Saigon 5 Card
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5 members have voted
June 2nd, 2018 at 8:51:36 AM
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Saigon 5 Card comes to us via way of Vietnam and Cambodia, where it is known as Ngau Ham. The game has been broached on a couple other old threads, but never went far, so forgive me for making a new thread for it. I've started on a new page for Saigon 5 Card. So far, I've only taken it through the rules, and I'm not sure I have those completely correct. Specifically, I don't know if the player can use any two cards for the Pot bet or the two cards as used in the Ante bet.
Please have a look at my new page. As always, I welcome all questions, comments, and especially corrections. Analysis coming soon.
The question for the poll is would you play Saigon 5 Card?
Please have a look at my new page. As always, I welcome all questions, comments, and especially corrections. Analysis coming soon.
The question for the poll is would you play Saigon 5 Card?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 2nd, 2018 at 9:01:31 AM
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There doesn't seem to be any real strategy to this game - since the 3-card hand must be a multiple of 10, your 2-card hand value is predetermined by your five cards.
June 2nd, 2018 at 9:13:53 AM
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I've played the tile version of this game before and thought it was pretty fun.
I would probably play the card version in a casino for low stakes and if the house edge didn't suck.
I would probably play the card version in a casino for low stakes and if the house edge didn't suck.
June 2nd, 2018 at 9:14:10 AM
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Quote: ThatDonGuyThere doesn't seem to be any real strategy to this game - since the 3-card hand must be a multiple of 10, your 2-card hand value is predetermined by your five cards.
I agree. I don't know if the player even has to set a hand or if the dealer does it. Note that I didn't say whether the cards are dealt face up or down because I don't know and it doesn't matter anyway.
Who is our man, or woman, in Tampa? Cambodia too, for that matter.
Last edited by: Wizard on Jun 2, 2018
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 2nd, 2018 at 9:56:43 AM
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Quote: TigerWuI would probably play the card version in a casino for low stakes and if the house edge didn't suck.
I'm not getting a very high house edge at all. After all, except for the "player wins with a 5 is paid at 1-2" rule, aren't the rules for the player and dealer the same?
The only house edge appears to be 1/2 of the bets when the player wins with a 5 - and how often does that happen?
When I do some quick simulation, I get that it happens only about 1 out of every 25 hands, which would be a house edge of about 2%.
In fact, when I do a count from a full deck, I get that only about 6.7% of the hands have a value of 5.
Last edited by: ThatDonGuy on Jun 2, 2018
June 2nd, 2018 at 11:24:14 AM
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Quote: WizardI agree. I don't know if the player even has to set a hand or if the dealer does it. Note I didn't say if cards are dealt face up or down because I don't know and it doesn't matter anyway?
Who is our man, or woman, in Tampa? Cambodia too, for that matter.
terapined has said before he's in/near tampa. Cambodia, NokTang, perhaps?
If the House lost every hand, they wouldn't deal the game.
June 2nd, 2018 at 12:58:52 PM
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Quote: beachbumbabsterapined has said before he's in/near tampa. Cambodia, NokTang, perhaps?
I'll stop by the Tampa Hard Rock in a few days and report back what I find about this game
Its not my favorite casino but it is the closest to me.
It does not surprise me the game is there
The casino really tries hard to attract the Asian market
Authentic Chinese food and a section of the casino dedicated just to Asians with Pai Gow tiles and other Asian games
I actually go there sometimes not to gamble but for the real Chinese food
Hmm, sounds like I will be able to satisfy my hunger for some genuine Asian food in a few days :-)
Last edited by: terapined on Jun 2, 2018
When somebody doesn't believe me, I could care less. Some get totally bent out of shape when not believed. Weird. I believe very little on all forums
June 2nd, 2018 at 1:47:39 PM
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Quote: terapined
Authentic Chinese food and a section of the casino dedicated just to Asians with Pai Gow tiles and other Asian games
I'm so jealous... haha...
I'm actually kind of surprised more casinos don't cater to Asian demographics. Where I live there's a very large Vietnamese population, but the casinos are 100% geared to "round eyes" like me. Last time I checked the casino near my house had ONE baccarat table.
June 2nd, 2018 at 2:06:14 PM
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Quote: terapinedI'll stop by the Tampa Hard Rock in a few days and report back what I find about this game
Thanks T! Some more back and forth on this hear and I think we'll have a succinct list of questions that need answering for you.
Here is a progress report. This is a count of scores of all possible combinations of 5 cards out of 53. Can anyone confirm or deny? So much of game programming is scoring a hand accurately.
| Points | Combinations | Probability |
|---|---|---|
| 0 | - | 0.000000 |
| 1 | 172,352 | 0.060060 |
| 2 | 176,856 | 0.061629 |
| 3 | 179,352 | 0.062499 |
| 4 | 175,710 | 0.061230 |
| 5 | 192,112 | 0.066945 |
| 6 | 181,184 | 0.063137 |
| 7 | 197,208 | 0.068721 |
| 8 | 219,552 | 0.076507 |
| 9 | 229,084 | 0.079829 |
| 10 | 246,608 | 0.085936 |
| Does not qualify | 899,667 | 0.313507 |
Note: Corrected 6/4/18
Last edited by: Wizard on Jun 4, 2018
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 2nd, 2018 at 4:06:09 PM
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Quote: WizardSpecifically, I don't know if the player can use any two cards for the Pot bet or the two cards as used in the Ante bet.
I would imagine whatever 2 cards were used to determine the winner after qualifying are also used to determine the pot bet
I can see why this game may be popular. If there are a lot a players a full table the pot bet is just among players and its winner take all which would be real fun to win. A bet among players with no casino edge or commission:-) .
Where did the picture come from? Somewhere I can play this for free on the internet?
Dealt some hands to myself and the dealer for practice
No strategy I can see :-(
If you qualify, its going to be either 10, 20 30. Looks slim that you could qualify for 2 numbers such as 10 or 20 then have a decision.
Its pretty much if you qualify or not
If I find an empty table, I only have to make 1 bet instead of 2? Due the pot bet is a players only bet right?
