Surprising pai gow tiles hand
December 12th, 2012 at 12:02:15 AM
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December 12th, 2012 at 4:32:39 AM
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The surprising part to me is that 6/7 has a 31.2% chance of winning. That's the only reason it's the right choice. 6/7 has a 28% chance of losing, while 2/Wong only has a 15.5% chance of losing.
If I put a massive bet out there, I might be playing the 2/wong...
If I put a massive bet out there, I might be playing the 2/wong...
December 12th, 2012 at 6:37:15 AM
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Yeah, that is a tough one. I guess because you have three very high tiles, go for the balance instead of the big high.
I probably would have played Wong or Gong.
I probably would have played Wong or Gong.
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
December 12th, 2012 at 7:23:29 AM
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The majority of the time, when you can make a Wong and a Gong in the high hand, you play neither and go with the best low hand instead. As always though, there are exceptions.
December 12th, 2012 at 8:59:38 AM
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It's also surprising to me that if you were given that hand every hand, you would show a profit over time.
December 12th, 2012 at 9:13:20 AM
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pairs are more common than you think, I believe around 1 in 6 hands have a pair....
So the wong or gong choices lose to almost all of those....
The highest 6 in the low hand doesnt lose often....
JB- can you do one of these every day?
Like a 'Tiles question of the day thread?'
So the wong or gong choices lose to almost all of those....
The highest 6 in the low hand doesnt lose often....
JB- can you do one of these every day?
Like a 'Tiles question of the day thread?'
December 12th, 2012 at 9:26:47 AM
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Quote: SOOPOOJB- can you do one of these every day?
Like a 'Tiles question of the day thread?'
That would be cool, but the frequency of questions is probably not enough to do it.
December 12th, 2012 at 10:17:58 AM
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In one of JB's many strategies it said to play 5/7, 6/7, or 7/7 if you can. I've learned playing with JB that usually when I want to play a Wong he admonishes me. So, if I remember correctly, as soon as I didn't play one, he told me I was supposed to. Those wongs are tricky. I would also hate to waste the high-8 in the gong, especially when it causes the low hand to have a low high tile. So, 6/7 is starting to feel right to me. I know Asian players will laugh at you if you play that at the table.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
December 12th, 2012 at 10:40:10 AM
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I'd play the 2/Wong for the expected push. I see how the win/loss is out of whack. I'm just saying what I'd actually do were I faced with this at the table with no chart, not what is best.
This is what makes it such a cool game, IMO.
This is what makes it such a cool game, IMO.
A falling knife has no handle.
December 12th, 2012 at 11:44:37 AM
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December 12th, 2012 at 11:49:43 AM
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Quote: WizardI've learned playing with JB that usually when I want to play a Wong he admonishes me. So, if I remember correctly, as soon as I didn't play one, he told me I was supposed to.
Yup, that very thing happened the last time we played. I think the first Wong hand was with L4 and L10, where the best play is 6/9. The next time it was with a Gee and H10, where the best play is 6/Wong.
At that same session, when you were dealt H8, L8, H6, 7, I was unable to convince you that playing the H6 with the H8 was the best play because (a) it looks very wrong, and (b) the guy to my left was louder than I was and he was telling you to play the H6 with the L8 (which looks right, but isn't). As I recall it didn't end up mattering anyway because of what the dealer had. You were dealt a lot of lousy hands that session.
December 12th, 2012 at 11:51:47 AM
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Quote: sodawaterCasino house way is to play the gong, right? My first instinct was to play the wong, but I can see how 6/7 is correct, especially given that it's the highest 6 and a very high 7.
They would because of the high 4. With a low 4, some places would play the Gong and some places would play the Wong. (The traditional strategy says to play the lowest of High Nine, Gong, or Wong in the high hand, as long as it puts a 3-with-H6 or better in the low hand. However, the traditional strategy also has an exception to that rule, which is that if the high hand choices are Wong and Gong, to play any 3/Gong even if it is lower than 3-with-H6.) Not all places remember that exception, or at least not all dealers do; I've seen it played both ways.
