[junyi_zhu]

BunnyGo, on Sep 29 2010, 05:37 AM, said:

junyi_zhu, on Sep 28 2010, 06:59 PM, said:

Zelandakh, on Sep 28 2010, 11:10 PM, said:

junyi_zhu, on Sep 28 2010, 10:35 PM, said:

The LHO shows two more trumps than RHO.

I do not think Fred said anything about trump length having been shown. Fred, would your rule also apply if we had 9 trumps and RHO had, say, opened a weak 2 and marked the distribution in a suit that way instead? (ie 6 opposite 4 = guess)

This is the correct way to count. His assumption is that 4 trumps are shown and trump Q is missing.
The magic number of 2 is just due to the shown trump number difference, which is also 2.

The other number 2 rule case is the 10 trumps case,
suppose your LHO gets a ruff and plays low under your Q, should you drop or finesse K?
This is also determined by the side suit shown cards difference.

I'm a little confused. For deciding "odds" shouldn't it also matter how many cards remain to be played? Or does that simply determine how much of an advantage these observations give you?

It is determined by the vacant space of your opp's unknown distributions.
Suppose, LHO leads singleton and gets a ruff, you get the complete picture of that suit. So the vacant space for LHO is 12 (13-1) and the vacant space for RHO is 13- length of that suit. After you draw one round of trumps, play another card and LHO follows, your totally 4 trumps are shown with Q missing, now LHO's vacant space is 13-1(singleton side suit)-3(trumps) = 9. RHO's vacant space is 13- length of that side suit - 1(trump).
Since the probability of Q is proportional to the vacant space, all you care is the difference of length of that side suit between RHO and LHO. If this number is 3 or more , you should finesse. If it is 1, you want to drop. If it is 2, it is 50% either way. Of course, it your opps show some distribution in other side suits (they could play out that suit, or they show it by bidding) the calculation can be different. The basic idea is still very simple, counting the vacant space.

[shyams]

I need a clarification here: Does LHO's play to the "decision trick" count as a shown card?

e.g. LHO starts with a singleton, RHO wins (he has 5) and gives LHO a ruff. LHO exits in a side suit (RHO following). Trump Ace produces x from both opps. So far, it is 1 lead+2 trumps+1 side suit for LHO vs. 5+1+1 for RHO (4 vs. 7 --> finesse)

When you play a trump and LHO plays x, does this x count? Is it now 5 vs. 7? Or do I use the count before play to this trick of 4 vs. 7?

[junyi_zhu]

shyams, on Sep 29 2010, 04:12 PM, said:

I need a clarification here: Does LHO's play to the "decision trick" count as a shown card?

e.g. LHO starts with a singleton, RHO wins (he has 5) and gives LHO a ruff. LHO exits in a side suit (RHO following). Trump Ace produces x from both opps. So far, it is 1 lead+2 trumps+1 side suit for LHO vs. 5+1+1 for RHO (4 vs. 7 --> finesse)

When you play a trump and LHO plays x, does this x count? Is it now 5 vs. 7? Or do I use the count before play to this trick of 4 vs. 7?

You can count the vacant space only when the suit distribution is clear. Suppose for one certain suit, opps have 8 cards, you play two rounds, both follow, you can't count this suit yet, because the distribution of this suit is still unclear. vacant space count can only be applied when the suit distribution is clear(or one card missing in your key suit). So for your example, the correct way to count vacant space is:
LHO: 13-1(singleton) -3(three trumps)=9
RHO: 13-5(5 in that side suit) -1 (one trump) = 7
So it is 9:7 better to play finesse vs. dropping.

[Hanoi5]

junyi_zhu, on Sep 29 2010, 12:49 PM, said:

shyams, on Sep 29 2010, 04:12 PM, said:

I need a clarification here: Does LHO's play to the "decision trick" count as a shown card?

e.g. LHO starts with a singleton, RHO wins (he has 5) and gives LHO a ruff. LHO exits in a side suit (RHO following). Trump Ace produces x from both opps. So far, it is 1 lead+2 trumps+1 side suit for LHO vs. 5+1+1 for RHO (4 vs. 7 --> finesse)

When you play a trump and LHO plays x, does this x count? Is it now 5 vs. 7? Or do I use the count before play to this trick of 4 vs. 7?

