5 Diamonds Play Problem

[CSGibson]

[hv=pc=n&s=s4hqdkq9742cakq84&n=sj93ht8653dat5c62&d=s&v=0&b=11&a=1dp1h2h(natural)3cp3dp5dppp]266|200[/hv]

 

The lead is the 9♥ to the 3-K-Q. Righty now plays the ♥A

 

E-W are not a regular partnership, but are both experts.

[JLOGIC]

Curious that RHO did not cash the spade ace, presumably they don't have it if they are an expert since it is a routine play. Given that LHO has the spade ace, I will not play him for 6 spades since he didn't overcall with 1S or 2S white over 1D.

 

Our first decision is whether to ruff high or ruff with the 9 (pitching seems dumb as another heart will come back, and we lost the possible line of pitching our spade later after a ruffing heart hook for no gain). RHO must be a strong favorite to have 6 hearts for their 2H overcall in this auction, especially if they have 4 good spades which they likely do (with 5 good spades LHO might have overcalled). Ruffing with the king seems indicated.

 

Now, assume LHO pitches. makes RHO 46xx. If RHO is 4612 without stiff J, and we ruff high, cash a diamond and hook a diamond, we are simply down now. This might make it seem like we need to play RHO for 4621 (in which case we just pull trumps, ruffing finesse hearts, and give up a black suit trick). However we have an alternative line of ruffing high and running the 9 of diamonds immediately. Now we can play a diamond to the ten, play the HT from dummy, pitching our spade if RHO ducks, and then ruffing out clubs. So RHO covers perforce, we ruff high, cross to the diamond ace and pitch our spade. If LHO has J86 of diamonds and covers the 9 of diamonds we can win the ace, lead the HT and ruff high, now we have set up a trump for LHO but we can just ruff a club and pitch our spade, so we're ok.

 

Which is more likely, Diamonds being 2-2 OR RHO having stiff J, vs diamonds being 3-1 without stiff J? My gut instinct is the former, but luckily since it's online we can try to do some math!

 

According to rpbridge.net, it is 5:3 that LHO has 3 diamonds rather than 2 when RHO has 3 empty spaces, and LHO has 7 (I ignored 4-0 since we can't make, as long as LHO remembers to cover the D9 with J86x).

 

So ruffing high and playing the DK and a diamond to the ace will win 3/8ths of the time plus 1/4th of 5/8ths which is 1.25 8ths, or 4.25/8ths of the time. Ruffing high and running the D9 will win on 3.75/8ths of the time.

 

On top of that some LHOs would pass with Axxxxx x xxx xxx over a 1D opener, and the chance of RHO being 36xx would make ruffing high and running the D9 immediately especially bad.

 

Cliffs: Ruff high, if LHO pitches then play queen of diamonds, diamond to the ace (unless RHO drops the jack)

If LHO follows to the 2nd heart then we will have to guess what to do.

[vianu2]

Spade discard and the next heart ruff high then finesse the jack :) Ruff a club in the dummy .

I think you go down with 4-0 diamonds ..hm i didn't see i don't have the 8 D in hand sry

[JLOGIC]

Spade discard and the next heart ruff high then finesse the jack :) Ruff a club in the dummy .

I think you go down with 4-0 diamonds ..logic:)

 

So do you? heh. I never said I'd make it with 4-0 diamonds.

[inquiry]

They could make 4♠ if diamonds are 3=1, but we are not going to be concerned with what they can make. We have to see how to make this.

 

Loser on loser (spade under the heart ACE) might be right, but you can hold that back in reserve in case diamonds split 3=1, so I plan to ruff. Question is With king, nine, or small. I think you can eliminate small. IF they can overruff they will take a spade and you are down. So the question is ruff with the King or the nine? (it is true that East could have only five hearts, but bidding hearts with so many spades out AND partner bidding hearts, and making the heart bid at the two level all points to six card suit).

 

The odds that West has the diamond Jack are fairly high at first blush (12 to 7 vacant spaces). This suggest ruffing high and trying to deal with the diamond jack and losing clubs. Vacant spaces maynot be this clear, but I am going with it.

