Useful bridge/math tidbit

[fred]

KJ109

 

A432

 

This is your trump suit. Your LHO gets a ruff early in the play. When you gain the lead, you cash the Ace of trump and lead a second round, but you see nothing except small cards. Finesse or drop?

 

This situation is not uncommon in real life and (I think!) I have found a simple rule for knowing what to do (though, as usual, I might have made a math error):

 

If your RHO has 3+ more known cards than your LHO, you should finesse.

 

If your RHO has exactly 2 more known cards than your LHO, you are faced with a complete guess (Qxxx on your left and Qx on your right are equally likely).

 

If your RHO has 1 or 0 more known cards than your LHO, you should play for the drop.

 

This is somewhat obvious if you think about it, but by remembering this rule you don't have to think about it :)

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[Little Kid]

Thanks for posting this! These kind of tips are useful for people like me who take forever doing the math at the table! :)

[jonottawa]

KJ109

 

A432

 

This is your trump suit. Your LHO gets a ruff early in the play. When you gain the lead, you cash the Ace of trump and lead a second round, but you see nothing except small cards. Finesse or drop?

 

This situation is not uncommon in real life and (I think!) I have found a simple rule for knowing what to do (though, as usual, I might have made a math error):

 

If your RHO has 3+ more known cards than your LHO, you should finesse.

 

If your RHO has exactly 2 more known cards than your LHO, you are faced with a complete guess (Qxxx on your left and Qx on your right are equally likely).

 

If your RHO has 1 or 0 more known cards than your LHO, you should play for the drop.

 

This is somewhat obvious if you think about it, but by remembering this rule you don't have to think about it :)

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

Any chance of an explanation for the somewhat idiots like myself who don't find this somewhat (or the least bit) obvious?

[junyi_zhu]

KJ109

 

A432

 

This is your trump suit. Your LHO gets a ruff early in the play. When you gain the lead, you cash the Ace of trump and lead a second round, but you see nothing except small cards. Finesse or drop?

 

This situation is not uncommon in real life and (I think!) I have found a simple rule for knowing what to do (though, as usual, I might have made a math error):

 

If your RHO has 3+ more known cards than your LHO, you should finesse.

 

If your RHO has exactly 2 more known cards than your LHO, you are faced with a complete guess (Qxxx on your left and Qx on your right are equally likely).

 

If your RHO has 1 or 0 more known cards than your LHO, you should play for the drop.

 

This is somewhat obvious if you think about it, but by remembering this rule you don't have to think about it :)

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

Any chance of an explanation for the somewhat idiots like myself who don't find this somewhat (or the least bit) obvious?

The LHO shows two more trumps than RHO.

Therefore, if the difference of side suit shown distribution of LHO and RHO < 2,

RHO is more likely to hold the Q. (because the probability of holding Q is proportional to the unknown cards in one's hand)

For example, LHO leads a doubleton to partner's AK and obtains a ruff and your side holds 8 card in that side suit, then LHO shows 2 cards and RHO shows 3 cards in that suit. Therefore, you should play to drop.

If it is greater than 2, LHO is more likely to hold Q.

For example, LHO leads his singleton to partner's ace and gets a ruff, his partner holds 5 card in that suit. You should take the finesse.

If it equals 2, it's just a guess.

For example, LHO leads a singleton, his partner holds Axx and gives him a ruff.

[Zelandakh]

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)

[bucky]

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)

I think what he meant was, at the time you played A and a second trump (and LHO followed low), LHO has shown up 3 trumps and RHO 1. At that point (RHO is yet to play), LHO showed 2 more trumps than RHO. That of course doesn't mean LHO actually holds 2 more trumps originally.

[gnasher]

I think of it in two stages: work out the relative likelihood of a specific break; then work out how many relevant breaks there are.

 

Suppose that a side-suit broke 2=4. RHO has been dealt two more cards than LHO. Then we deal LHO three specific trumps, and RHO one specific trump. Now each of them has been dealt five cards. Therefore it is evens whether the remaining trump goes to LHO or to RHO. Hence a specific 4=1 break is exactly as likely as a specific 3=2 break.

 

There are four possible Qxxx-x breaks, and four possible xxx-Qx breaks. Hence the two breaks are equally likely.

[aguahombre]

add into the mix that a good defender might try for taps, rather than roughs(whether it would be sucessful or not on the particular hand). with qxxx of trump. Gotta know the whole hand.

[junyi_zhu]

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.

[Little Kid]

So wait, this is simply a matter of counting vacant spaces (including cards played in the critical suit)? If so I have been making life so much harder than it needed to be!

[gnasher]

Sorry - gibberish

[jonottawa]

Sorry - gibberish

Dude, don't self-edit like that, gnasher gibberish is way more interesting/insightful than 95% of the stuff I read on here anyway.

[ritong]

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?

[rogerclee]

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?

Yes when it's Qxxx.

[wclass___]

OP gives you a ''fish'', but it is way better to learn ''fishing'' to get many more.

[BunnyGo]

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?

[Mbodell]

So wait, this is simply a matter of counting vacant spaces (including cards played in the critical suit)? If so I have been making life so much harder than it needed to be!

You can't count cards for vacant spaces that have been played in a suit when only some of the cards of a suit have been played. However, you can subdivide a suit into "interesting cards" and "spots" and count them for vacant spaces as if they were two different suits and count one of the suits once it has been played (all the spot cards in this example). Essentially there are "two" opponents trump suits in this example: Q and 5678. In Fred's example we've already seen the full set of spot cards (one trump, one card each on the A, and a small card on the 2nd round of trump). Basically an opponent can play the spot cards in any order, but can't play the Q until they play the spot cards (without losing a trick), so you can count the spot cards in the vacant spaces calculation. So if some side suit was 1=3 (the one that the trump was scored in maybe) and you've got a complete count on it and don't have a complete count on any other suit then it is 50-50. If the side suit were 1=4 you'd want to finesse.

[JLOGIC]

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?

Yes when it's Qxxx.

lol

[pooltuna]

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?

generally a good question but given our spots I can see it is easy going for a ruff in this situation

[junyi_zhu]

So wait, this is simply a matter of counting vacant spaces (including cards played in the critical suit)? If so I have been making life so much harder than it needed to be!

yeah, just a simple matter of counting vacancies....

[junyi_zhu]

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]

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]

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]

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.