think it will be along the lines of what I just wrote.
Another possibility (though unlikely to be the case here) is that a strategy for play will have to differ from optimal play sometimes in order to be reasonably memorized by a human.
If the dealer has a pair you are very likely beat. Splitting means you have the highest 7 possible on both hands which will require the dealer to have at least an 8 on the low to beat you. Unlikely they have the other teen and/or day.
This is one of my favorite combinations because there is more than meets the eye. Keep in mind that a Gong is worth 10 points, a Wong is worth 11, and a pair is worth 12. That means that keeping the 5's together (playing 4/Pair) is worth 16 points, but splitting them to play 7/7 is only worth 14 points -- or so it would seem. But this is a unique situation. Splitting to play 7/7 with this particular combination is actually like playing 8/8. The reason why is because you have both 5's, so neither 7-point hand can copy, regardless of whether the dealer has a Teen or Day. And since it plays like 8/8 it is considered a 16-point play, just like 4/Pair, except the weight is evenly distributed among both hands.
Furthermore, your low hand is one rank higher than a Yun 7 (a High 8 with a 9). Having a Yun 7 in the low hand is a bit of a holy grail in this game, because it wins the low hand comparison more than 75% of the time.
Quote: AussieI would split this hand for sure.
If the dealer has a pair you are very likely beat. Splitting means you have the highest 7 possible on both hands which will require the dealer to have at least an 8 on the low to beat you. Unlikely they have the other teen and/or day.
This makes sense to me. Because the 2 and 12 have been removed from the deck, it is much less likely that the dealer will get a gong or wong in their high hand. This decreases the likelihood that the pair is a winner in the 4/pair combination, and increases the likelihood that the high 7 is a winner in the 7/7 combination.
Without considering removal of the 2 and 12, I'd consider this decision to be a wash, or slightly in favor of the 4/pair. Including removal, it seems that the advantage shifts considerably toward the 7/7.
1. Does the caclulator take into account the tiles the player has? That is, if I look at this hand, does the calculator take into account that I have a teen and day? If so, then the calculator numbers are what counts and the analysis, above, - as incredibly helpful as it is to gain intuition - is secondary.
2. Your comments about there not being a copy, so it plays like an 8/8 are interesting. I agree that this means it will beat all other 7's, but it also loses to all other 8's, so not sure I buy into this being a 16 point hand. I get it, but don't completely buy in. Not saying I don't buy into splitting the fives (which I do), just not that it is a 16 point hand. I may be splitting hairs here.
3. The stat about Yun 7 wins 75% of low hands is a great stat. I've always wondered how certain hands will do as high or low hands. The charts with the strategy definition are great for that too.
Quote: PaiGowFanThanks WIzard and JB. This is great analysis. A couple of follow up questions...
1. Does the caclulator take into account the tiles the player has? That is, if I look at this hand, does the calculator take into account that I have a teen and day? If so, then the calculator numbers are what counts and the analysis, above, - as incredibly helpful as it is to gain intuition - is secondary.
2. Your comments about there not being a copy, so it plays like an 8/8 are interesting. I agree that this means it will beat all other 7's, but it also loses to all other 8's, so not sure I buy into this being a 16 point hand. I get it, but don't completely buy in. Not saying I don't buy into splitting the fives (which I do), just not that it is a 16 point hand. I may be splitting hairs here.
3. The stat about Yun 7 wins 75% of low hands is a great stat. I've always wondered how certain hands will do as high or low hands. The charts with the strategy definition are great for that too.
1. Yes, absolutely. It loops through all the ways the dealer could get 4 tiles out of the remaining 28.
2. That was more of a memory device. The program doesn't go by points, but exact probabilities. That is why it gives you exact expected value figures.
3. Not that you asked, but the median high hand is a 9 with the 1-3 tile, and the median low is a 5 with the 1-3 tile.
Quote: PaiGowFanYour comments about there not being a copy, so it plays like an 8/8 are interesting. I agree that this means it will beat all other 7's, but it also loses to all other 8's, so not sure I buy into this being a 16 point hand. I get it, but don't completely buy in. Not saying I don't buy into splitting the fives (which I do), just not that it is a 16 point hand. I may be splitting hairs here.