When somebody doesn't believe me, I could care less. Some get totally bent out of shape when not believed. Weird. I believe very little on all forums
June 2nd, 2018 at 4:28:34 PM
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Okay guys, I think this is the first published analysis of Saigon 5 Card. Hopefully it's right. What'd'ya think?
I have to respect any game with a house edge of only 0.60%.
| Event | Pays | Count | Probability | Return |
|---|---|---|---|---|
| Both don't qualify | 0 | 481,649,866,016 | 0.098020 | 0.000000 |
| Player 1 wins with 1 | 1 | 9,733,909,104 | 0.001981 | 0.001981 |
| Player 1 wins with 2 | 1 | 10,706,973,088 | 0.002179 | 0.002179 |
| Player 1 wins with 3 | 1 | 16,528,229,168 | 0.003364 | 0.003364 |
| Player 1 wins with 4 | 1 | 28,676,031,164 | 0.005836 | 0.005836 |
| Player 1 wins with 5 | 0.50 | 58,484,390,752 | 0.011902 | 0.005951 |
| Player 1 wins with 6 | 1 | 84,533,343,740 | 0.017203 | 0.017203 |
| Player 1 wins with 7 | 1 | 138,467,802,336 | 0.028180 | 0.028180 |
| Player 1 wins with 8 | 1 | 203,945,516,176 | 0.041505 | 0.041505 |
| Player 1 wins with 9 | 1 | 326,602,760,752 | 0.066467 | 0.066467 |
| Player 1 wins with 10 | 1 | 1,086,260,155,840 | 0.221064 | 0.221064 |
| Player 1 outscored | -1 | 905,085,575,368 | 0.184194 | -0.184194 |
| Player 1 does not qualify | -1 | 1,058,853,536,752 | 0.215487 | -0.215487 |
| Tie | 0 | 504,245,013,984 | 0.102619 | 0.000000 |
| Total | 4,913,773,104,240 | 1.000000 | -0.005951 |
I have to respect any game with a house edge of only 0.60%.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 2nd, 2018 at 7:15:02 PM
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On your WoO page, Rule 10 says,
Is that correct, that aces do that? Or is it a typo and the first bolded aces should be joker?
Be fun to have 5 wild cards in a deck, if so. I would enjoy that.
Quote:For purposes of the Bonus bet, aces are partially wild. They can be used to complete a straight, flush, straight flush, or royal flush. Otherwise they count as an ace. I know of two pay tables as shown below.
Is that correct, that aces do that? Or is it a typo and the first bolded aces should be joker?
Be fun to have 5 wild cards in a deck, if so. I would enjoy that.
If the House lost every hand, they wouldn't deal the game.
June 2nd, 2018 at 7:31:25 PM
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Wiz, do you have any way to retrieve stats on Player 1 hands that have a joker?
How often do hands with a joker qualify?
How often do hands with a Joker Win 1? Win 0.5? Win 0 (Tie + Both DNQ)? Lose -1?
**********************************
Mathematically this is an interesting game, but from a gameplay point of view it is lame.
- All bets are before any cards are dealt.
- Any 5 card combination will either Not Qualify or have one unique 2 card total.*
So, the entire game is just an elaborate way of assigning a "rank" to a 5 card hand that is completely different than the flush, straight and pairing of conventional poker. But otherwise it is 5 card stud with only one bet -and the one bet is before any cards are dealt.
*Edit: Actually this is not true. Some hands with a joker can be set in different ways such that the two card hand has different point totals. Consider: (Joker) -7-7-6-5. It can be set with 6-5 on top or with 7-7 on top. But certainly all 5 cards hands have one unique maximum 2 card total.
How often do hands with a joker qualify?
How often do hands with a Joker Win 1? Win 0.5? Win 0 (Tie + Both DNQ)? Lose -1?
**********************************
Mathematically this is an interesting game, but from a gameplay point of view it is lame.
- All bets are before any cards are dealt.
- Any 5 card combination will either Not Qualify or have one unique 2 card total.*
So, the entire game is just an elaborate way of assigning a "rank" to a 5 card hand that is completely different than the flush, straight and pairing of conventional poker. But otherwise it is 5 card stud with only one bet -and the one bet is before any cards are dealt.
*Edit: Actually this is not true. Some hands with a joker can be set in different ways such that the two card hand has different point totals. Consider: (Joker) -7-7-6-5. It can be set with 6-5 on top or with 7-7 on top. But certainly all 5 cards hands have one unique maximum 2 card total.
Last edited by: gordonm888 on Jun 2, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 2nd, 2018 at 9:21:49 PM
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Quote: beachbumbabsIs that correct, that aces do that? Or is it a typo and the first bolded aces should be joker?
Good catch; thanks. I did mean a joker.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 2nd, 2018 at 9:28:35 PM
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Quote: gordonm888Wiz, do you have any way to retrieve stats on Player 1 hands that have a joker?
I did not implicitly calculate joker hands separately. Some coding tweaks and I could tell you but I'm sure having a joker is powerful.
Quote:So, the entire game is just an elaborate way of assigning a "rank" to a 5 card hand that is completely different than the flush, straight and pairing of conventional poker. But otherwise it is 5 card stud with only one bet -and the one bet is before any cards are dealt.
*Edit: Actually this is not true. Some hands with a joker can be set in different ways such that the two card hand has different point totals. Consider: (Joker) -7-7-6-5. It can be set with 6-5 on top or with 7-7 on top. But certainly all 5 cards hands have one unique maximum 2 card total.
I agree this would otherwise* get laughed out of most casinos, but I think this is an old Vietnamese game that has survived the test of time. The way I coded it was to store the score of every possible set of 5 ranks in an array. If there was a joker, it scored it as both 3, 6, and 9 points, and went with the way that maximized the hand value.
* Is this a split infinitive?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 3rd, 2018 at 11:58:52 AM
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An analysis has been posted to my page on Saigon 5 Card.
As always, I welcome all questions, comments, and especially corrections.
As always, I welcome all questions, comments, and especially corrections.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 3rd, 2018 at 5:15:59 PM
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Here's a puzzler I'm trying to work in my head:
Can you identify a Saigon 5 Card Poker hand which has a joker and no pairs (a joker and four different ranks) and does not qualify?