 

After the diamond finesse (assuming it wins, of course), I cash the diamond ACE. If east shows out, I lead the ♥Ten from dummy, ruffing high (establishing West jack of diamonds). Cash two top clubs, ruff a small club and discard the spade 4 on the good heart eight.

 

This line works anytime West has one, two or three diamonds including the jack, however if West plays a clever Jack of diamonds on first round, you could run into a little trouble. The obvious line seems to be then to lead the heart Ten before a second diamond, ruffing with the NINE when east covers or throwing the spade if not. Then cash two clubs, ruff a club HIGH, and hook the diamond 8 with east. This wins 12 tricks if WEST had singleton jack. If west has three diamonds, it doesn't matter. The tricky case is when West had ♦Jx. He will ruff the heart, and give his partner a club ruff. Perhaps we shouldn't fall for that because if West is really 7=1=1=4 he would have preempted over the 1♦ opening bid. So when you ruff the club and East shows out, you will think perhaps West is trying to pulling the wool over your eyes and he is really 6=1=2=4. I would hate a player who made such a deceptive play against me... hopefully not too many people have read "tiger and fly" yet so we don't have to worry about that type of trickery.

[JLOGIC]

Even though west is more likely to have the diamond jack, it doesnt make a first round finesse in diamonds necessarily the best line, losing to stiff jack on your right is a big deal.

 

Basically you are picking up 3 combinations of Jxx on your left, and losing to 3 combinations of Jx on your right, and 1 combo of stiff jack. So it is 4 combinations to 3, meaning you need LHO to be MUCH more likely to hold the jack. Obviously when they're 2-2 it's equal who has the jack, so really you need them to be MUCH more likely to be 3-1 than 2-2 to overcome that deficit.

[gnasher]

Doesn't running D9 also work against Jx-xx ?

[inquiry]

Even though west is more likely to have the diamond jack, it doesnt make a first round finesse in diamonds necessarily the best line, losing to stiff jack on your right is a big deal.

 

Basically you are picking up 3 combinations of Jxx on your left, and losing to 3 combinations of Jx on your right, and 1 combo of stiff jack. So it is 4 combinations to 3, meaning you need LHO to be MUCH more likely to hold the jack. Obviously when they're 2-2 it's equal who has the jack, so really you need them to be MUCH more likely to be 3-1 than 2-2 to overcome that deficit.

 

First, I don't think you can make the hand if EAST has 4=6=2=1 distribution even if you correctly guess who has the diamond jack. At least I can't find a way to make it, if you pull trumps, you lose two clubs plus the heart. So in theory, I think we can safely ignore the doubleton jack offside. If I am overlooking a way to make it with Jx offside, let me know (of course if we give West a lot of spades, say six, Jx becomes a possibility).

 

So working with the most likely distribution (West 5S,1H), you pretty much need him to have 3D and 4C to make. And you have to decide how to play the diamond suit. If West has Jxx, you can never make it if you start with high diamond from hand (after ruffing high). So high from hand caters to singleton jack with East, that is it if the most likely distribution exist. This is a strong reason for the first round hook (wins 3 times out of 4 with the most likely distribution, while cashing high diamond from hand loses to 3 out of 4).

 

Now, if we expand West hand to include the possibility of six spades, or West having 2 hearts, the play becomes more complicated. The major complication is trying to figure out the likelyhood of six spades with West if West fails to follow to the 2nd heart. WE can agree he will not have seven.

 

This is the situation that exist.

6S-1H-3D-3C <-- finesse 1st or 2nd round when WEST has jack. Cash Queen protects against singleton JACK

6S-1H-2D-4C <- must not finesse either time when jack is offside

5S-1H-3D-4C <- must finessee first round to make.

 

(Again, I ignore hands with 4 diamonds or hand were West is 5S-1H-2D-5C because I don't think you can make versus those).

 

By comparing these distributions, you find this

 

C(9,6)*7*C(4,3)*C(6,3) = 47040 = 84

C(9,6)*7*C(4,2)*C(6,4) = 60480 = 108

C(9,5)*7*C(4,3)*C(6,4) = 45360 = 81

 

The middle one involves cashing two top diamonds, and it comes home. the top one and bottom one require different plays. The bottom one, you MUST hook on the first round, the top one if the jack doesn't fall you MUST hook on the 2nd round (wins 100% of the time with that pattern).