It is the equivalent of playing the lowest-ranking 8-point hand possible. Normally the lowest-ranking 8-point hand is a 5 with a joker. Since you have both 5's, your opponent cannot make that hand either. Therefore your high 7's assume the position of the lowest-ranking 8-point hand.
It helps to keep in mind that point totals are somewhat arbitrary, because not all point totals have the same number of ways to make them. Normally, there are 10 rankings of 7-point hands and 8 rankings of 8-point hands. With both 5's removed (because they are in your hand), there are only 8 rankings of 7-point hands and 7 rankings of 8-point hands. By reassigning where each point total begins and ends due to the tiles in your hand, it starts to make sense why that particular 7/7 can be thought of as 8/8.
Quote: PaiGowFanThanks for the added analysis. I appreciate it. I love the game and the better I understand it, the more I'll enjoy it.
You're welcome.
If I may digress a bit, another of one my favorite combinations is Teen and Day with a red 8 and an 11. Probably 99.99% of players will play 3/Gong (with the 12 in the high hand). Perhaps surprisingly, the best play is 4/9 (Teen and Day in the low hand, red 8 and 11 in the high hand).
I have been dealt that combination a few times, but one in particular stands out in my memory. There was myself and one other player at the table. When I got my tiles and saw what they were, I set them as 4/9, and as I did so I said to the dealer, "You're probably going to laugh at me for doing what I did" (of course, she didn't know what my tiles were at that point).
She then flipped over her tiles: 4, 5, H7, L7, which has only one way to play: 4/9. I had the higher 4 and the higher 9, resulting in a win, whereas 3/Gong, the 'logical' play, would have only pushed. She was dumbfounded and confused well into the next hand, and told me that it was a "risky move" to have done that. I couldn't help but wonder if they thought I was cheating, but I was only betting the table minimum anyway.
But again, this is a case where, with a Teen and Day removed, the chances of the dealer having a High Nine are reduced, and the next-highest nine is the one I played, a Yun 9. It's almost the same as playing a High Nine instead of a Gong in order to boost the low hand.
Quote: JBBut again, this is a case where, with a Teen and Day removed, the chances of the dealer having a High Nine are reduced, and the next-highest nine is the one I played, a Yun 9. It's almost the same as playing a High Nine instead of a Gong in order to boost the low hand.
I have played pai gow for 25 years and have always played the "traditional" way. Having a strong math/comp sci background, I've always thought about doing the analysis to take into account the impact of taking my tiles out of the house's universe. Haven't had the time. In any case, your analysis makes perfect sense. In this case, you are taking minimal risk on the high hand - given you have 2 of 4 teen/day tiles - while upgrading your low materially.
This brings me to something I have been "struggling" with as I study your strategy. The traditional way generally leans towards balancing the high and low hands. Your strategy very often leans the other way - maximizing the high hand at the cost of lowering the low hand. I'd love your thoughts on this. I'd like to boost my understanding/intuition for this. I don't think taking into account my tiles and it's impact on the house's possible hands is driving this shift. I'm guessing it has more to do with factoring in the house way. That is, factoring in your knowledge of how the house will play its hand. Is that it?
Rule 5: "...If given a choice between Low 7 and High 7, play the High 7 in the low hand if it will improve it."
It does not matter which 7 you include in the the high hand. Is there a reason why you do not simplify the rule and say to play the high 7 in the low hand all the time?
Rule 6: "Play a Low 8 Gong whenever possible, except when you also have a High 8 and cannot use it to make a low hand of 7 or better..."
Same type of question. It does not matter to the high hand which 8 you play in the Gong, so why not simplify the rule and say to play the High 8 in the low hand all the time?
I just want to make sure I'm not missing anything.
Quote: PaiGowFanRule 5: "...If given a choice between Low 7 and High 7, play the High 7 in the low hand if it will improve it."