Can you identify a Saigon 5 Card Poker hand which has a joker and no pairs (a joker and four different ranks) and does not qualify?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 3rd, 2018 at 5:30:12 PM
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W,2,5,T, K
W, 5,8,T, K (both any 2 non-pair tens)
W, 3, 5, T K
W, 2,3, T, K
W, 3, 9, T K
W, 6, 9, T, K
W, 5,8,T, K (both any 2 non-pair tens)
W, 3, 5, T K
W, 2,3, T, K
W, 3, 9, T K
W, 6, 9, T, K
If the House lost every hand, they wouldn't deal the game.
June 3rd, 2018 at 5:38:49 PM
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Babs is correct, for the way that I stated the problem
I realized after I posted the problem, that I had made the mistake of thinking that any two cards with a value of 10 were a pair. It turns out that the problem is easy to solve when there are two cards with the same amount of points.
So let me ask it this way:
Can you identify a Saigon 5-card hand with a joker and 4 cards of different point values that Does Not Qualify? That is, 5 cards that Do Not Qualify consisting of a Joker and 4 different ranks if you count T-K as a single rank?
I realized after I posted the problem, that I had made the mistake of thinking that any two cards with a value of 10 were a pair. It turns out that the problem is easy to solve when there are two cards with the same amount of points.
So let me ask it this way:
Can you identify a Saigon 5-card hand with a joker and 4 cards of different point values that Does Not Qualify? That is, 5 cards that Do Not Qualify consisting of a Joker and 4 different ranks if you count T-K as a single rank?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 3rd, 2018 at 5:43:01 PM
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W, 2, 3, 6, T
W, A,2,3,4
If the House lost every hand, they wouldn't deal the game.
June 3rd, 2018 at 6:14:38 PM
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Quote: beachbumbabs
W, 2, 3, 6, T
W, A,2,3,4
Doesn't W, A, 2, 3, 4 qualify with (6)-A-3 / 2-4?
A quick way to determine your hand:
If you have no joker, it's easy - add up the points of all five cards, and if any pair adds up to the corresponding "modulo 10" value, use that hand. It does not matter if there are multiple ways to make a qualifying hand, as all of the 2-card hands will have the same value.
If you have a joker, it's a little more complicated. It is the highest of:
(a) Add up the points of the other four cards, and if any one card has the sum's "modulo 10" value, use that card and the joker value that gives you the highest two-card total (3, if your card is 5-7; 6, if it is 2-4; 9, if it is anything else)
(b) For each pair of non-joker cards, if they add up to 4, 7, 11, 14, or 17, use the value of the other two cards (for example, with Joker-2-3-5-6, (3)-2-5/3-6 is worth 9, and (9)-5-6/2-3 is worth 5.
June 3rd, 2018 at 6:32:07 PM
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Bab's first answer is correct. One of only two correct answers I have been able to find so far (but I have not been using a spreadsheet or computer.) Congrats !
I believe Bab's 2nd answer is not correct.
This is harder than it looks.
Edit: I believe I have found 5 correct answers (without using a computer) by employing a mathematical insight.
I believe Bab's 2nd answer is not correct.
Bab's 2nd answer was (W,A,2,3,4) but, unfortunately, 4+3+W =10
This is harder than it looks.
Edit: I believe I have found 5 correct answers (without using a computer) by employing a mathematical insight.
Last edited by: gordonm888 on Jun 3, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 3rd, 2018 at 6:40:38 PM
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Quote: gordonm888Bab's first answer is correct. One of only two correct answers I have been able to find so far (but I have not been using a spreadsheet or computer.) Congrats !
I believe Bab's 2nd answer is not correct.Bab's 2nd answer was (W,A,2,3,4) but, unfortunately, 4+3+W =10
This is harder than it looks.
Yeah, darn. (6)A3 does qualify.
Added that one too fast. Was trying to find one specific with an Ace in it. Hmmm.
If the House lost every hand, they wouldn't deal the game.
June 3rd, 2018 at 7:03:35 PM
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Quote: beachbumbabsAdded that one too fast. Was trying to find one specific with an Ace in it. Hmmm.
There is only one - Joker, A, 2, 4, 8
Note that any hand with Joker, Ace, and any of 3, 6, or 10 can qualify (with (6)-A-3, (3)-A-6, and (9)-A-10, respectively).
This leaves 2, 4, 5, 7, 8, and 9 as the possible cards that can be included; there are (6)C(3) = 20 such hands.
A 2 4 5 qualifies with (3)-2-5
A 2 4 7 qualifies with (9)-4-7
A 2 4 8 does not qualify
A 2 4 9 qualifies with (9)-2-9
A 2 5 7 qualifies with A-2-7
A 2 5 8 qualifies with (3)-2-5
A 2 5 9 qualifies with (3)-2-5
A 2 7 8 qualifies with A-2-7
A 2 7 9 qualifies with A-2-7
A 2 8 9 qualifies with (3)-8-9
A 4 5 7 qualifies with A-4-5
A 4 5 8 qualifies with A-4-5
A 4 5 9 qualifies with A-4-5
A 4 7 8 qualifies with (9)-4-7
A 4 7 9 qualifies with 4-7-9
A 4 8 9 qualifies with (3)-8-9
A 5 7 8 qualifies with 5-7-8
A 5 7 9 qualifies with (6)-5-7
A 5 8 9 qualifies with (3)-8-9
A 7 8 9 qualifies with (3)-8-9
June 3rd, 2018 at 9:29:42 PM
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I had not found the solution that ThatDonGuy came up with. Congrats to Don.
Here's the solutions that I did in my head:
W + any 4 of the following 5 cards: 2,3,6,9,10
W,2,3,6,9
W,2,3,6,10 (Bab's solution)
W,2,3,9,10
W,2,6,9,10
W,3,6,9,10
My thoughts went like this: we want to avoid any 3 cards that sum to 10 or 20. 10 is 1mod(3) and 20 is 2mod(3).