 

So cashing AK wins 108 of the middle cases, and 1/4 of the top and bottom, let's call that 150 times out of 273 or 55%. Blindly hooking on the first round of diamond wins in 3/4 of the first and last case and half of the middle cases. That comes to 178 cases or 65%.

 

I think our bridge judgement is that the 5=1 in the majors is much more likely (from bidding) than 6=1. Which would seem to even increase the likelyhood the first round finesse is right.

 

 

[JLOGIC]

Doesn't running D9 also work against Jx-xx ?

 

Yes lol, I'm a moron.

[vianu2]

why do we lose 2CL if East is 4-6-2-1 There are only 2 losers in club (we discard a loser on the heart and the other on the 3rd trump..)

[inquiry]

why do we lose 2CL if East is 4-6-2-1 There are only 2 losers in club (we discard a loser on the heart and the other on the 3rd trump..)

 

Ok, then you lose the spade. I had you throwing the spade on the established heart. It is hard to throw both a club and a spade on the one good heart. Count your winners... three clubs, one club ruff, the good heart, and five diamonds in your hand. That comes to only 10.

[manudude03]

Ok, then you lose the spade. I had you throwing the spade on the established heart. It is hard to throw both a club and a spade on the one good heart. Count your winners... three clubs, one club ruff, the good heart, and five diamonds in your hand. That comes to only 10.

 

and the heart you ruffed high (if you counted this, then should be six diamond tricks)?

[inquiry]

and the heart you ruffed high (if you counted this, then should be six diamond tricks)?

 

 

You are right. I was thinking five diamonds for some reason. If East continues a heart when he is 4=6=2=1 then you can make it. This will affect the error I thought I must be missing when I disagreed with Justin (doing so is a sure way to be proven wrong). So you can make it against that distribution on this line of defense. The spade switch or a low heart instead of the ACE would, of course, set you. When diamonds are 3-1, the low heart will not work, and neither the spade cash or a low diamond will set you. But the bottom line is I have to go back and figure in WEST being 5=1=2=5 into the calculation. That will probably mean justin's math will be right.

[MrAce]

Curious that RHO did not cash the spade ace, presumably they don't have it if they are an expert since it is a routine play. Given that LHO has the spade ace, I will not play him for 6 spades since he didn't overcall with 1S or 2S white over 1D.

 

Our first decision is whether to ruff high or ruff with the 9 (pitching seems dumb as another heart will come back, and we lost the possible line of pitching our spade later after a ruffing heart hook for no gain). RHO must be a strong favorite to have 6 hearts for their 2H overcall in this auction, especially if they have 4 good spades which they likely do (with 5 good spades LHO might have overcalled). Ruffing with the king seems indicated.

 

Now, assume LHO pitches. makes RHO 46xx. If RHO is 4612 without stiff J, and we ruff high, cash a diamond and hook a diamond, we are simply down now. This might make it seem like we need to play RHO for 4621 (in which case we just pull trumps, ruffing finesse hearts, and give up a black suit trick). However we have an alternative line of ruffing high and running the 9 of diamonds immediately. Now we can play a diamond to the ten, play the HT from dummy, pitching our spade if RHO ducks, and then ruffing out clubs. So RHO covers perforce, we ruff high, cross to the diamond ace and pitch our spade. If LHO has J86 of diamonds and covers the 9 of diamonds we can win the ace, lead the HT and ruff high, now we have set up a trump for LHO but we can just ruff a club and pitch our spade, so we're ok.

 

Which is more likely, Diamonds being 2-2 OR RHO having stiff J, vs diamonds being 3-1 without stiff J? My gut instinct is the former, but luckily since it's online we can try to do some math!

 

According to rpbridge.net, it is 5:3 that LHO has 3 diamonds rather than 2 when RHO has 3 empty spaces, and LHO has 7 (I ignored 4-0 since we can't make, as long as LHO remembers to cover the D9 with J86x).

 

So ruffing high and playing the DK and a diamond to the ace will win 3/8ths of the time plus 1/4th of 5/8ths which is 1.25 8ths, or 4.25/8ths of the time. Ruffing high and running the D9 will win on 3.75/8ths of the time.