It does not matter which 7 you include in the the high hand. Is there a reason why you do not simplify the rule and say to play the high 7 in the low hand all the time?
The last bit is there just for clarification, in case a beginner is reading it. I think it's better to encourage someone to learn the difference between when it matters and when it doesn't. (You obviously already know the difference, which is good.)
Quote: PaiGowFanRule 6: "Play a Low 8 Gong whenever possible, except when you also have a High 8 and cannot use it to make a low hand of 7 or better..."
Same type of question. It does not matter to the high hand which 8 you play in the Gong, so why not simplify the rule and say to play the High 8 in the low hand all the time?
You may have a valid point. I will have to dig through the data to see why I worded it the way I did. The toughest part was not the analysis itself, but trying to put the strategy into words without introducing any ambiguities. I remember carefully crafting each rule, based on the previous rules having been followed correctly. I'm inclined to think that there must have been a reason why I worded it that way, though I can't at the moment think of any combination where your version wouldn't apply. Stay tuned...
Quote: DJTeddyBearThis may not apply to PG Tiles, but a pit boss at PG Poker once told me that "house way" is not to maximize the house's chance of winning the most hands, but to minimize the house's chance of losing. I grant you it's subtle, but....
I think you're right about the house way. In fact, the house is playing multiple people at the same time, while we are playing one-on-one. However, I have read books on the "traditional" way, which is supposedly how most players are supposed to play - I guess the way it has been learned over centuries without computers.
Quote: PaiGowFanRule 6: "Play a Low 8 Gong whenever possible, except when you also have a High 8 and cannot use it to make a low hand of 7 or better..."
Same type of question. It does not matter to the high hand which 8 you play in the Gong, so why not simplify the rule and say to play the High 8 in the low hand all the time?
Without even looking at the data, a quick run through of all possible 4th tiles seems to indicate that the simpler rule is just as accurate. When three tiles are H8, L8, and 2 or 12, the best play with each possible fourth tile is:
11 = covered by rule #3
10 = covered by rule #3
8 = covered by rule #2
7 = covered by rule #5
12 = covered by rule #2 or #3
2 = covered by rule #2 or #3
9 = H8+ 9 in the low hand (7/Gong)
6 = H8+L8 in the low hand (6/8)
GJ = H8+L8 in the low hand (6/8)
5 = H8+L8 in the low hand (6/7)
4 = H8+L8 in the low hand (6/6)
Therefore it would be correct to change the rule to:
"Play a Low 8 Gong whenever possible, except play the best low hand if you also have a High 8. If given a choice between 2 and 12, play the 12 in the high hand."
Quote: PaiGowFanThanks JB. Any thoughts on what I'm noticing regarding your strategy/optimal strategy boosting the high hand (at the expense of the low hand) relative to the "traditional" way? I'm sure your numbers are right. I'm just looking for some intuition.
A lot of it has to do with trying to push instead of playing 2 lousy hands. If the house doesn't have a High Nine/Gong/Wong, then they almost always play the best low hand.
This is rarely good for the player unless it's a fairly decent low hand (5, 6, or 7 points, as long as it doesn't waste a high tile). For example, with 5-6-8-9, the house will play 4/4 but that's a terrible hand for the player, as it is almost guaranteed to lose. 1/7, on the other hand, will push (and in some cases win) if the dealer has 0/7, 1/2, 1/3, 1/4, 1/5, 1/6, 2/2, 2/3, 2/4, 2/5, 2/6, 3/3, 3/4, 3/5, 3/6, 4/4, 4/5, 4/6, 5/5, 5/6, or 6/6, and sometimes any low hand with a 7-point high hand that ranks lower than yours. The value of pushing often outweighs the value of trying to go for a win with two weak hands.
The house never loses their full bet -- that is, when you lose, you lose 100% of your bet. When the house loses, they only lose 95% of their bet. The commission depresses the value of a win. If there were no commission, the optimal strategy would be more aggressive with the low hand than it is since a win would be worth more.