Now the wild card is 3,6, or 9 so it is always 0mod(3). If the other cards are also of the form 0mod(3) then they (combined with the wild card) can only sum to a total that is 0mod(3) and thus cannot be combined in any way to make a sum of 10 or 20. So, I started with W,3,6,9 because 3,6 and 9 are all 0mod(3). But I needed a fifth card so, by inspection, I determined that W,3,6,9,2 and W,3,6,9,10 were the only possibilities that worked. And then I realized that 2+10=12 and 12 is also 0mod(3).
From there, it was a short leap to see that any 4 numbers of the set (2,3,6,9,10) could be combined with a Joker and not qualify.
Of course, none of that deduction indicates that other solutions could not exist, but I suspected that those 5 solutions were all there were. ThatDonGuy has found an additional solution. And maybe there are more.
Here's the solutions that I did in my head:
W + any 4 of the following 5 cards: 2,3,6,9,10
W,2,3,6,9
W,2,3,6,10 (Bab's solution)
W,2,3,9,10
W,2,6,9,10
W,3,6,9,10
My thoughts went like this: we want to avoid any 3 cards that sum to 10 or 20. 10 is 1mod(3) and 20 is 2mod(3).
Now the wild card is 3,6, or 9 so it is always 0mod(3). If the other cards are also of the form 0mod(3) then they (combined with the wild card) can only sum to a total that is 0mod(3) and thus cannot be combined in any way to make a sum of 10 or 20. So, I started with W,3,6,9 because 3,6 and 9 are all 0mod(3). But I needed a fifth card so, by inspection, I determined that W,3,6,9,2 and W,3,6,9,10 were the only possibilities that worked. And then I realized that 2+10=12 and 12 is also 0mod(3).
From there, it was a short leap to see that any 4 numbers of the set (2,3,6,9,10) could be combined with a Joker and not qualify.
Of course, none of that deduction indicates that other solutions could not exist, but I suspected that those 5 solutions were all there were. ThatDonGuy has found an additional solution. And maybe there are more.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 4th, 2018 at 8:56:41 AM
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Quote: gordonm888
W + any 4 of the following 5 cards: 2,3,6,9,10
W,2,3,6,9
W,2,3,6,10 (Bab's solution)
W,2,3,9,10
W,2,6,9,10
W,3,6,9,10
I think those with W29 would add up to 20. It seems you need to numbers
(a) Two of them don't add up to 10x+1, 10x+4, 10x+7 or
(b) obviously any three (not the joker) to 10x.
The method I've tried runs as follows.
If your first card is a 10 then you can't have a second card that is 1 4 or 7 (as this with the joker would qualify).
Use a similar idea for all the other possible starting cards.
Then consider all starting 2-cards 10 9, 10 8, 10 6, 10 5, 9 7.....
This gives a list of numbers which can't be considered.
10 9 (1 4 7 2 5 8) leaving 10 9 6 3 as possible.
10 8 (1 4 7 3 6 9) leaving 10 8 5 2 - but W25 adds up to 10 (this can be seen by seeing whether any numbers rejected by using 5 then 2 are already in the numbers used).
Continue this idea gives
10 9 6 3
10 6 3 2
9 7 6 3
8 4 2 1
7 6 3 2
edit - removed one erroneous entry 8541 as 541 add up to 10!
(a) Two of them don't add up to 10x+1, 10x+4, 10x+7 or
(b) obviously any three (not the joker) to 10x.
The method I've tried runs as follows.
If your first card is a 10 then you can't have a second card that is 1 4 or 7 (as this with the joker would qualify).
Use a similar idea for all the other possible starting cards.
| 10 | 1 | 4 | 7 |
| 9 | 2 | 5 | 8 |
| 8 | 3 | 6 | 9 |
| 7 | 4 | 10 | |
| 6 | 1 | 5 | 8 |
| 5 | 2 | 6 | 9 |
| 4 | 3 | 7 | 10 |
| 3 | 1 | 4 | 8 |
| 2 | 5 | 9 | |
| 1 | 3 | 6 | 10 |
Then consider all starting 2-cards 10 9, 10 8, 10 6, 10 5, 9 7.....
This gives a list of numbers which can't be considered.
10 9 (1 4 7 2 5 8) leaving 10 9 6 3 as possible.
10 8 (1 4 7 3 6 9) leaving 10 8 5 2 - but W25 adds up to 10 (this can be seen by seeing whether any numbers rejected by using 5 then 2 are already in the numbers used).
Continue this idea gives
10 9 6 3
10 6 3 2
9 7 6 3
8 4 2 1
7 6 3 2
edit - removed one erroneous entry 8541 as 541 add up to 10!
Last edited by: charliepatrick on Jun 4, 2018
June 4th, 2018 at 9:31:23 AM
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These come by way of my program. If I'm missing any, I must have a programming error.
