Combining Odds

[pigpenz]

interesting little hand came up in imp pairs game

auction:

1♣ pass pass 1♠

2♣ 4♠ pass pass

pass

 

 

 

[hv=n=sj982ha53dkj5c952&s=skq654hk96da432c6]133|200|[/hv]

 

opps lead a♣ continure club you ruff

opps then win second spade and exit club which you ruff.

 

ok what is best percentage play now?

[pigpenz]

my feeling is to now play ak♥ and a third heart and still have diamond finesse to fall back on if west wins third heart....if east wins they are endplayed.

 

I fell out of my chair when my partner hooked j♦ :( It won and he made 11 tricks...ouch!

 

using Pavliceks calculator

diamond hook first round 26%

AK♦ then third one 45%

I guess heart throw in probably around 70%

[inquiry]

my feeling is to now play ak♥ and a third heart and still have diamond finesse to fall back on if west wins third heart....if east wins they are endplayed.

 

I fell out of my chair when my partner hooked j♦ :(  It won and he made 11 tricks...ouch!

 

using Pavliceks calculator

diamond hook first round 26%

AK♦ then third one 45%

I guess heart throw in probably around 70%

AK and a heart blantatly like that after pulling trumps and strippig ♣s will "never" work against any bridge player in EAST seat (unless he has five hearts or QJT, or QJTx). So the "throw in" is a lot worse than 70%, but of course if the throw in fails, you are back to the 50% diamond hook, but you lose advantage of 3-3 diamond split with hook offside. IF you are going to go with this HEART AK line, you have to try to hide your plans a little better. Heart to the ACE for a ♠ "finessee" for example might make it difficult for east to unblock with heart QJx for example and diamond queen. But on your lune, he will be throwing the top two hearts without any problem.

 

Not sure why PAvelik's calculater thinks a diamond hook is only 26%, 2!C ruff, 3!S in dummy, 2!H and 3!D is 10 tricks, and ♦ hook looks like roughly 50%, not 26.

 

I would guess playing on diamonds (50% hook is on, 35% of remaining time, diamonds are 3-3, total chance 0.5 + 0.35.5*0.5 = 0.5 + .17 = 67%, plus the odd chance to catch singleton queen of diamonds offside, is probably better. Now if EAST isn't a bridge player and would never unblock, your line would increase in merit.

[awm]

Why is a finesse 26%? I'm confused. Certainly LHO has more clubs than RHO, but LHO also has more points. I don't see why the diamond queen is much less than 50% to be onside.

 

I think the first order of business is to pull trumps, starting with the king from hand. If trumps are 3-1, the elimination play won't really succeed because you can't pull three rounds and ruff all dummy's clubs and retain a trump in hand. In this case your best chance is to take the diamond finesse and hope that either the queen is on or diamonds are 3-3.

 

If trumps are 2-2, then we may as well ruff out the third club. If RHO follows to this, then LHO is marked with 2 spades and 6 clubs. If he has only two hearts, then diamonds are 3-3 and taking the diamond finesse is a 100% line (even if the queen is off, we can pitch a heart on the fourth diamond). If he has three hearts, odds are the throw in would fail (LHO can win the third).

 

In fact I think the diamond finesse is a better line in general. You make any time the diamond queen is on, or diamonds are 3-3. Also, if RHO has both the fourth diamond and five hearts, you have a squeeze position against him. The opponents can usually arrange for LHO to win the third heart when hearts are 4-3, so the only time the throw-in really works when the diamond finesse followed by playing for 3-3 break and/or squeeze fails is if the opponents misdefend.

[HeartA]

I would play DQ on side OR D 3-3, the chance should be more than 50%.

 

There are two altenative lines:

1) To cash HAK and H exit (throw-in). The highest spot is only 9, and alerted opps would not fall in this trap (unless East has all high spots 10,J,Q). So most likely you would have to rely on DQ on side again.

2) To cash DAK and hope to drop DQ. If DQ doesn't appear, cash HAK and exit with 3rd H. Hope the one who wins doesn't have 3rd D. This again goes back to 1): an alerted opp will win the 3rd H with 4 Ds.

[Finch]

I assume spades were 2-2.

 

Against vaguely competent opponents the heart throw-in won't work unless East has either QJ10 of hearts or five+ of them.

 

Playing on diamonds is way better than 26% - I don't know where you get that from. There's no real point cashing the DA first as that only picks up singleton queen on our right, making LHO 2-0-5-6 and RHO xx QJ10xxxx Q xxx who probably would have bid.