 

On top of that some LHOs would pass with Axxxxx x xxx xxx over a 1D opener, and the chance of RHO being 36xx would make ruffing high and running the D9 immediately especially bad.

 

Cliffs: Ruff high, if LHO pitches then play queen of diamonds, diamond to the ace (unless RHO drops the jack)

If LHO follows to the 2nd heart then we will have to guess what to do.

 

Tell us WHY ? ♥ :P

 

I am just joking, very well explained imo.

[vianu2]

First time when i red the post i thought S has the 8 D. Then we could make the contract against 4-0 D too ( and E 4-6-0-3 ) Does it change our declarer, if we have the 8 ?

[inquiry]

 

Even though west is more likely to have the diamond jack, it doesnt make a first round finesse in diamonds necessarily the best line, losing to stiff jack on your right is a big deal.

 

Basically you are picking up 3 combinations of Jxx on your left, and losing to 3 combinations of Jx on your right, and 1 combo of stiff jack. So it is 4 combinations to 3, meaning you need LHO to be MUCH more likely to hold the jack. Obviously when they're 2-2 it's equal who has the jack, so really you need them to be MUCH more likely to be 3-1 than 2-2 to overcome that deficit. <emphasis added>

 

 

Here I tried to answer the question, is the chance WEST holds 3 diamonds high enough to overcome the 3 to 4 ratio Justin correctly points out. BTW, the combination math shown above is correct. One might realize that there are 11 such combinations (not 7), but singleton jack on side (one combination) and doubleton jack on side (three cases) (7+4=11) either line works, so Justin correctly left those lines out. 3 to 4 is hard odds to overcome. Justin then adds the key statement: “you need them to be MUCH more likely to be 3-1 than 2-2 to overcome that deficit.”

 

So this gets to where we have to consider what are the odds WEST has three diamonds versus two diamonds? There are three ways to consider this situation. First, all theoretically possible holdings for West. Second potentially likely (on the bidding) holding for west. And, finally, all potentially likely holdings for West that will allow us to find a successful line of play. These are three different subsets, but we will start at the END of trick two where WEST shows out on hearts. But for this discussion the one thing we know, East has six hearts and WEST has only one. These are the possible distributions that WEST could hold.

 

Case one: all theoretical possible West hands when East has 6 hearts, west one (given they have a total of 9♠, 7♥, 4♦ and 6♣ between their two hands).

 

9=1=3=0, 9=1=2=1, 9=1=1=2, 9=1=0=3, 8=1=4=0, 8=1=3=1, 8=1=2=2, 8=1=1=3, 8=1=0=4, 7=1=4=1, 7=1=3=2, 7=1=2=3, 7=1=1=4, 7=1=0=5, 6=1=4=2, 6=1=3=3, 6=1=2=4, 6=1=1=5, 6=1=0=6, 5=1=4=3, 5=1=3=4, 5=1=2=5, 5=1=1=6, 4=1=4=4, 4=1=3=5, 4=1=2=6, 3=1=4=5, 3=1=3=6, 2=1=4=6, a total of 352,716 hands.

 

 

 

In these holdings, West will hold 3♦’s 39.73% of the shapes, and 2♦ 35.76% of the time. However, we are certain that West does not have either 9 or 8 spades, and I think we can be reasonable certain that he does not have 7 spades. So we can remove those hands. We are also sure that East does not have 7 or 6 spades, so we can remove those hands as well.

 

 

Case two: Holdings for West consistent with the bidding

 

 

9=1=3=0, 9=1=2=1, 9=1=1=2, 9=1=0=3, 8=1=4=0, 8=1=3=1, 8=1=2=2, 8=1=1=3, 8=1=0=4, 7=1=4=1, 7=1=3=2, 7=1=2=3, 7=1=1=4, 7=1=0=5, 6=1=4=2, 6=1=3=3, 6=1=2=4, 6=1=1=5, 6=1=0=6, 5=1=4=3, 5=1=3=4, 5=1=2=5, 5=1=1=6, 4=1=4=4, 4=1=3=5, 4=1=2=6, 3=1=4=5, 3=1=3=6, 2=1=4=6 a total of 269,010 hands

 

Once we remove the wildly unlikely distributions based upon the bidding, we find the West will hold 3♦ 45.03% of the time, and 2♦ 33.44% of the time. So we begin to get to the question is this increase enough to overcome the 3 to 4 odds Justin mentioned? And what about case three?

