Percentage play?

[Dinarius]

In 6 Hearts.

 

Trumps are...

 

A, 8, 3, in dummy

 

Opposite...

 

K, Q, 9, 7, 2

 

Having already lost ♣️A to opening lead, I cashed ❤️K. West played small, East played the ❤️J.

 

After some consideration, I finessed ❤️8 and claimed.

 

6❤️ was played 12 times, 6NT twice. I was the only one to make the slam.

 

Was I playing against the odds?

 

D.

[sfi]

Assuming East is up to playing an honour from JTx, yes.

 

If not, no.

[Dinarius]

Assuming East is up to playing an honour from JTx, yes.

 

If not, no.

 

Not sure if that answers my question.

 

1. After trick one, the Opps. hold, 10, x, x.

 

2. When I play a second heart from hand and West again plays low, Opps. now hold 10, x.

 

So, now the finesse of the 8 wins against, 10,x and 10 with West and loses to 10,x and 10 with East - a straight 50% shot.

 

Therefore, as I see it, the question is does restricted choice come into play in view of East's J play on trick one, and is the finesse play on trick two now more than a 50% shot?

 

D.

 

Ps. And yes, the play of the J from J,10,x on trick one is a useful false-card that can't cost.

[sfi]

The idea behind restricted choice is always a factor in cases like these.

 

Assume East will play an honour from JTx. Finessing the ten wins in one layout (when East holds J) and loses in four (when East holds JT or JTx). Restricted choice makes each of the loss cases half as likely, so the odds are about 2-1 to play the King on the second round.

 

If East will not play an honour, there is one winning layout (J) and one losing layout (JT). Using restricted choice again, now finessing the eight is approximately a 2-1 favourite.

 

If East will only play an honour 1/3 of the time, then you have a 50-50 guess about which line to take. But you'll never be able to work out East's behaviour that accurately. If they will ever play one, it's a good guide to assume they will always play one and follow those odds.

 

(Since each 3-2 break is a bit more likely than each 4-1 break, the odds are slightly better than 2-1 in the first scenario and slightly worse in the second. But not enough to matter in most cases.)

[Tramticket]

East's possible holdings are

J

JT

JX (X3)

JTX (X3)

 

The only time that it is correct to finesse is when is when East holds J - so it must be right to play for the 3-2 break.

 

But if East will not play the J from JX or JTX - then it is right to finesse, The two remaining possibilities are:

J

JT

 

But the play of J from JT is a restricted choice situation - he might have played the T - so it is more likely that East holds the singleton J.

 

Now imagine that East is really bad - and would play his lowest card (i.e. the T) from JT. Now the finesse is a 100% certainty!

 

[My reply crossed with sfi's]

[Dinarius]

Thanks for the replies.

 

TBH, knowing that a strong player will automatically play J from J,10 or J,10,x, I took the J as genuine from someone I knew was more honest than good, if you see what I mean. That’s why I finessed.

 

D.

[pescetom]

TBH, knowing that a strong player will automatically play J from J,10 or J,10,x, I took the J as genuine from someone I knew was more honest than good, if you see what I mean. That’s why I finessed.

 

I know what you mean :)

But I suspect a strong player would only make that play automatically if he thought you were weak, or it was the first time you met.

Probably he would randomise against a known strong opponent, at least the choice between JT.

[sfi]

Thanks for the replies.

 

TBH, knowing that a strong player will automatically play J from J,10 or J,10,x, I took the J as genuine from someone I knew was more honest than good, if you see what I mean. That’s why I finessed.

 

D.

 

It helps to know your customers. :)

[Dinarius]

It helps to know your customers. :)

 

Indeed.

 

Though, strictly speaking, I can only guard against 5/0 with East, so I should have cashed the Ace first.

 

D.

[PhilG007]

In 6 Hearts.

 

Trumps are...

 

A, 8, 3, in dummy

 

Opposite...

 

K, Q, 9, 7, 2

 

Having already lost ♣️A to opening lead, I cashed ❤️K. West played small, East played the ❤️J.