You can count the vacant space only when the suit distribution is clear. Suppose for one certain suit, opps have 8 cards, you play two rounds, both follow, you can't count this suit yet, because the distribution of this suit is still unclear. vacant space count can only be applied when the suit distribution is clear(or one card missing in your key suit). So for your example, the correct way to count vacant space is:
LHO: 13-1(singleton) -3(three trumps)=9
RHO: 13-5(5 in that side suit) -1 (one trump) = 7
So it is 9:7 better to play finesse vs. dropping.

Wouldn't you have a complete guess since the difference is 2?

[junyi_zhu]

Hanoi5, on Sep 29 2010, 05:09 PM, said:

junyi_zhu, on Sep 29 2010, 12:49 PM, said:

shyams, on Sep 29 2010, 04:12 PM, said:

I need a clarification here: Does LHO's play to the "decision trick" count as a shown card?

e.g. LHO starts with a singleton, RHO wins (he has 5) and gives LHO a ruff. LHO exits in a side suit (RHO following). Trump Ace produces x from both opps. So far, it is 1 lead+2 trumps+1 side suit for LHO vs. 5+1+1 for RHO (4 vs. 7 --> finesse)

When you play a trump and LHO plays x, does this x count? Is it now 5 vs. 7? Or do I use the count before play to this trick of 4 vs. 7?

You can count the vacant space only when the suit distribution is clear. Suppose for one certain suit, opps have 8 cards, you play two rounds, both follow, you can't count this suit yet, because the distribution of this suit is still unclear. vacant space count can only be applied when the suit distribution is clear(or one card missing in your key suit). So for your example, the correct way to count vacant space is:
LHO: 13-1(singleton) -3(three trumps)=9
RHO: 13-5(5 in that side suit) -1 (one trump) = 7
So it is 9:7 better to play finesse vs. dropping.

Wouldn't you have a complete guess since the difference is 2?

No, this is the difference of total vacant space, which just gives your final answer. If The difference of your opps' total vacant space is zero, it's 50% to finesse or to drop.
What Fred suggested is that vacant space difference other than the trump suit. When that number is 2, subtract the difference in trumps, which is 2, you get your total vacant space, which is 0, that gives even money to finesse or drop.

[junyi_zhu]

ritong, on Sep 29 2010, 03:20 AM, said:

hi!

i certainly agree with fred about the arithmetical side of his demonstration

however, the fact that lho has got an early ruff basically means that he led to get one..do we all do that with a potential trump trick?

Against Henri, it could be different.

[bucky]

junyi_zhu, on Sep 29 2010, 11:49 AM, said:

shyams, on Sep 29 2010, 04:12 PM, said:

I need a clarification here: Does LHO's play to the "decision trick" count as a shown card?

e.g. LHO starts with a singleton, RHO wins (he has 5) and gives LHO a ruff. LHO exits in a side suit (RHO following). Trump Ace produces x from both opps. So far, it is 1 lead+2 trumps+1 side suit for LHO vs. 5+1+1 for RHO (4 vs. 7 --> finesse)

When you play a trump and LHO plays x, does this x count? Is it now 5 vs. 7? Or do I use the count before play to this trick of 4 vs. 7?

You can count the vacant space only when the suit distribution is clear. Suppose for one certain suit, opps have 8 cards, you play two rounds, both follow, you can't count this suit yet, because the distribution of this suit is still unclear. vacant space count can only be applied when the suit distribution is clear(or one card missing in your key suit). So for your example, the correct way to count vacant space is:
LHO: 13-1(singleton) -3(three trumps)=9
RHO: 13-5(5 in that side suit) -1 (one trump) = 7
So it is 9:7 better to play finesse vs. dropping.