December 12th, 2012 at 11:52:55 AM
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December 12th, 2012 at 11:53:46 AM
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December 12th, 2012 at 10:34:48 PM
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A couple more comments about the hand in question (H2, H4, H8, 9) —
1) With this particular hand, none of the three options really "feel" right, however, you have 3 of the 14 tiles that can be used to make a Wong, Gong, or High Nine, and the dealer needs at least two of the remaining 11. By reducing the chance of him making one of those high hands, it is more likely that he will be playing the best low hand, therefore so should you with this combination because both hands are very high-ranking among their point totals.
2) Yun Seven, the 7-point hand made from a H8 and a 9, is a powerful hand. The majority of the time when it is viable to play it, whether it ends up in the low hand or the high hand, you should. As an example, it would not be viable to play it when the other two tiles are 10 and 11, because this would make 1/7 instead of the obviously better 9/9. The few times you should not play it are with the following combinations:
1) With this particular hand, none of the three options really "feel" right, however, you have 3 of the 14 tiles that can be used to make a Wong, Gong, or High Nine, and the dealer needs at least two of the remaining 11. By reducing the chance of him making one of those high hands, it is more likely that he will be playing the best low hand, therefore so should you with this combination because both hands are very high-ranking among their point totals.
2) Yun Seven, the 7-point hand made from a H8 and a 9, is a powerful hand. The majority of the time when it is viable to play it, whether it ends up in the low hand or the high hand, you should. As an example, it would not be viable to play it when the other two tiles are 10 and 11, because this would make 1/7 instead of the obviously better 9/9. The few times you should not play it are with the following combinations:
| Other two tiles | Best Play |
|---|---|
| H10 and 4 | 2/9 |
| L8 and L7 | high 5/7 |
| L8 and 6/Gee | 5/6* |
| 7 and 7 | 5/6 |
| 7 and 6/Gee | 5/5 |
| 6 and 6 | 4/5 |
* with L8 and L6/Gee, play high 4/7 when you are banking
If you've memorized the pair-splitting strategies, then you know that Yun Seven is the only combination which makes 6/8 or better that you should not split paired Teen or Day with. You are even giving up two points by not splitting: 7/Pair = 7+12 = 19 points, Gong/Wong = 10+11 = 21 points — that's how powerful Yun Seven is.
December 12th, 2012 at 11:26:43 PM
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Awesome post, JB. On your last point, I did know that you shouldn't split teen or day pair if you can make a yun 7 -- but that is a similarly counterintuitive hand as well.
What I did NOT know about that last example (h2, h2, h8, 9) is that not only will you lose fewer hands with the pair of teen intact -- you will win more, too, than if you played gong/wong. That does blow my mind.
What I did NOT know about that last example (h2, h2, h8, 9) is that not only will you lose fewer hands with the pair of teen intact -- you will win more, too, than if you played gong/wong. That does blow my mind.
December 18th, 2012 at 11:15:29 PM
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December 18th, 2012 at 11:25:19 PM
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Nope. With a L10 you would play 4/5 though. Other hands where you make 2/7 are:
1) any 4, high 8, low, 9 (2/high 7 -- Yun Seven strikes again!)
2) high 6, low 6, any 7, any 10
3) teen, day, 5, any 10 (high 2/7 -- teen in low hand)
4) 5, any 7, any 8, 9
I think that's all of them...
1) any 4, high 8, low, 9 (2/high 7 -- Yun Seven strikes again!)
2) high 6, low 6, any 7, any 10
3) teen, day, 5, any 10 (high 2/7 -- teen in low hand)
4) 5, any 7, any 8, 9
I think that's all of them...
December 18th, 2012 at 11:55:37 PM
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December 19th, 2012 at 5:34:23 AM
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Quote: sodawateralthough i would never in a million years think that the teen goes in the low hand... especially since you are "going high" with t he 2/7 instead of the 4/5
This one actually had me puzzled up until now. It's not just Teen+Day+5+10, but also Teen+Day+5+11 which makes you play the lower 7-point high hand and the teen in the low hand.