 

Taking a diamond finesse makes the contract when

- the DQ is onside (roughly 38% if clubs are 6-3) or

- Diamonds are 3-3 with the Q offside (another 16%), or

- LHO has a diamond void and RHO 5+ hearts (another 2%), or

- Either hand has 4 diamonds and the QJ10 of hearts (another % of so)

 

which is a little under 60%

 

Playing for the heart throw-in makes the contract when

- RHO has 5+ hearts (32-41%) - would RHO have responded on QJ10xxx and out?

or

- RHO has 3 or 4 hearts including the QJ10 (about 6%)

or

- hearts are 4-3/3-4 and the DQ is right (roughly 1/3 of the remainder) or another 14%

 

 

which is somewhere between 50 and 60% depending on RHO's responding tendencies

 

These seem very close to me, but with a slight preference for your partner's chosen line. To decide the best line you definitely need to know on what hands with 6 (or 7) hearts RHO would have responded. You haven't mentioned if East had a club honour - with the Queen of clubs there's no point in playing for the throw-in, because you know it won't work.

 

By the way, what on earth was North's 4S bid? Do you not have any way of showing an invite?

[kenberg]

I'm also curious about the 28%. Assuming spades split and E followed to the third club we give W 8 black cards exactly and thus 5 red cards. The opponents, together, have 13 red cards. This gives 5/13 which, as Frances says, is about 38%. Some distributions are not possible, for example West's red cards are presumably not all hearts, but I imagine 38% is about right a priori and I don't see any real reason to shift it. There is this general notion that once a player shows enough for his bid you should tend to place the other cards with his partner, but I am not so sure that it applies here.

 

I think at the table my thoughts would be something like this: If W has three hearts the chance of endplaying E are remote. If W has two hearts then he has three diamonds, the contract is safe and I finesse for the overtrick. If W has one heart then he has four diamonds and is a favorite to hold the Q. All roads lead to a finesse.

 

But 28%? On what assumptions?

[awm]

Supposing spades are 2-2, we discover the club distribution when we ruff the third club (assuming LHO didn't rebid clubs with five). If clubs are 6-3 we have:

 

(1) LHO has 2 hearts, 3 diamonds. The throw-in will work, but playing on diamonds will also work and may produce an overtrick 50% of the time.

 

(2) LHO has 1 heart, 4 diamonds. The throw-in will work. However, this gives RHO 2623 shape. If he holds the ♦Q he would usually bid with this shape (okay, unless opener has stiff heart queen). So finessing is substantially better than the obvious 66%.

 

(3) LHO has 0 hearts, 5 diamonds. The throw-in will work. However, with 2713 shape RHO would almost surely bid. And the diamond finesse is 100% if we bang down the ace before hooking.

 

(4) LHO has 3 hearts, 2 diamonds. The throw-in will almost surely fail. Playing on diamonds is 33% or so to work. On those occasions when the throw-in succeeds we can probably manufacture a red suit squeeze (i.e. RHO has QJTx of heart).

 

(5) LHO has 4+ hearts, 1- diamond. The throw-in will almost surely fail. Playing on diamonds will fail too.

 

On the other hand, suppose clubs are 7-2. Now LHO has 2137 or 2227 or 2317 most of the time. In these cases:

 

(1) LHO has 1 heart, 3 diamonds. The throw-in will work. However, the diamond hook also works and sometimes makes the overtrick.

 

(2) LHO has 2 hearts, 2 diamonds. The throw-in will work. The diamond finesse is only 33%.

 

(3) LHO has 3 hearts, 1 diamond. The throw-in will usually fail, but playing on diamonds will usually fail also. At least the throw-in if cleverly executed offers a chance to misdefend.

 

So at IMPs, it seems like playing on diamonds is better when clubs are 6-3, but the throw-in play is better when clubs are 7-2.

[pigpenz]

yes its an intersting little hand, thats why I asked what do most think is the best line to combine the play for the best odds.

 

To me I couldnt see how taking a first round hook in♦ was exactly a high percentage play. From the actual hand all we have to go on is that right hand opp did have 3 ♣'s.

[Dwingo]

(2) LHO has 2 hearts, 2 diamonds. The throw-in will work. The diamond finesse is only 33%

 

In this scenario, RHO is guarding ♥'s and ♦'s and throw is not neccessary and the ♥ - ♦ squeeze will work as well.

[pigpenz]

thats the point of this little gem, there are alot of options to choose from...so what play combines all the odds to give us the best chance.

 

in actual play right hand opp followed to all the clubs, with West playing akq♣'s.

so most likely we can play west

with 2♠'s

6♣'s

 

so with the other five slots left for west 3-2 in which red suits? Can we afford to play ak♥ or ak♦ to get a better count on west and still retain the chances for playing the other suit. If we play ak♦ then we need to rely on them being 3-3 in order to make or Qx♦...if we play ak♥ and third heart then we still have possiblity of playing for diamonds hook...so percentage wise what play is better?