I think the answer to the original question is: the x counts, so now it is 5 vs. 7. You always count the vacant space at the decision point, which is AFTER lho followed 2nd trump and BEFORE rho has played. When the side suit breaks 1-5, the vacant space is: LHO 8, RHO 6.

[kgr]

junyi_zhu, on Sep 29 2010, 06:49 PM, said:

....
You can count the vacant space only when the suit distribution is clear. ....

What is the logic about this?
(Before I read this I thought making a post to ask this & I was almost sure that you could do it always.)
Logically you would think that if LHO leads a Heart then vacant spaces are 12:13..?
I can only remember this if I understand it.

[gwnn]

I think, kgr, the argument I wrote in this thread applies to this case as well. Caveat emptor.

[bucky]

kgr, on Sep 29 2010, 05:27 PM, said:

Logically you would think that if LHO leads a Heart then vacant spaces are 12:13..?
I can only remember this if I understand it.

Actually yes, IF LHO picked a totally random card to lead, and that you need to make a decision right before RHO plays. After trick 1 is completed (assuming RHO follows heart), the vacant space is back to 12:12.

[kgr]

gwnn, on Sep 30 2010, 12:39 AM, said:

I think, kgr, the argument I wrote in this thread applies to this case as well. Caveat emptor.

I didn't understand it. I'll reread it later

[kgr]

bucky, on Sep 30 2010, 12:57 AM, said:

kgr, on Sep 29 2010, 05:27 PM, said:

Logically you would think that if LHO leads a Heart then vacant spaces are 12:13..?
I can only remember this if I understand it.

Actually yes, IF LHO picked a totally random card to lead, and that you need to make a decision right before RHO plays. After trick 1 is completed (assuming RHO follows heart), the vacant space is back to 12:12.

Are you saying?:
that if LHO leads a random card then probability that RHO holds another not shown specific card is 13:12.
that if LHO is a bridger and leads a card then probability that RHO holds another not shown specific card is 13:13.
(what if LHO is a beginner and does not have a clue what he is doing??)

[junyi_zhu]

kgr, on Sep 29 2010, 10:27 PM, said:

junyi_zhu, on Sep 29 2010, 06:49 PM, said:

....
You can count the vacant space only when the suit distribution is clear. ....

What is the logic about this?
(Before I read this I thought making a post to ask this & I was almost sure that you could do it always.)
Logically you would think that if LHO leads a Heart then vacant spaces are 12:13..?
I can only remember this if I understand it.

Because vacant space calculation is an approximation in some situations. For example, suppose opps have 8 spades, you draw two rounds, both follow. Therefore, spades can't be 8-0 or 7-1. However, 6-2, 5-3, 4-4 are all possible, so you just don't really know the exact distribution of that suit. In this sense, you can't include this suit into your calculation. All you know is that spades distribution is rather unknown and it's impossible to be 8-0 or 7-1, which is still a very small percentage comparing with all the possible spades distributions. Therefore, It's still fairly good approximation to assume that you don't know the spade distribution at all. In the other thread talking about the probabilities, one post was very well said: what's the average number of your heart suit if you open 1H showing 5 or more? I guess it can't be 6 and should be in the middle of 5-6, because frequency of 5, 6, 7 hearts holdings are very different. In this case, it's the same logic. When they hold 8 card, even if you know the distribution can't be 7-1 or 8-0, you still don't know the exact distribution and 7-1 8-0 are very rare events, so you can't really take those out of your approximation easily. Therefore, you'd just stick to what you have and consider the distribution of spades is unknown. The real percentage can be calculated by computer simulations in a quite accurate way, which should be slightly different from the vacant space calculation. However, at the table, vacant space counting is still your best friend. Still, in many situations, vacant space counting actually gives the accurate result.

[bucky]

kgr, on Sep 29 2010, 06:32 PM, said:

Are you saying?:
that if LHO leads a random card then probability that RHO holds another not shown specific card is 13:12.
that if LHO is a bridger and leads a card then probability that RHO holds another not shown specific card is 13:13.
(what if LHO is a beginner and does not have a clue what he is doing??)