| Joker | 1 | 1 | 1 | 1 |
| Joker | 1 | 1 | 1 | 2 |
| Joker | 1 | 1 | 1 | 4 |
| Joker | 1 | 1 | 1 | 5 |
| Joker | 1 | 1 | 1 | 7 |
| Joker | 1 | 1 | 1 | 9 |
| Joker | 1 | 1 | 2 | 4 |
| Joker | 1 | 1 | 4 | 4 |
| Joker | 1 | 1 | 4 | 9 |
| Joker | 1 | 1 | 5 | 5 |
| Joker | 1 | 1 | 5 | 7 |
| Joker | 1 | 1 | 7 | 9 |
| Joker | 1 | 1 | 9 | 9 |
| Joker | 1 | 2 | 4 | 8 |
| Joker | 1 | 2 | 8 | 8 |
| Joker | 1 | 4 | 4 | 4 |
| Joker | 1 | 4 | 4 | 8 |
| Joker | 1 | 4 | 4 | 9 |
| Joker | 1 | 4 | 9 | 9 |
| Joker | 1 | 5 | 5 | 5 |
| Joker | 1 | 5 | 5 | 7 |
| Joker | 1 | 5 | 5 | 8 |
| Joker | 1 | 5 | 8 | 8 |
| Joker | 1 | 7 | 8 | 8 |
| Joker | 1 | 7 | 9 | 9 |
| Joker | 1 | 8 | 8 | 8 |
| Joker | 1 | 9 | 9 | 9 |
| Joker | 2 | 3 | 3 | 3 |
| Joker | 2 | 3 | 3 | 6 |
| Joker | 2 | 3 | 3 | 7 |
| Joker | 2 | 3 | 3 | 10 |
| Joker | 2 | 3 | 6 | 6 |
| Joker | 2 | 3 | 6 | 7 |
| Joker | 2 | 3 | 6 | 10 |
| Joker | 2 | 3 | 10 | 10 |
| Joker | 2 | 4 | 6 | 6 |
| Joker | 2 | 6 | 6 | 6 |
| Joker | 2 | 6 | 6 | 7 |
| Joker | 2 | 6 | 6 | 10 |
| Joker | 2 | 6 | 10 | 10 |
| Joker | 2 | 7 | 8 | 8 |
| Joker | 2 | 8 | 8 | 8 |
| Joker | 3 | 3 | 3 | 3 |
| Joker | 3 | 3 | 3 | 5 |
| Joker | 3 | 3 | 3 | 6 |
| Joker | 3 | 3 | 3 | 7 |
| Joker | 3 | 3 | 3 | 9 |
| Joker | 3 | 3 | 3 | 10 |
| Joker | 3 | 3 | 5 | 5 |
| Joker | 3 | 3 | 5 | 7 |
| Joker | 3 | 3 | 5 | 10 |
| Joker | 3 | 3 | 6 | 6 |
| Joker | 3 | 3 | 6 | 7 |
| Joker | 3 | 3 | 6 | 9 |
| Joker | 3 | 3 | 6 | 10 |
| Joker | 3 | 3 | 7 | 9 |
| Joker | 3 | 3 | 9 | 9 |
| Joker | 3 | 3 | 9 | 10 |
| Joker | 3 | 3 | 10 | 10 |
| Joker | 3 | 5 | 5 | 5 |
| Joker | 3 | 5 | 5 | 7 |
| Joker | 3 | 5 | 10 | 10 |
| Joker | 3 | 6 | 6 | 6 |
| Joker | 3 | 6 | 6 | 7 |
| Joker | 3 | 6 | 6 | 9 |
| Joker | 3 | 6 | 6 | 10 |
| Joker | 3 | 6 | 7 | 9 |
| Joker | 3 | 6 | 9 | 9 |
| Joker | 3 | 6 | 9 | 10 |
| Joker | 3 | 6 | 10 | 10 |
| Joker | 3 | 7 | 9 | 9 |
| Joker | 3 | 9 | 9 | 9 |
| Joker | 3 | 9 | 9 | 10 |
| Joker | 3 | 9 | 10 | 10 |
| Joker | 4 | 4 | 4 | 4 |
| Joker | 4 | 4 | 4 | 5 |
| Joker | 4 | 4 | 4 | 6 |
| Joker | 4 | 4 | 4 | 8 |
| Joker | 4 | 4 | 4 | 9 |
| Joker | 4 | 4 | 5 | 5 |
| Joker | 4 | 4 | 5 | 8 |
| Joker | 4 | 4 | 6 | 6 |
| Joker | 4 | 4 | 6 | 9 |
| Joker | 4 | 4 | 9 | 9 |
| Joker | 4 | 5 | 5 | 5 |
| Joker | 4 | 5 | 5 | 8 |
| Joker | 4 | 6 | 6 | 6 |
| Joker | 4 | 6 | 6 | 9 |
| Joker | 4 | 6 | 9 | 9 |
| Joker | 4 | 9 | 9 | 9 |
| Joker | 5 | 5 | 5 | 5 |
| Joker | 5 | 5 | 5 | 7 |
| Joker | 5 | 5 | 5 | 8 |
| Joker | 5 | 5 | 8 | 8 |
| Joker | 5 | 8 | 8 | 8 |
| Joker | 5 | 8 | 8 | 10 |
| Joker | 5 | 8 | 10 | 10 |
| Joker | 6 | 6 | 6 | 6 |
| Joker | 6 | 6 | 6 | 7 |
| Joker | 6 | 6 | 6 | 9 |
| Joker | 6 | 6 | 6 | 10 |
| Joker | 6 | 6 | 7 | 9 |
| Joker | 6 | 6 | 9 | 9 |
| Joker | 6 | 6 | 9 | 10 |
| Joker | 6 | 6 | 10 | 10 |
| Joker | 6 | 7 | 9 | 9 |
| Joker | 6 | 9 | 9 | 9 |
| Joker | 6 | 9 | 9 | 10 |
| Joker | 6 | 9 | 10 | 10 |
| Joker | 7 | 8 | 8 | 8 |
| Joker | 7 | 9 | 9 | 9 |
| Joker | 8 | 8 | 8 | 8 |
| Joker | 8 | 8 | 8 | 10 |
| Joker | 8 | 8 | 10 | 10 |
| Joker | 9 | 9 | 9 | 9 |
| Joker | 9 | 9 | 9 | 10 |
| Joker | 9 | 9 | 10 | 10 |
| Joker | 1 | 2 | 4 | 8 |
| Joker | 2 | 3 | 6 | 7 |
| Joker | 2 | 3 | 6 | 10 |
| Joker | 3 | 6 | 7 | 9 |
| Joker | 3 | 6 | 9 | 10 |
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 4th, 2018 at 10:04:07 AM
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Ah, Charlie and Wiz are both right. Three of my solutions were in error because I didn't notice that any five cards with a W,2,9 in it will qualify.
Based on their list, an unexpected conclusion is that if your hand has a Joker and a five and no duplicate ranks, the hand will always qualify (will always have 3 cards that add up to either 10 or 20.)
There is a weird mathematics here that probably no one has ever looked at. Of course, it is probably utterly useless.
Based on their list, an unexpected conclusion is that if your hand has a Joker and a five and no duplicate ranks, the hand will always qualify (will always have 3 cards that add up to either 10 or 20.)
There is a weird mathematics here that probably no one has ever looked at. Of course, it is probably utterly useless.
Last edited by: gordonm888 on Jun 4, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 4th, 2018 at 10:21:29 AM
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Quote: WizardThese come by way of my program. If I'm missing any, I must have a programming error.
...Full list (including duplicate ranks)...Short list (no duplicate ranks)....