And while I can't be 100% sure, I think some of it also has to do with trying to do the opposite of what the dealer does, to protect your bet in the event of a copy if you were to play using the same strategy the house uses.
Quote: PaiGowFanThanks JB. Any thoughts on what I'm noticing regarding your strategy/optimal strategy boosting the high hand (at the expense of the low hand) relative to the "traditional" way? I'm sure your numbers are right. I'm just looking for some intuition.
My thought process works like this: If I have a below average hand (total points less than 12, for instance), I'm not really planning to win the hand. I want to maximize my chance of a push. The dealer will play these hands to maximize the low hand at the expense of the high hand. If I want to achieve a push, my best bet is to maximize my high hand, and play my strength against the dealers weakness.
This logic works really well for a weak hand against a weak hand. But it backfires on dealer hands with gongs, wongs and pairs, where the low hand is sacrificed resulting in 1's and 2's. So ultimately the value of this strategy depends on how often the dealer is maximizing the low hand, vs. how often he/she is sacrificing the low hand.
One of the things that fascinates me about this game is that it has existed for thousands of years. Yet computer analysis is just now uncovering new and improved ways to play.
Quote: AussieI emailed the wizard some time ago about the effect of strategy changes made when you know how many teens or days other players have. What effect would knowledge of other specific tiles make? Is it possible that the pai gow calculator could have a funtion whereby you tell it what other tiles you know are out and give adjusted EVs accordingly?
Anything is possible, but I don't plan on it. JB says there is not that much to gain by knowing if other players have the teen/day tiles.
Quote: AussieI emailed the wizard some time ago about the effect of strategy changes made when you know how many teens or days other players have. What effect would knowledge of other specific tiles make? Is it possible that the pai gow calculator could have a funtion whereby you tell it what other tiles you know are out and give adjusted EVs accordingly?
I actually studied this for a bit, and quickly came to the conclusion that it is definitely not worth the effort, for several reasons: the reduction in house edge is tiny, the opportunity to see another player's tiles AND to see a Teen and/or Day among them is rare, and the strategy changes are so scattered and nuisance-like that they would be impossible to remember.
Here are the reductions in house edge if you learn every single strategy change:
Seeing a Teen in another player's hand: 0.07%
Seeing a Day in another player's hand: 0.08%
Seeing a Teen and Day in another player's hand: 0.35%
Keep in mind these are merely reductions in the house edge, and are not sufficient enough to gain an advantage overall.
Quote: JBI actually studied this for a bit, and quickly came to the conclusion that it is definitely not worth the effort, for several reasons: the reduction in house edge is tiny, the opportunity to see another player's tiles AND to see a Teen and/or Day among them is rare, and the strategy changes are so scattered and nuisance-like that they would be impossible to remember.
Here are the reductions in house edge if you learn every single strategy change:
Seeing a Teen in another player's hand: 0.07%
Seeing a Day in another player's hand: 0.08%
Seeing a Teen and Day in another player's hand: 0.35%
Keep in mind these are merely reductions in the house edge, and are not sufficient enough to gain an advantage overall.
I agree that it is very unlikely that you will (1) see another player's tiles and (2) that will be the hand where the player has a teen and/or day in his hand and (3) that it is a hand where you have choices and you would switch your choice based on the knowledge that the house is less likely to have a teen/day.. It's not worth learning how to adapt to it. In fact, the casinos do not allow players to show other players their tiles or talk about their tiles and they are very serious about this.
Quote: AussieThe reason I asked the wizard originally was because the casino I play it in for whatever reason rarely seems to enforce the no talking rule. The players most hands will tell each other how many teens or days they hold.
What casino do you play at? I think it is a big advantage to know how many teens/days are out.
For example, the pair of fives, teen, day example JB gave earlier in the thread. It's slightly better to split the fives if you only know your hand, but if you know one or both of the other teen/day are out, it's a no brainer.
"Whenever possible, play 5/7, 6/7, 7/7 instead of high nine when the tiles include a 2 with any 4, 5, or 8."