 

After some consideration, I finessed ❤️8 and claimed.

 

6❤️ was played 12 times, 6NT twice. I was the only one to make the slam.

 

Was I playing against the odds?

 

D.

 

I fail to understand the role of percentages in this game. Bridge is supposed to be a game of deduction/detection....NOT a study in Higher Mathematics (!)

[Tramticket]

I fail to understand the role of percentages in this game. Bridge is supposed to be a game of deduction/detection....NOT a study in Higher Mathematics (!)

 

I agree. Who needs higher mathematics and probability theory? The game would be so much better if we used proper deduction methods - which are what the game is all about. WBF approved methods include:Crystal balls; Ouija boards; water divining; lucky heather; psychic crystals and the octopus which predicts football result.

 

Please, stop counting up to 13. It really is against the spirit of the game.

[eagles123]

I agree. Who needs higher mathematics and probability theory? The game would be so much better if we used proper deduction methods - which are what the game is all about. WBF approved methods include:Crystal balls; Ouija boards; water divining; lucky heather; psychic crystals and the octopus which predicts football result.

 

Please, stop counting up to 13. It really is against the spirit of the game.

 

this made me laugh :)

[PhilG007]

I agree. Who needs higher mathematics and probability theory? The game would be so much better if we used proper deduction methods - which are what the game is all about. WBF approved methods include:Crystal balls; Ouija boards; water divining; lucky heather; psychic crystals and the octopus which predicts football result.

 

Please, stop counting up to 13. It really is against the spirit of the game.

 

You forgot to include "Eeeny Meeny Miiny Mo" oh and of course that fickle Bitch

"Lady Luck" :)

[PhilG007]

this made me laugh :)

 

Obviously easily amused (!) :(

[maartenxq]

Assuming East is up to playing an honour from JTx, yes.

 

If not, no.

This reminds me of Zia's story of his win of the Cavendish Calcutta years ago. He was facing this situation against an unknown young European pair. After some reflection he decided to believe east, took the finesse for down 1. Zia: 'I missed the point of the tabel, these younsters had themselves a kibitzers who had come by plane all the way from Europe to watch these kids.' Opponents turned out to be the later world champs Leufkens Westra.

 

Maarten Baltussen

[thawp66]

Not sure if that answers my question.

 

1. After trick one, the Opps. hold, 10, x, x.

 

2. When I play a second heart from hand and West again plays low, Opps. now hold 10, x.

 

So, now the finesse of the 8 wins against, 10,x and 10 with West and loses to 10,x and 10 with East - a straight 50% shot.

 

Therefore, as I see it, the question is does restricted choice come into play in view of East's J play on trick one, and is the finesse play on trick two now more than a 50% shot?

 

D.

 

Ps. And yes, the play of the J from J,10,x on trick one is a useful false-card that can't cost.

 

I believe no one has analyzed the probabilities correctly. If East won’t make the obligatory falsecard from JTx, then it’s a straight restricted choice situation and the finesse is 2-1 vs the drop. So I’ll assume East will make the falsecard.

 

Assuming random plays from East, all 4 of D’s possibilities are theoretically possible. However, if West has the T and East the x, then East played the J from a holding of Jx. Not only would this be an rather odd play, but both the finesse and the drop would now succeed.

 

Since there’s only 1 x left, that leaves 3 specific possibilities. East has either J, JT, or JTx. JT and JTx are both subject to restricted choice, so each has a probability of 1/2 x 1/3 or 1/6. Both combined is 1/3. The odds of the J is also 1/3, therefore the drop and the finesse are 50/50.

 

I believe that both “sfi” and “Tramticket” make incorrect assumptions. When it’s time to decide what to play from dummy, we’ve seen 2 of the 3 small cards, therefore there’s only 1 holding each of JTx and Jx and if East plays the J from Jx, the dummy play becomes irrelevant. In addition, once we’ve seen 3 of the 5 cards from the defense, the original odds are no longer valid.