However, I just figured it out, and it makes perfect sense. It is like playing the best high hand, except both 7-point high hands you can make are almost equal, so you might as well boost the low hand.
First you need to figure, how often does the house make a 7-point high hand whose high tile is teen or day? Let's call either of these two hands a "big 7". If they've got a teen or day, they're most likely going to be playing a Wong, Gong, or High Nine in their high hand. But forget that for now.
Let's look at what you have in your hand. You've got a teen, which they could use to make a big 7. You've also got a day, same thing. They would desperately need a 5 to make a big 7, and you've got one of those too. Now, if the dealer did manage to get a Teen/Day and the other 5, what sort of tile combinations for their other two tiles would force them to play the big 7 in their high hand? It would have to be something like 6-10, 6-11, Gee-10, or Gee-11. And lo and behold, your fourth tile is a 10 or an 11.
So you have basically crippled their chances of playing a big 7 in their high hand based solely on what you have in your hand, which is what makes both 7-point high hands nearly equal for Teen+Day+5+(10 or 11).
Looking at whether your fourth tile is a 10 or an 11, here are the probabilities of the dealer making a big 7 in their high hand:
| Fourth Tile | Dealer 7 with Teen | Dealer 7 with Day | Dealer 7 with Teen or Day |
|---|---|---|---|
| 10 | 32/20475 = 0.001563 | 36/20475 = 0.001758 | 68/20475 = 0.003321 = 1 in 301 |
| 11 | 34/20475 = 0.001661 | 38/20475 = 0.001856 | 72/20475 = 0.003516 = 1 in 284 |
December 19th, 2012 at 11:28:54 AM
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December 19th, 2012 at 3:37:45 PM
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They would play 6/7. Some places would play the high 6 and the low 7 (the correct split as a player by the way), and some places would play the low 6 and the high 7, either intentionally or mistakenly.
December 19th, 2012 at 5:25:23 PM
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December 19th, 2012 at 6:00:04 PM
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Yes, but you have a teen + day + 5 in your hand, the dealer would need all three of the others, and one of the four 4s, which would not be easy. You'll note in the combinations at the end of the first page that there are 4 more ways for them to make a Day 7 than the number of ways for them to make a Teen 7, and that's because of the teen-day-4-5 hand (1 teen * 1 day * 1 five * 4 fours = 4 combinations).
January 6th, 2013 at 1:25:30 PM
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January 6th, 2013 at 3:27:49 PM
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Quote: sodawaterWould never think to make such a crappy 9 here over 5/6.
I find 5, 7, 9, 10 just as surprising.
January 6th, 2013 at 5:25:29 PM
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January 6th, 2013 at 5:26:24 PM
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January 6th, 2013 at 6:10:31 PM
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Quote: sodawaterJB, any chance you could add a button/option to show the EV of each hand setting to the practice game? That would save me so much time.
I recall trying to do so but discovered that it wasn't feasible using only JavaScript, and adding a Java applet for it would be overkill. I may try it again in JavaScript, but I wouldn't necessarily count on it being added.
January 7th, 2013 at 7:12:35 PM
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Quote: JBI recall trying to do so but discovered that it wasn't feasible using only JavaScript, and adding a Java applet for it would be overkill. I may try it again in JavaScript, but I wouldn't necessarily count on it being added.
Makes sense, I would have no idea how to do it.
About the calculator on the odds site, I was under the impression that it only listed a setting as "invalid" if it's worse on both the high and the low hand than another option. But I got this one, and obviously the pair is better than 8 on the high. So why is it invalid?
January 7th, 2013 at 7:53:16 PM
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A Gong is worth 10 points, a Wong 11 points, and a pair 12 points. So 0/Pair is worth 12 points whereas 8/8 is worth 16 points, making it the better play.
Although, with pairs, you don't necessarily always go with the highest point total. Splitting or not splitting a pair is usually valid if it is within 2 points of the highest point total. For example:
High 8 + 9 with paired Teen or Day: 7/Pair is 19 points and Gong/Wong is 21 points, but 7/Pair is the better play.