After the lead, 13:13 no longer applies, there is just not this much room for hidden cards.

When I said about random card, I am not using information on bidding and lead agreement. You can always rule out certain shape from the bidding, and the lead will also tell you something (if the lead is a low heart, even a beginner LHO probably wouldn't have AKQx in that suit). But strictly in terms of vacant space, after the opening lead and before RHO plays to the first trick, a particular unseen card can be anywhere among 12 remaining cards in LHO hand, or 13 remaining cards in RHO hand.

Of course in reality it is not going to be 13:12, you always have clues in the bidding and lead. If you can rule out the possibility of RHO being void in hearts even before he plays to the first trick, you are back to 12:12. If you are certain that LHO has longer hearts than RHO, you will know that RHO is more likely to hold a specific card in a side suit.

[MBV53]

Good point/tip fred!
MBV

[kgr]

junyi_zhu, on Sep 30 2010, 01:33 AM, said:

kgr, on Sep 29 2010, 10:27 PM, said:

junyi_zhu, on Sep 29 2010, 06:49 PM, said:

....
You can count the vacant space only when the suit distribution is clear. ....

What is the logic about this?
(Before I read this I thought making a post to ask this & I was almost sure that you could do it always.)
Logically you would think that if LHO leads a Heart then vacant spaces are 12:13..?
I can only remember this if I understand it.

Because vacant space calculation is an approximation in some situations. For example, suppose opps have 8 spades, you draw two rounds, both follow. Therefore, spades can't be 8-0 or 7-1. However, 6-2, 5-3, 4-4 are all possible, so you just don't really know the exact distribution of that suit. In this sense, you can't include this suit into your calculation. All you know is that spades distribution is rather unknown and it's impossible to be 8-0 or 7-1, which is still a very small percentage comparing with all the possible spades distributions. Therefore, It's still fairly good approximation to assume that you don't know the spade distribution at all. In the other thread talking about the probabilities, one post was very well said: what's the average number of your heart suit if you open 1H showing 5 or more? I guess it can't be 6 and should be in the middle of 5-6, because frequency of 5, 6, 7 hearts holdings are very different. In this case, it's the same logic. When they hold 8 card, even if you know the distribution can't be 7-1 or 8-0, you still don't know the exact distribution and 7-1 8-0 are very rare events, so you can't really take those out of your approximation easily. Therefore, you'd just stick to what you have and consider the distribution of spades is unknown. The real percentage can be calculated by computer simulations in a quite accurate way, which should be slightly different from the vacant space calculation. However, at the table, vacant space counting is still your best friend. Still, in many situations, vacant space counting actually gives the accurate result.

Thanks for the effort. I want to believe the above, but I wonder how far off both methods are:

---

♠ is trumps.
LHO leads a small ♥, RHO return a ♥ and LHO ruffs.
LHO plays a random ♦ and RHO follows that suit.
You cash ♠A and lead a second round. All follow with small ♠'s.
 
Probability that LHO has ♠Q according to vacant space theory:
13-1-3:13-6-1=9:6=0.6
 
Probability if WRONGLY taking the ♦ play into account:
13-1-3-1:13-6-1-1=8:5=0.615385
 
If Playing ♣/♦ before the 2nd trump then:
- for Vacant Spaces this will always be 0.6
- for the WRONG calculation this will be:
1 minor: 0.615385
2 minors: 0.636364
3 minors: 0.666667
4 minors: 0.714286
5 minors: 0.8
==> Is anyone able to calculate the real probabilities?
BTW: Does it make a difference for vacant space theory if opps always play their small cards from low to high?

[hanp]

Yes you can compute the exact probabilities. It is easy but takes a considerable amount of work.

[junyi_zhu]

kgr, on Sep 30 2010, 07:02 AM, said:

junyi_zhu, on Sep 30 2010, 01:33 AM, said:

kgr, on Sep 29 2010, 10:27 PM, said:

junyi_zhu, on Sep 29 2010, 06:49 PM, said:

....
You can count the vacant space only when the suit distribution is clear. ....