If you have a high nine with a 2, you also have a 7. You can get to a 5/7 if the last two are a 5 and an 8. I get that. Are you saying with a 5 and 9, you make a 6/7 and with a 5 and 10, you make a 7/7?
Quote: PaiGowFanIf you have a high nine with a 2, you also have a 7. You can get to a 5/7 if the last two are a 5 and an 8. I get that.
I think you uncovered a typo in that exception. 5/7 should only be played when the 8 is a high 8 (play 2/Gong with a low 8).
Quote: PaiGowFanAre you saying with a 5 and 9, you make a 6/7 and with a 5 and 10, you make a 7/7?
No and yes, respectively. The 6/7 that you can make with a 5 and 9 was an oversight (the best play is 2/Wong). 6/7 should only be played with a 4 and 10. So, the corrected version would be:
Play 5/7 with H8 and 5
Play 6/7 with 10 and 4 (even L10 and H4, as wasteful as it appears to be)
Play 7/7 with 10 and 5
When I came up with that strategy, I was still somewhat new to Pai Gow. I may spend some time putting together a better strategy now that I a have a thorough understanding of it. If I do, I'll probably make it against the Traditional Way (that most Vegas casinos use, with some variations) as opposed to the Foxwoods house way.
Quote: JBI may spend some time putting together a better strategy now that I a have a thorough understanding of it. If I do, I'll probably make it against the Traditional Way (that most Vegas casinos use, with some variations) as opposed to the Foxwoods house way.
That would be great. I'd love to see it. I'm not sure there would be material changes though. The Traditional way also maximizes the low hand at the expense of the high hand. I'm liking the slightly more aggressive approach and I'm going to try it when I hit Vegas in a couple of weeks.
I was practicing and got a high 8, high 4, high 10 and low 8. Following the rules for a 10 point hand, I think I should play the best high, which is H4/L8 and H8/H10 for a 2/8. The calculator shows that the 4/6 is slightly better. Am I missing an exception here?
In case it isn't obvious, none of the strategies list every single exception, because there are far too many.
Quote: DeMangoIs there a book maybe at the Gamblers bookstore on paigow tiles that you all reccomend?
Not a book, but I recommend the tutorials at www.paigow.com.
Quote: PapaChubbyNot a book, but I recommend the tutorials at www.paigow.com.
I highly recommend www.paigow.com. It is a great way to learn the game and the traditional strategy. After you feel you understand the traditional strategy, you should read the Wizard and JB strategies - which are better. By better, I mean over the long term statistically the Wizard and JB strategies should do better. That being said, there is a lot to be said for ease of use and the traditional strategy is easier to use. If you are not playing a lot, I suggest using the traditional strategy and not worrying about that last fractional percentage. Just my opinion, but I am getting far more out of the Wizard and JB strategies because I have played for a number of years and really understand distribution of hands and the rankings of the tiles and how they impact the values of the hands and your choices.
Quote: PapaChubbyMy thought process works like this: If I have a below average hand (total points less than 12, for instance), I'm not really planning to win the hand. I want to maximize my chance of a push. The dealer will play these hands to maximize the low hand at the expense of the high hand. If I want to achieve a push, my best bet is to maximize my high hand, and play my strength against the dealers weakness.
This logic works really well for a weak hand against a weak hand. But it backfires on dealer hands with gongs, wongs and pairs, where the low hand is sacrificed resulting in 1's and 2's. So ultimately the value of this strategy depends on how often the dealer is maximizing the low hand, vs. how often he/she is sacrificing the low hand.
This thought process intrigues me. I find myself falling back to the traditional way a lot, but not really wanting to memorize a detailed alternate strategy (I gamble for entertainment mostly, although it's more entertaining to win to be sure!). When playing against the house way, and assuming an adequate knowledge of tile and hand rankings, are there any simple rules one can use to help reduce the house edge without resorting to a more detailed strategy?