[Finch]

so percentage wise what play is better?

Can't answer that without knowing if RHO plays weak jump shifts, and what is the minimum requirement for a 1H or 2H response to 1C.

[kenberg]

Playing off the AK of diamonds seems completely wrong to me. If the Qx is to the left it will come down down, but the finesse works as well. If the diamonds are 3-3 the Q won't come down, although you will make your contract just giving up on the overtrick. If the Qx is to the right this is the right play but surely that is heavily against the odds. Firstly it isn't likely that there are four diamonds to your left, and if there are it is more likely than not that the Q is with the four.

 

I can sort of see playing off three hearts hopng for a throw in, although I think the finesse is better, but I can't see playing off the AK of diamonds at all.

 

I know it will work when the Qx is to the right but this appears to me to be a variant of the Rabbi's rule for dropping singleton kings.

 

Or am I missing the point somehow?

[pigpenz]

Or am I missing the point somehow?

every card you play the %'s change for what the opps can have.

If you play one suit the hand tightens but may reomove options for you delcarer inthe other suit.

So we know west has 8 cards(6♣' and 2♠'s).

If we play AK♥ and third and he follows we now know 11 or 10 of his cards.

If we play AK ♦ and Q doesnt fall we know 10 of his cards.

so all i am curious about is what is the percentages at this crossroad, no one is missing anything its just what is best way to combine percentages to your advantage.

 

BridgeBaseIII used to have a suit calculator in it which would show the %'s insuits as each card was played along with the card combinations.

[kenberg]

Mathematics has its limitations. Here is an argument for playing off the AK of diamonds (yes, i know, I said it was a bad idea):

 

Suppose the club plays have been AKQ so we place lho with AKQxxx. Conider the auction. Would he just bid 2D holding

Ax

x

Qxxx

AKQxxx

If you think the answer is no, he would have bid 2D over 1C then the AK of diamonds is more attractive:

If lho holds Qx it falls, if he holds 3D we make whther it falls or not, if he holds four diamonds and we agree that it cannot be Qxxx then the Qx must fall on the right.

 

Actually I sort of like this argument the more I think about it.

 

Now if we want to just do the sort of calculation a BBIII calculator might do, it's easy enough.

 

 

There are 13 red cards to be placed, 5 to the left. So C(13, 5) is the number of ways of doing it. Ths number (often called 13 choose 5) is on a typical calculator I think. But it is )13 times 12 times 11 time 10 times 9) divided by ( 5 times 4 times 3 tmes 2)

 

If we want to get the probability of 3 diamonds ono the left, note that there are 6 diamonds to be placed and 7 hearts. We can place 3 diamonds and two hearts to the left in C(6,3) times C(7,2) ways.

 

So the probability is C(6,3) times C(7,2) divided by C(13,5). I get .32634. Half of these will have the Q on the left.

 

And so on. But I think the issue of whether lho would actually bid 2C rather than 2D on the second round holding the strong hand above is far more important.

 

Ken

[pigpenz]

And so on. But I think the issue of whether lho would actually bid 2C rather than 2D on the second round holding the strong hand above is far more important.

 

Ken

one of the problems with online bridge is that most of the time you have no idea what the llevel of your opponents are...at least at real bridge youcan say oh i have at leat seen them before.

 

people have asked questions well do opps play weak jump shifts, now e have an question about how they would rebid would a hand as such. In internet bridge almost all bets are off as to what the opps may have :D

 

so the play is up to you!

[kenberg]

In most hands, including this one, you cannot really evaluate the probability of success without making some assumptions about the opponents.

For example: Suppose rho holds

Qxxx in hearts,

Qxxx in diamonds.

 

Playing on diamonds will fail, since the Q is offside and the suit is 4-2. Will playing off the top hearts and leading a third round from dummy succeed? Depends on the opponents, right? Rho might notice that if he plays the Q and all follow then he is in a pickle. He might also wonder why declarer, if holding the Jack of hearts, would play the suit this way. So he might well play a small heart trusting that partner will produce the Jack and lead a diamond from his side of the table. Then again, he might hop up with the Q. We have all seen worse plays. I have made worse plays, fortunately not often.

 

Any attempt to evaluate lines of play must take into account some sort of estimate of the opponents. Even if they are online folks you have never seen before, so that your information is scanty and your guess just a guess on general principles, still you must make it.

 

In the post at the beginning, you give an estimate of 28%. It's based on some assumption about something. It's inevitable.