What is the logic about this?
(Before I read this I thought making a post to ask this & I was almost sure that you could do it always.)
Logically you would think that if LHO leads a Heart then vacant spaces are 12:13..?
I can only remember this if I understand it.

Because vacant space calculation is an approximation in some situations. For example, suppose opps have 8 spades, you draw two rounds, both follow. Therefore, spades can't be 8-0 or 7-1. However, 6-2, 5-3, 4-4 are all possible, so you just don't really know the exact distribution of that suit. In this sense, you can't include this suit into your calculation. All you know is that spades distribution is rather unknown and it's impossible to be 8-0 or 7-1, which is still a very small percentage comparing with all the possible spades distributions. Therefore, It's still fairly good approximation to assume that you don't know the spade distribution at all. In the other thread talking about the probabilities, one post was very well said: what's the average number of your heart suit if you open 1H showing 5 or more? I guess it can't be 6 and should be in the middle of 5-6, because frequency of 5, 6, 7 hearts holdings are very different. In this case, it's the same logic. When they hold 8 card, even if you know the distribution can't be 7-1 or 8-0, you still don't know the exact distribution and 7-1 8-0 are very rare events, so you can't really take those out of your approximation easily. Therefore, you'd just stick to what you have and consider the distribution of spades is unknown. The real percentage can be calculated by computer simulations in a quite accurate way, which should be slightly different from the vacant space calculation. However, at the table, vacant space counting is still your best friend. Still, in many situations, vacant space counting actually gives the accurate result.

Thanks for the effort. I want to believe the above, but I wonder how far off both methods are:

---

♠ is trumps.
LHO leads a small ♥, RHO return a ♥ and LHO ruffs.
LHO plays a random ♦ and RHO follows that suit.
You cash ♠A and lead a second round. All follow with small ♠'s.
 
Probability that LHO has ♠Q according to vacant space theory:
13-1-3:13-6-1=9:6=0.6
 
Probability if WRONGLY taking the ♦ play into account:
13-1-3-1:13-6-1-1=8:5=0.615385
 
If Playing ♣/♦ before the 2nd trump then:
- for Vacant Spaces this will always be 0.6
- for the WRONG calculation this will be:
1 minor: 0.615385
2 minors: 0.636364
3 minors: 0.666667
4 minors: 0.714286
5 minors: 0.8
==> Is anyone able to calculate the real probabilities?
BTW: Does it make a difference for vacant space theory if opps always play their small cards from low to high?

You made a mistake in your vacant space count, spade situation is still unknown.
You can apply vacant space counting only when the situation of a suit is clear, or missing one key card in your key suit. Here, you just don't know the spade distribution yet. It could be 3-4, 4-3, 5-2, 6-1.

[dkharty]

kgr, on Sep 30 2010, 02:02 AM, said:

Dealer: ????? Vul: ???? Scoring: Unknown

♠ KJT9 ♥ KQJx ♦ xx ♣ xxx ♠ Ax ♥ xxxxx ♦ AKQ ♣ AKQ

♠ is trumps.

I would love to see this auction...

[bucky]

kgr, on Sep 30 2010, 02:02 AM, said:

♠ is trumps.
LHO leads a small ♥, RHO return a ♥ and LHO ruffs.
LHO plays a random ♦ and RHO follows that suit.
You cash ♠A and lead a second round. All follow with small ♠'s.
 
Probability that LHO has ♠Q according to vacant space theory:
13-1-3:13-6-1=9:6=0.6
 
Probability if WRONGLY taking the ♦ play into account:
13-1-3-1:13-6-1-1=8:5=0.615385

How did you derive this?

What is "13-1-3-1:13-6-1-1"? I can see "13-1-3-1" as "13 cards minus one H minus 3 S minus 1D", but what is "13-6-1-1"? And why taking ♦ play into account is WRONG?