 

As to Phil, bridge is rarely a game of higher mathematics, but knowing how and when to use math can be important. It is a game of deduction, detection, and especially OBSERVATION. However, there are other considerations as well. For example, in this case, what do I know about East’s tendencies and what does East know about mine? If you observed West looking at the J curiously, it might indicate his Txxx just became interesting. Will the field play for the drop, and if so, do I want to finesse and get a top or bottom rather than the ave? Maybe if I’m having an above average game I’ll go for the top, but if I’m having a great game I’ll take the average. If the field isn’t bidding the slam, I’ll probably want to take the best line to make it regardless.

 

Lastly, (I hope!)) Tram’s comment was amusing. We should all try to laugh just a little bit more. The world would be a better place or at least seem to be!! 😀😂

[msjennifer]

Personally speaking, in this particular hand the percentages and principle of restricted choice have no place.It all depends upon the level of opponents.I have seen many players who have the habit of 'giving the count' whenever they held anything less than a Queen when following a suit.I congratulate the OP for guessing correctly when someone like Zia failed.

[sfi]

I believe that both “sfi” and “Tramticket” make incorrect assumptions. When it’s time to decide what to play from dummy, we’ve seen 2 of the 3 small cards, therefore there’s only 1 holding each of JTx and Jx and if East plays the J from Jx, the dummy play becomes irrelevant. In addition, once we’ve seen 3 of the 5 cards from the defense, the original odds are no longer valid.

 

It's true you can play the restricted choice game with the spot cards as well, but it's more complex to do so and leads to the same answer. The cards we are missing are the 4-5-6-T-J. Let's assume a few things:

• The first six cards in trumps have been K-4-3-J; 2-6. So we have not yet seen the 5 or the T.
  
• East would always play an honour on trick one when holding JT or JTx. Choice of honour would be random.
  
• West would play their spot cards in a random order no matter their holding. It is clear that there is no reason to play the 4 before the 6 when holding T64. However, West would never play the T unless required.
  
• All of the combinations occur with equal probability. As I mentioned before, any particular 3-2 break is slightly more likely than any 4-1 break. But not enough to significantly affect the calculations.
  

 

Given all this, we have three relevant holdings to analyse:

• T654 - J: West had six ways to play to the first two tricks and East only had one, so the concept of restricted choice means the weighting of this holding is 1/6.
  
• 654 - JT: Here, West had six ways to play but East had two. So this weighting is 1/6*1/2 = 1/12.
  
• 64 - JT5: Here, both West and East each had two ways to play. The weighting for this holding is 1/2*1/2 = 1/4.
  

 

The comparative success of the finesse versus the drop is:

1/6 : 1/12 + 1/4

= 2/12 : 1/12 + 3/12

= 2/12 : 4/12

= 2 : 4

= 1 : 2

 

Which are the odds I calculated earlier.

 

For these types of situations, it really is easier to treat all the small cards as equivalent and not worry too much about them.

 

One other thing to mention - West's play of the 4-6 may not be random after all. If they are trying to signal club strength to partner, then you have to rethink the calculations. What the actual numbers are depend on how likely West is to start with the 5 vs. the 4 holding (T)654, but all possibilities make the 64-JT5 combination more likely and make playing for the drop better.

[Povratnik]

Sorry, I'm pretty tired, so maybe I erred somewhere in my calculations. And I certainly haven't read all posts carefully enough. Anyway, I'll give my two cents now; if I'm wrong, will try to correct it tomorrow...

 

...

Was I playing against the odds?

Well... It depends.

 

So you're missing two high cards (J and T) and three small cards (6,5,4)

 

Event A

LHO has at least two small cards and RHO has at least one high card.

(That you learned before deciding whether to play Ace or 8 from Dummy.)

 

Event B

LHO has at least two small cards and RHO has both high cards.

 

We want to know P(B|A) - the probability that B will happen, knowing that A has happened.

Before you played first heart, there was 32 possible splits, each with roughly equal probability. So we can say that P(A) was (roughly) 12/32 or 0.375.