Quote: RodneyWhen playing against the house way, and assuming an adequate knowledge of tile and hand rankings, are there any simple rules one can use to help reduce the house edge without resorting to a more detailed strategy?
I have to give credit to the Wizard and JB, but here are my thoughts based on their strategies...
1. What gives the house it's real edge is the commission. If you can trade a few wins a losses for pushes, you save a lot on commissions.
2. If you have a clearly good hand, you want to play. If you have a clearly bad hand, you have no choice, but to play. If you have a middling hand and can trade it for a push, you do.
Sorry if I have been stating the obvious.
Wizard said that the most likely high hand for the house is a 9 with a high 4 and the most likely low is a 5 with a high 4.
The traditional strategy maximizes the low hand for most hands if the low is above a 3 with a high 6 (Chong). Not doing math here, but if the house is most likely to get a low hand of 5 with a high 4, then you are wasting high hand power pushing up the low if it is better than 3 with Chong and lower than a solid 5.
What I notice about the Wizard and JB strategy is that they push the low hand up to a 5 or better or do not try. They also try to get the high hand at or above the high 9 level.
So, to answer your question, if you are using the traditional strategy and have 9-12 points, you may want to consider using the highest high hand instead of the highest low hand. THIS WILL NOT MATCH THE WIZARD OR JB STRATEGY. I am way over simplifying. However, I think this will capture a lot of the spirit. That is, you will do a lot of 0-3/9, 0-2/Gong, 0-1/Wong as opposed to 4/5, 4/6 or 4/7, etc...
Quote: PaiGowFanWizard said that the most likely high hand for the house is a 9 with a high 4 and the most likely low is a 5 with a high 4.
<snip>
What I notice about the Wizard and JB strategy is that they push the low hand up to a 5 or better or do not try. They also try to get the high hand at or above the high 9 level.
This is the sort of information that makes me think. What would be the value to a casual player to play with this information as an assumption? Is there anything to be gained by playing to beat a 4H/9, and it that's not possible, to beat a 4H/5 as a sort of simple priority system when the play of your hand it not otherwise obvious?
I'm really enjoying this thread. Pai Gow has become my favorite table game, hands down. My thanks to everyone who has contributed!
Quote: RodneyThis is the sort of information that makes me think. What would be the value to a casual player to play with this information as an assumption? Is there anything to be gained by playing to beat a 4H/9, and it that's not possible, to beat a 4H/5 as a sort of simple priority system when the play of your hand it not otherwise obvious?
For the casual player, it does not make much difference. I go to the casino once or twice a year for a long weekend - playing 20-40 hours of Pai Gow tiles each year. I'm not sure it makes much difference to my bottom line, but I play Pai Gow because it is an interesting game, so I like to think about these issues and use them.
Again, I want to stress, what I am discussing is purely my intuition on what is happening with the Wizard and JB strategy. This is not a substitution for actually reading/studying their strategies. Additionally, if you want the actual prbabilities, you can use the Pai Gow calculator.
Suppose I have a nine point hand and I can choose between a 4/5 and a 0/9. CLearly, if the house has a 5/gong or above, it does not matter what I do. I'm looking at the block of house hands in the 4-15 point range where the house is likely to maximize the low hand, at the expense of the high hand, and play a 2/2 to a 7/8. If I play a 4/5, I beat the 2/2, 2/3, 2/4, 3/3, 3/4 and some 2/5, 3/5 and 4/5 hands. I will lose to 5/6, 5/7, 5/8, 6/7, 6/8, 7/8 and some 4/5 hands. You get the idea. If I would win half and lose half, I end up paying the commission on half the hands. If I play the 0/9, I push all of them and do not pay any commission. I know I am way over simplifying.
Why does the house play the middling hand? It makes sense for the house, because they get the commission. The house is happy to win half and lose half the hands on every deal.
Pair/4 EV = .280537
8/8 EV = .359004
There were no Asian players to laugh at me, but the dealer rolled her eyes and said "It's your money, do what you want."
Did your decision give you a better result than the alternative?