I agree with the number in your long and short lists.
June 4th, 2018 at 11:02:14 AM
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I caught an error but I see error was caught, BBB 2nd spoiler, o deleted
When somebody doesn't believe me, I could care less. Some get totally bent out of shape when not believed. Weird. I believe very little on all forums
June 4th, 2018 at 4:02:57 PM
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Wizard, my numbers come out slightly differently than yours:
(DNQ = Did Not Qualify)
I get a house advantage of 1.8675%, which is close to what I get in simulations.
(DNQ = Did Not Qualify)
| Player | ||||||
|---|---|---|---|---|---|---|
| Dealer | DNQ | 1 | 2 | 3 | 4 | 5 |
| DNQ | 481649866016 | 91792807704 | 94536234488 | 95706153640 | 93892174512 | 102871588944 |
| 1 | 91792807704 | 17462798256 | 18098082352 | 18358209760 | 17982030744 | 19714019296 |
| 2 | 94536234488 | 18098082352 | 18474571432 | 18907749504 | 18464626480 | 20270209904 |
| 3 | 95706153640 | 18358209760 | 18907749504 | 19032515120 | 18751463112 | 20543861104 |
| 4 | 93892174512 | 17982030744 | 18464626480 | 18751463112 | 18230367992 | 20134053344 |
| 5 | 102871588944 | 19714019296 | 20270209904 | 20543861104 | 20134053344 | 21991599152 |
| 6 | 96935013664 | 18577547648 | 19095286800 | 19381775568 | 19147508968 | 20789238656 |
| 7 | 106073159712 | 20365173104 | 20855192064 | 21339774608 | 20730921696 | 22633053600 |
| 8 | 119005247784 | 22934347696 | 23517258544 | 23717303616 | 23217597328 | 25260095360 |
| 9 | 124326196496 | 24132904464 | 24401147280 | 24743143936 | 24258230064 | 26385678160 |
| 10 | 133714959808 | 25701097984 | 26210877376 | 26623197040 | 26059961600 | 28360748528 |
| Player | |||||
|---|---|---|---|---|---|
| Dealer | 6 | 7 | 8 | 9 | 10 |
| DNQ | 96935013664 | 106073159712 | 119005247784 | 124326196496 | 133714959808 |
| 1 | 18577547648 | 20365173104 | 22934347696 | 24132904464 | 25701097984 |
| 2 | 19095286800 | 20855192064 | 23517258544 | 24401147280 | 26210877376 |
| 3 | 19381775568 | 21339774608 | 23717303616 | 24743143936 | 26623197040 |
| 4 | 19147508968 | 20730921696 | 23217597328 | 24258230064 | 26059961600 |
| 5 | 20789238656 | 22633053600 | 25260095360 | 26385678160 | 28360748528 |
| 6 | 19442946728 | 21351853136 | 23834964288 | 24893783504 | 26792168976 |
| 7 | 21351853136 | 23033727536 | 25664113936 | 26777861136 | 28855216704 |
| 8 | 23834964288 | 25664113936 | 27955571304 | 29203481936 | 31629786016 |
| 9 | 24893783504 | 26777861136 | 29203481936 | 30245078416 | 32893944144 |
| 10 | 26792168976 | 28855216704 | 31629786016 | 32893944144 | 35425906656 |
I get a house advantage of 1.8675%, which is close to what I get in simulations.
June 4th, 2018 at 4:23:15 PM
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Thanks for your results. Clearly one of us is in error, and it could very well be me. To help us find our point of departure, I present the following table of possible outcomes for just the player, by your numbers and mine:
So we at least agree on the probability of qualifying. However, I'm clearing getting higher scores than you. The question is why. Let me think about it.
| Dealer | TDG | MS |
|---|---|---|
| DNQ | 0.313507 | 0.313507 |
| 1 | 0.060060 | 0.006356 |
| 2 | 0.061629 | 0.006873 |
| 3 | 0.062499 | 0.010460 |
| 4 | 0.061230 | 0.017654 |
| 5 | 0.066945 | 0.034546 |
| 6 | 0.063137 | 0.045905 |
| 7 | 0.068721 | 0.066897 |
| 8 | 0.076507 | 0.084342 |
| 9 | 0.079829 | 0.113352 |
| 10 | 0.085936 | 0.300108 |
| Total | 1.000000 | 1.000000 |
So we at least agree on the probability of qualifying. However, I'm clearing getting higher scores than you. The question is why. Let me think about it.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 4th, 2018 at 4:43:51 PM
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Quote: ThatDonGuyI get a house advantage of 1.8675%, which is close to what I get in simulations.
You're absolutely right. I found an error in implementing the rule about subtracting 10 if the two-card hand goes over 10.
Thank you very much for the correction. I definitely owe you more than a beer for that one.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 4th, 2018 at 4:45:51 PM
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Quote: WizardYou're absolutely right. I found an error in implementing the rule about subtracting 10 if the two-card hand goes over 10.
Thank you very much for the correction. I definitely owe you more than a beer for that one.
This time, You're On - I arrive in Vegas on Monday 6/18 in the afternoon, leaving Friday morning.
June 4th, 2018 at 7:01:35 PM
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Very good. I have been wondering how it was possible that 30% of hands wound up as ten points. No matter what the three cards are in the bottom hand, I imagine that the two cards up front are pretty close to being random. Even given how often the 2-card hands are T-T, why should the two-card combinations add up to 10 or 20 as frequently as 30%? It was bothering me.
But, LOL, I was too lazy to make up a spreadsheet listing all the hands. Thanks to ThatDonGuy for doing the work that I was too slothful to do, and shining light on the issue.
But, LOL, I was too lazy to make up a spreadsheet listing all the hands. Thanks to ThatDonGuy for doing the work that I was too slothful to do, and shining light on the issue.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 4th, 2018 at 8:06:16 PM
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Quote: gordonm888Very good. I have been wondering how it was possible that 30% of hands wound up as ten points.