High 7's with H10-L10 when banking: 0/Pair is 12 points and 7/7 is 14 points but 0/Pair is the better play when banking (but 7/7 is better when the dealer is banking).
Although, with pairs, you don't necessarily always go with the highest point total. Splitting or not splitting a pair is usually valid if it is within 2 points of the highest point total. For example:
High 8 + 9 with paired Teen or Day: 7/Pair is 19 points and Gong/Wong is 21 points, but 7/Pair is the better play.
High 7's with H10-L10 when banking: 0/Pair is 12 points and 7/7 is 14 points but 0/Pair is the better play when banking (but 7/7 is better when the dealer is banking).
January 7th, 2013 at 7:56:39 PM
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so how does the calculator decide when to display the word invalid?
January 7th, 2013 at 9:59:19 PM
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For hands with a pair, a split is considered invalid if it is at least 3 points lower than the highest point total.
For hands with no pairs, a split is considered invalid if it has fewer points than the highest point total, or if it has the highest point total but a lower-ranking low or high hand than another split with the highest point total.
For hands with no pairs, a split is considered invalid if it has fewer points than the highest point total, or if it has the highest point total but a lower-ranking low or high hand than another split with the highest point total.
January 14th, 2013 at 4:25:42 AM
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Here is another surprising situation.
The standard strategy for certain hands that have High 10 + Low 10 + High 6 is:
However, there is one peculiar exception: when you are banking, and the fourth tile is a low 8, you should play the high 6 and high 10 together in the low hand (and the low 8 and low 10 in the high hand). It looks and feels wrong, but it's about 1% better than 6/high 8.
The standard strategy for certain hands that have High 10 + Low 10 + High 6 is:
- with any 7: play 6/high 7
- with low 8: play 6/high 8
- with any 9: play 6/high 9
However, there is one peculiar exception: when you are banking, and the fourth tile is a low 8, you should play the high 6 and high 10 together in the low hand (and the low 8 and low 10 in the high hand). It looks and feels wrong, but it's about 1% better than 6/high 8.
January 14th, 2013 at 11:55:20 AM
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that's crazy, i guess it's because there's a good chance on having a copy hand with the mooy 6
February 3rd, 2013 at 1:09:48 AM
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This one came up in the casino this weekend. Unsurprisingly, I picked the worst way to set the hand.
February 3rd, 2013 at 1:34:46 AM
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Quote: sodawaterThis one came up in the casino this weekend. Unsurprisingly, I picked the worst way to set the hand.
House sets it 'the worst' way as 7 - 0. But as the banker the 0 is far more powerful than as player. This is another great example of why we trust in JB nd don't play house ways!
February 3rd, 2013 at 2:05:03 PM
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yes i agree
February 16th, 2013 at 10:29:05 AM
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Normally when you have a L4, high 10, low 10, and any Gee/6/7/8/9, you separate the two high tiles:
Gee ... 4/high 6
L6 .... 4/high 6
H6 .... high 4/6
L7 .... 4/high 7
H7 .... 4/high 7
L8 .... 4/high 8
H8 .... high 4/8
9 ..... 4/high 9
...except in one situation when you are banking: with L4, H6, H10, L10, you play the L4 and L10 in the low hand, and H6 and H10 in the high hand. It's only marginally better than high 4/6, but strangely it is the correct play.
Here are a few more seemingly bizarre plays when you are banking:
H6, L7, L8, 11 - play 3/9 instead of the expected 5/7
H6, L7, L8, L10 - play 3/8 instead of the expected 5/6
H6, L8, H10, L10 - play high 6/8 (the H6 and H10 in the low hand) instead of 6/high 8
Gee ... 4/high 6
L6 .... 4/high 6
H6 .... high 4/6
L7 .... 4/high 7
H7 .... 4/high 7
L8 .... 4/high 8
H8 .... high 4/8
9 ..... 4/high 9
...except in one situation when you are banking: with L4, H6, H10, L10, you play the L4 and L10 in the low hand, and H6 and H10 in the high hand. It's only marginally better than high 4/6, but strangely it is the correct play.