The same way, we can tell that P(B) was (about) 4/32 or 1/8.

 

P(A|B) is obviously 1, so according to Bayes' theorem: P(B|A) = P(A|B)*P(B)/P(A) = 0.33

 

So your decision to make an impass was the correct one... According to mathematics. HOWEVER...

 

That was pure math, without real understanding of bridge. The mandatory bridge question is: would your RHO ever throw Jack from Jx doubleton? If he would, how often?

I certainly don't know the answers, but IF the RHO would never played Jack from Jx doubleton, we have slightly different version of the first event...

 

Event A1

LHO has at least two small cards and RHO has at least one high card, BUT NOT a high-low doubleton.

 

P(A1) = 6/32 = 0.1875; P(B|A1) = 0.67

 

So when we mix math and bridge, we come to conclusion:

 

The probability that you played against the odds is somewhere between one and two thirds, depending on your right hand opponent...

 

Now I should check are there some new posts, but I'll just press SUBMIT. Wherever I'm wrong, tomorrow is not to late for correction(s)...

[dokoko]

Assuming the entries are there, I see three reasonable lines:

 

A. Cash the ace. If West shows out, finesse twice against East. If West plays an honor, cash an honor and finesse against East if West shows out on the second round. Otherwise play for the drop.

B. Cash an honor from hand. If East plays an honor, finesse against West. If West plays an honor, cross to the ace and finesse against East if necessary. Otherwise play for the drop.

C. Cash an honor from hand. If West plays an honor, cross to the ace and finesse against East if necessary. Otherwise play for the drop.

 

Line C is obviously inferior to line A (assuming your entries are safe).

 

If you are sure East would not play an honor from J10x:

 

- line A is better than B when East holds J10 or J10xxx: 3.39%+1.96%=5.35%

- line B is better than A when East holds J or 10: 2x 2.82%=5.64%

 

The odds of East holding J10x is 10.17%. If he will play an honor from that holding 3 times in hundred, line A is better.

 

You can improve on line B if East known to always play a certain card from J10: If he plays the card he would play from J10, play for the drop, otherwise take the "marked" finesse. But you better be sure: if East would play "the wrong honor" one time in ten against you, you should finesse.

[Dinarius]

An interesting variation on all of this “what would East do with J, x,?” is the following:

 

In a recent Pairs event, I was South playing in 4♠️ with a 6/3 fit. I had K, 10, x, in Dummy opposite A six times.

 

East (a very good player) won the first trick and immediately played Q♠️. I won with the A♠️ and finessed the 10 losing to the J♠️. I made 10 tricks for average minus. No one in the entire room made this East ♠️ switch. So, every South played for the drop and claimed +1.

 

East’s reasoning was, “I have no easy exit card, so I may as well play a trump since I’m going to lose them both anyway.” As I played it, she only lost one.

 

Should I have still played for the drop in that situation?

 

D.

[sfi]

Should I have still played for the drop in that situation?

 

The real answer to your question is "it depends". It depends on the bidding, the lead, the play, the level of your opposition, the ability of the overall field, your opponents assessment of your level of play and, most importantly, what the entire hand is.

 

Ignoring all that, let's assume that 4S is a normal contract, there is no opposition bidding to guide you and you simply want to draw all the trumps with no losers. From a purely probability point of view, East's holding of Q is more likely than QJ because sometimes they would lead the Jack from the second holding (making your play the favourite). Balancing that, it is less likely East would switch to a singleton queen than to QJ doubleton. But probability plays a much smaller role than the logic of the rest of the hand. East's play of the SQ should be viewed with suspicion, and you need to work out why they might have switched to it.

 

Going back to the suit in question, if you play it without them leading one first you would simply start with the Ace. If East drops an honour the finesse is a 2:1 favourite to win (this is straight restricted choice). If not, you plan to play for trumps 2-2.

 

The fact nobody did that suggests either you had the 9 in your hand and it was more convenient to play for a singleton honour in West rather than East, the field is very bad or something else is going on in the hand.