That didn't feel quite right to me either but I've never once played the same so dismissed my doubts too easily. If I wrote a simulation, I'm afraid the exact same error would have caused the same mis-scoring of hands. My mistake was not properly scoring the hands. The rule about deducting 10 points of the score was over 10 was where I screwed up. Just goes to show that an error in one line of code out of hundreds will screw up the bottom line.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 5th, 2018 at 5:24:01 AM
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I like the notion of the pot bet that allows you to compete against other players at the table. This seems like a twist which might be incorporated into other table games. Is the pot bet optional? It seems to me that the amount of the pot bet must be consistent between the players (can't have one player betting $25 and others betting $5). I think the picture shows $100 on the pot bet; I doubt that would be typical.
I hate the fact that there is no decision-making or skill involved in this game. And no hand development. I don't play baccarat because I view it to be a boring coin-flip style game with no skill. But at least there can be some excitement when the banker is dealt a 3rd card with the outcome of the hand in the balance. Nothing like that here.
I would like to see this game incorporate some sort of decision point. Maybe a bet/fold/raise decision after the player receives their first 4 cards. Or the player is dealt 4 cards, chooses one to discard, then receives two final cards. Something like that.
I will try to play this game next time I'm in Tampa, just to investigate. But I'm sure I will not be interested in playing this game on a regular basis.
Oh, and congratulations on your bike ride, Wiz!
I hate the fact that there is no decision-making or skill involved in this game. And no hand development. I don't play baccarat because I view it to be a boring coin-flip style game with no skill. But at least there can be some excitement when the banker is dealt a 3rd card with the outcome of the hand in the balance. Nothing like that here.
I would like to see this game incorporate some sort of decision point. Maybe a bet/fold/raise decision after the player receives their first 4 cards. Or the player is dealt 4 cards, chooses one to discard, then receives two final cards. Something like that.
I will try to play this game next time I'm in Tampa, just to investigate. But I'm sure I will not be interested in playing this game on a regular basis.
Oh, and congratulations on your bike ride, Wiz!
June 5th, 2018 at 5:48:34 AM
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Quote: PapaChubbyI like the notion of the pot bet that allows you to compete against other players at the table. This seems like a twist which might be incorporated into other table games. Is the pot bet optional? It seems to me that the amount of the pot bet must be consistent between the players (can't have one player betting $25 and others betting $5). I think the picture shows $100 on the pot bet; I doubt that would be typical.
There is also that element of a non-raked community bet in the game Flop Poker. I agree the bet amount should be equal among players, but don't know what it is. Terapined is supposed to check out the game this week to provide more information.
Quote:I would like to see this game incorporate some sort of decision point. Maybe a bet/fold/raise decision after the player receives their first 4 cards. Or the player is dealt 4 cards, chooses one to discard, then receives two final cards. Something like that.
I agree. However, there is room on the shelf for mindless games of luck too. It is hard to criticize they old games because at least they have a following. If nobody had invented craps and suddenly a single table went on field trial, I bet everybody would say it was the worst new game ever.
Quote:Oh, and congratulations on your bike ride, Wiz!
Thanks! Was hoping someone would say that.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 5th, 2018 at 8:50:29 AM
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No Saigon 5 card at the Seminole Tampa Hard Rock
Spoke to a pit boss
Gone over a year
Never caught on
Nobody played it
The Asian food place is gone. A replacement coming so that space is walled off. Hopefully something bigger and better. Last place had real good food but more of a coffee shop atmosphere with just a long twisting counter for seating.
Boy this place is getting big. Saw more expansion. I think this is the 6th largest in the world. No competition for hundreds of miles.
Spoke to a pit boss
Gone over a year
Never caught on
Nobody played it
The Asian food place is gone. A replacement coming so that space is walled off. Hopefully something bigger and better. Last place had real good food but more of a coffee shop atmosphere with just a long twisting counter for seating.
Boy this place is getting big. Saw more expansion. I think this is the 6th largest in the world. No competition for hundreds of miles.
When somebody doesn't believe me, I could care less. Some get totally bent out of shape when not believed. Weird. I believe very little on all forums
June 5th, 2018 at 9:01:11 AM
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News on the expansion: Tampa Hard Rock Casino Expansion
Is the Asian food place to which you refer the noodle bar in the corner of the Asian gaming room? It was open when I was there a couple of weeks ago, and packed as usual. Maybe they're expanding, as they only had room for about 15 customers at the bar (and I could never find a seat).
Is the Asian food place to which you refer the noodle bar in the corner of the Asian gaming room? It was open when I was there a couple of weeks ago, and packed as usual. Maybe they're expanding, as they only had room for about 15 customers at the bar (and I could never find a seat).
June 5th, 2018 at 9:17:16 AM
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Quote: PapaChubbyNews on the expansion: Tampa Hard Rock Casino Expansion
Is the Asian food place to which you refer the noodle bar in the corner of the Asian gaming room? It was open when I was there a couple of weeks ago, and packed as usual. Maybe they're expanding, as they only had room for about 15 customers at the bar (and I could never find a seat).
Yes, thats the place I was referring to.
Spoke to another pit boss, i asked him if he knew any casinos with Saigon 5 and he did not know
When somebody doesn't believe me, I could care less. Some get totally bent out of shape when not believed. Weird. I believe very little on all forums
June 5th, 2018 at 9:45:09 AM
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The hand: Joker-10-9-7-4
has 4 different ways to qualify, yielding point totals of 3,6,9 and 9! It might be easy for a player to not notice the highest scoring arrangement. So, there is an element of skill involved on a small number of hands that contain a joker.
Edit: The hand Joker-10-7-4-3 has 5 ways to qualify!
has 4 different ways to qualify, yielding point totals of 3,6,9 and 9! It might be easy for a player to not notice the highest scoring arrangement. So, there is an element of skill involved on a small number of hands that contain a joker.
Edit: The hand Joker-10-7-4-3 has 5 ways to qualify!
Last edited by: gordonm888 on Jun 5, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 5th, 2018 at 12:53:47 PM
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?T743 : Interesting that the way to find the highest total is to add all 5 and see if you can get to a total of 10x. T743 add up to 24, so with ?=6 this can be achieved. Provided you can make 10 with two cards, that must be the maximum. Thus ?T4/73 or T73/?4 work (Joker=6). ?T7/43 or T73/?4 give a 7-hand (Joker=3), ?74/T3 gives a 3-card (Joker=9).