Here are a few more seemingly bizarre plays when you are banking:
H6, L7, L8, 11 - play 3/9 instead of the expected 5/7
H6, L7, L8, L10 - play 3/8 instead of the expected 5/6
H6, L8, H10, L10 - play high 6/8 (the H6 and H10 in the low hand) instead of 6/high 8
March 4th, 2013 at 11:58:44 PM
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Still getting surprised by some of these...
When I was dealt this hand, I wanted to play it 4/high 5, to get maximum value out of my yun and chong tiles. But the correct way to play this, surprisingly, is to put the yun and chong tiles together, to make the higher 4, and to have a very low 5 for the high hand. Very counterintuitive considering how close in ranking the yun and chong tiles are.
When I was dealt this hand, I wanted to play it 4/high 5, to get maximum value out of my yun and chong tiles. But the correct way to play this, surprisingly, is to put the yun and chong tiles together, to make the higher 4, and to have a very low 5 for the high hand. Very counterintuitive considering how close in ranking the yun and chong tiles are.
March 7th, 2013 at 4:40:44 AM
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Quote: sodawaterStill getting surprised by some of these...
When I was dealt this hand, I wanted to play it 4/high 5, to get maximum value out of my yun and chong tiles. But the correct way to play this, surprisingly, is to put the yun and chong tiles together, to make the higher 4, and to have a very low 5 for the high hand. Very counterintuitive considering how close in ranking the yun and chong tiles are.
This one should not surprise you. The likelihood of the strength of the total '5' when played in the high hand mattering is very rare, while the strength of the "4" hand in the low hand mattering is high. As per the analysis, the difference is a full 1 1/2% in EV. I am wondering if there is any scenario where you would play high 5 at the expense of your low hand? I wouldn't think so, but maybe JB can help....
March 7th, 2013 at 5:56:17 AM
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Would the calculation to find out how much this mistake would cost you be .629578 - .614652 = .0149 or 1.49% of your bet size times the likelihood of this hand occurring? Meaning if I play $25 a hand, picking choice 2 costs me on average about 37 cents? Or am I completely off base?
April 5th, 2013 at 2:45:21 AM
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Quote: FinsRuleWould the calculation to find out how much this mistake would cost you be .629578 - .614652 = .0149 or 1.49% of your bet size times the likelihood of this hand occurring? Meaning if I play $25 a hand, picking choice 2 costs me on average about 37 cents? Or am I completely off base?
I think that's right
April 5th, 2013 at 2:47:42 AM
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Ok... anyone want to take a shot at explaining this one to me?
teen, high eight, low eight, high six. When opponent is banking, the correct set is 6/8, but it's super close with 4/gong. However, when you are banking, the set is 4/gong, and it's not even close.
My guess is that the house way "overvalues" playing gongs, and when you are banking you can exploit the copy. But it seems strange the disparity is that great compared to when playing.
I guess the lesson is always bank when you can.
PS: JB, I like how the "single-strategy" on the game chooses the 4/gong set because of the weighted average. Nice work.
teen, high eight, low eight, high six. When opponent is banking, the correct set is 6/8, but it's super close with 4/gong. However, when you are banking, the set is 4/gong, and it's not even close.
My guess is that the house way "overvalues" playing gongs, and when you are banking you can exploit the copy. But it seems strange the disparity is that great compared to when playing.
I guess the lesson is always bank when you can.
PS: JB, I like how the "single-strategy" on the game chooses the 4/gong set because of the weighted average. Nice work.
April 5th, 2013 at 3:22:11 AM
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Quote: sodawaterWhen I was dealt this hand, I wanted to play it 4/high 5, to get maximum value out of my yun and chong tiles. But the correct way to play this, surprisingly, is to put the yun and chong tiles together, to make the higher 4, and to have a very low 5 for the high hand. Very counterintuitive considering how close in ranking the yun and chong tiles are.
Yup, and you'll most likely get a lecture by the dealer and/or other players when you play high 4/5 at a live game.