 

Case three: Holdings for West consistent with the bidding where you can make the hand if you guess right.

 

9=1=3=0, 9=1=2=1, 9=1=1=2, 9=1=0=3, 8=1=4=0, 8=1=3=1, 8=1=2=2, 8=1=1=3, 8=1=0=4, 7=1=4=1, 7=1=3=2, 7=1=2=3, 7=1=1=4, 7=1=0=5, 6=1=4=2, 6=1=3=3, 6=1=2=4, 6=1=1=5, 6=1=0=6, 5=1=4=3, 5=1=3=4, 5=1=2=5, 5=1=1=6, 4=1=4=4, 4=1=3=5, 4=1=2=6, 3=1=4=5, 3=1=3=6, 2=1=4=6 a total of 189,924 hands

 

From this mixture we find 3♦ with West 57.38% compared to 2♦ at 42.62% (of course, we made two assumptions. One you can't make with 4=0 split, two, you can't make if West has singleton diamond and singleton heart). I happen to also believe we can also remove the 4=1=3=5 hand because for the life of me, I can not find a way to make it with that pattern. That leaves us with these hand patterns.

 

WEst hand patterns
6=1=3=3	47040	24.77%
6=1=2=4	52920	27.86%
5=1=3=4	52920	27.86%
5=1=2=5	31752	16.72%
4=1=2=6 	5292     2.79%

 

This shows the percentage of 2=2 splits as 2.79+16.72+27.86 = 47.37%, the chance of a 3=1 split is 52.63%. So the bottom line is this good enough to overcome the 3 to 4 combination ratio? Well in all the 2=2 splits with these shapes, AK of diamonds wins. That is 47.37%. In addition, 1/4 th of the 3=1's, cashing the AK of diamonds will work because the Jack falls. This adds 0.25 * 52.63 = 13.16% for a total of 60.53% of the hands where you can make it, you will by the line of cashing the AK of diamonds. Taking the first round finesse works when the Jack is not singleton on 3-1 splits (0.75*52.63% = 39.47%) plus half of the 2=2 splits (when jack is onside) which is 0.5 x 47.37 = 23.68%), for a total of 63.16%.

 

 

So it seems if I excluded the right hand types, and correctly calculated which hands make and don't make with the various lines of play, first round diamond hook is slightly better than cashing the AK of diamonds.

 

 

If you are really going to get into factoring unlikely hand patterns (like West having 7, 8 or 9 spades or East having 7 or 6 spades), you might want to consider how likely it is that West will hold 6S's. If you decide it is highly unlikley, you can drop the two patterns with six spades. If you think he is about 50-50 to overcall with six spades, you could cut the hand frequency with 6 spades in half. Either change would increase the frequency of WEST having three diamonds because of the two hand patterns where West held six spades the frequency of 2♦ holding is higher than 3♦ on those hands. Thus increasing the success rate of the first round diamond finesse.

 

This last case is what I did for my earlier answer. I figured West almost surely held five spades on this auction, so I only dealt with the two hand patterns: 5-1-3-4 and 5-1-2-5, in deciding what to play. If you don't want to eliminate the possibility of six spades with WEST, you still get close to the same answer. If you are going with the diamond finesse, a key part is NOT to cash the diamond ACE trying to drop the singleton JACK offside. The reason is that when WEST is 5=1=3=4 you can only afford to pull two rounds of trumps, then you need to take the ruffing heart finesse (if east doesn't cover pitch your spade). If you cashed your high diamond, WEST will overruff and cash a spade. You have to ruff with the diamond honor, then ruff a club, and pitch your spade on the the good heart. West gets his diamond jack, but that is the last trick for the defense.

 

 

Anyway, both plays are close, the odds for the first round diamond finesse should be a little higher than the 63.13% above and odds of banging AK a little less than above as well, because of decreased real world chances West has six spades on this auction.