June 5th, 2018 at 12:56:37 PM
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Quote: terapinedNo Saigon 5 card at the Seminole Tampa Hard Rock
Thank you for checking.
To be honest, I'm not surprised authentic Chinese food is a bit difficult to find in west Florida. Your next Vegas visit, I'll treat you to some good stuff.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 6th, 2018 at 10:25:11 AM
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I was wondering if the player will ever have a choice between arranging his hand so that it makes either 5 points or a lower point total 1-4. Because a 5 point hand has a 1:2 payout, I wondered whether optimal strategy would involve the player actually choosing the hand arrangement with the lower point total.
Quick summary: No. Choosing the arrangement of a hand with the highest point total is always correct.
I found 8 distinct hands in which it is possible to arrange the cards so that the hand is either 5 points or 1-4 points.
5 or 1 points: WT651
5 or 2 points: WT432, WT321, W8641, WT775, W8774, WT522 and W9322
For example, consider WT432:
5 points: WT4-32 EV= -0.03514
2 points: W43-T2 EV= -0.13524
Quick summary: No. Choosing the arrangement of a hand with the highest point total is always correct.
I found 8 distinct hands in which it is possible to arrange the cards so that the hand is either 5 points or 1-4 points.
5 or 1 points: WT651
5 or 2 points: WT432, WT321, W8641, WT775, W8774, WT522 and W9322
For example, consider WT432:
5 points: WT4-32 EV= -0.03514
2 points: W43-T2 EV= -0.13524
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 6th, 2018 at 11:18:06 AM
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Quote: gordonm888I was wondering if the player will ever have a choice between arranging his hand so that it makes either 5 points or a lower point total 1-4. Because a 5 point hand has a 1:2 payout, I wondered whether optimal strategy would involve the player actually choosing the hand arrangement with the lower point total.
Good question.
One one thing, I'm not even sure if the player is even allowed to set his hand. In this online game it is done automatically.
However, if you could, here is an estimate of the expected value of each total. This is based on independent decks between player and dealer.
| Points | EV |
|---|---|
| 0 | -28.70% |
| 1 | -22.70% |
| 2 | -19.12% |
| 3 | -6.71% |
| 4 | 5.66% |
| 5 | -9.47% |
| 6 | 31.49% |
| 7 | 44.67% |
| 8 | 59.20% |
| 9 | 74.83% |
| 10 | 91.41% |
| Does not qualify | -68.65% |
What this seems to show is that playing 3 or 4 would beat a 5 in expected value, but not 2 or less.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 6th, 2018 at 11:24:40 AM
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Quote: WizardGood question.
One one thing, I'm not even sure if the player is even allowed to set his hand. In this online game it is done automatically.
However, if you could, here is an estimate of the expected value of each total. This is based on independent decks between player and dealer.
Points EV 0 -28.70% 1 -22.70% 2 -19.12% 3 -6.71% 4 5.66% 5 -9.47% 6 31.49% 7 44.67% 8 59.20% 9 74.83% 10 91.41% Does not qualify -68.65%
What this seems to show is that playing 3 or 4 would beat a 5 in expected value, but not 2 or less.
Yes, those are generic EVs not considering the five cards in your hand. However, all hands that can be arranged to make two or more different point totals have a Joker in them. Removing the Joker from the deck will change all of those values by a considerable amount. FYI:
| Points | EV with 53 cards | EV -Joker removed |
|---|---|---|
| 0 | -28.70% | -32.89% |
| 1 | -22.70% | -26.58% |
| 2 | -19.12% | -14.11% |
| 3 | -6.71% | -0.01% |
| 4 | 5.66% | 13.08% |
| 5 | -9.47% | ]-3.24% |
| 6 | 31.49% | 40.02% |
| 7 | 44.67% | 52.29% |
| 8 | 59.20% | 65.51% |
| 9 | 74.83% | 78.20% |
| 10 | 91.61% | 92.43% |
| Does not qualify | -68.65% | -66.44% |
Not really sure what a zero point hand is, given that DNQ is a separate entry?
Anyway, your basic advice appears to be perfectly correct. A 5 point hand is worse than a 4 or 3 point hand.
Last edited by: gordonm888 on Jun 6, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 6th, 2018 at 1:40:05 PM
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If you got 5 ten-value cards, or 3 face cards and a 6-4, for example, all of those hands would both qualify and be worth 0. There would be a fair number of zero hands, I would think.
If the House lost every hand, they wouldn't deal the game.
June 7th, 2018 at 3:25:33 AM
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I'm not sure how you can get a 0-point hand since you only subtract 10 if the total is over 10. A simple idea is If you add up all five cards and ignore the 10's then if you can qualify you are subtracting 10's so the last digit of the 2-card hand will be the same (or 10 if the digit is 0). Without a joker there is only one possible total, albeit you may be able to make it different ways (e.g. T7643 = T73/64 or T64/73; both total=30 so lo hand = 10).
With a joker you have a variety of totals which will be something like 32 35 38, 35 38 41, 29 32 35; thus the difference between them is 3 and if you can make a 5 then the other totals will include an 8 or 9 (as well as a 1 or 2).
Note According to the wizard write-up a picture card is worth 10 and all other cards are positive, thus two cards cannot add up to 0. The rule about exceeding ten says
With a joker you have a variety of totals which will be something like 32 35 38, 35 38 41, 29 32 35; thus the difference between them is 3 and if you can make a 5 then the other totals will include an 8 or 9 (as well as a 1 or 2).
Note According to the wizard write-up a picture card is worth 10 and all other cards are positive, thus two cards cannot add up to 0. The rule about exceeding ten says
Thus were people assuming two picture cards were considered as zero (e.g. TT866)?Quote: https://wizardofodds.com/games/saigon-5-card/the point value of the remaining two cards shall be the sum of the point value of the two cards, except if that total is greater than 10, then ten will be subtracted from the total.
June 7th, 2018 at 7:51:59 AM
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It's true you cannot get a zero point hand. I shouldn't have confused the topic by putting the line in my table. My value was simply equal to prob(dealer doesn't qualify)-prob(dealer qualifies).
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