Quote: FinsRuleWould the calculation to find out how much this mistake would cost you be .629578 - .614652 = .0149 or 1.49% of your bet size times the likelihood of this hand occurring? Meaning if I play $25 a hand, picking choice 2 costs me on average about 37 cents? Or am I completely off base?
Correct.
Quote: sodawaterteen, high eight, low eight, high six. When opponent is banking, the correct set is 6/8, but it's super close with 4/gong. However, when you are banking, the set is 4/gong, and it's not even close.
My guess is that the house way "overvalues" playing gongs, and when you are banking you can exploit the copy.
Yup, when you're banking you play Gong and High Nine more often, hoping to copy. (Hands where all you can make is a Wong are played the same as when the dealer is banking.) It is easier to copy hands that have a Gong or High Nine, a Wong not so much. A similar example is day, high 8, any 6/Gee, any 7. When the dealer is banking you play 5/8 but when you are banking you play 4/9 like the house would.
Quote: sodawaterPS: JB, I like how the "single-strategy" on the game chooses the 4/gong set because of the weighted average. Nice work.
Thanks.
April 5th, 2013 at 4:10:27 PM
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Quote: SOOPOOI am wondering if there is any scenario where you would play high 5 at the expense of your low hand? I wouldn't think so, but maybe JB can help....
Yes, apparently there is:
April 5th, 2013 at 4:11:52 PM
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Quote: JB
Yup, when you're banking you play Gong and High Nine more often, hoping to copy. (Hands where all you can make is a Wong are played the same as when the dealer is banking.) It is easier to copy hands that have a Gong or High Nine, a Wong not so much. A similar example is day, high 8, any 6/Gee, any 7. When the dealer is banking you play 5/8 but when you are banking you play 4/9 like the house would.
Makes total sense.
April 9th, 2013 at 11:01:25 PM
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If you did this one in the casino, the other players would think you were absolutely bonkers:
April 10th, 2013 at 9:50:35 AM
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Quote: sodawaterIf you did this one in the casino, the other players would think you were absolutely bonkers: (Teen-Day-9-H10)
That happened to me at Palace Station a few years ago. It backfired because the dealer ended up with 6/9 where the 9 was made from 5 & H4. Fortunately, I was the only player at the table, so I only got an earful from the dealer (and actually he was rather pleasant about it). I kind of like situations like this because it makes it look like you don't know what you're doing, which might earn you extra comps if the pit boss is watching.
I don't think I have ever had 4/9 with Teen-Day-High 8-11 backfire on me. I recall one hand at the MGM where I played 4/9 and the dealer flipped over high 7-low 7-low 4-5, which was a welcome sight.
Quote: sodawaterQuote: SOOPOOI am wondering if there is any scenario where you would play high 5 at the expense of your low hand? I wouldn't think so, but maybe JB can help....
Yes, apparently there is:
The example given (high 6, low 6, any 7, 9 = 3/high 5) is the only combination I see where you play the higher-ranking tile in a 5-point high hand. Intuition tells me that the reason must be because high 3 is the cutoff for the house and therefore almost just as likely to lose as the low 3, so you might as well play the high 5, except that you play 3/high 5 when you are banking too, so I'm not entirely sure what the reason is. 3/high 5 is about 1.4% better (than high 3/5) when the dealer is banking, and about 0.57% better when you are banking.
April 10th, 2013 at 1:52:36 PM
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Quote: JB
The example given (high 6, low 6, any 7, 9 = 3/high 5) is the only combination I see where you play the higher-ranking tile in a 5-point high hand. Intuition tells me that the reason must be because high 3 is the cutoff for the house and therefore almost just as likely to lose as the low 3, so you might as well play the high 5, except that you play 3/high 5 when you are banking too, so I'm not entirely sure what the reason is. 3/high 5 is about 1.4% better (than high 3/5) when the dealer is banking, and about 0.57% better when you are banking.
And the amazing thing is, I randomly got dealt that hand a few hours after I read SOOPOO's question.
