What are the best odds?

[Valardent]

[hv=pc=n&s=sa42hakjt73dcj973&w=sh5dc&n=sh4dc&e=skj86h62dqjt875c8]399|300|Imps[/hv]

 

Bidding went (west dealer)

 

1NT - P - 2♣ - 2♥

2♠- 3♥ - 4♠ end

 

1NT is 15-17

 

♥4 lead, 2, K, 5.

 

You play 3/5 leads as a general rule. When one's own number of cards is most probably known we might lead attitude.

 

What now?

 

♥K hoping for a minor Ace or ♦K in p's hand

 

or

 

♥10 asking for a ♦ ruff hoping for ♥Q or ♣A in p's hand?

[Fluffy]

♥10 if partner is awake, but playing with a random parner low heart should be just as obvious, and saves you from his lazyness (or maybe he is on the phone)

[inquiry]

This is really simple. First, your partner DOES NOT hold an Ace, thus he does not have the have the ♣A). However, he does have the ♥Queen and the king of one of the minors (you might bet this two). Return a heart (the ten is fine, but a lower one is still clear). There is no upside thinking about him having the club ace.

 

This is not a math problem, it is a double dummy one. If partner raised without an honor, he would lead a high heart (your "attitude" issue). The fact is you are going to set it.

 

------------------

 

Now for the math problem you asked. You are asking what are the best odds. Unstated, but clear your parnter has three hearts for his raise (surely West does not have a singleton, and partner didn't raise on doubleton and then lead his smallest card).

 

I am assuming a 15-17 hcp 1NT opening, this give partner 3, 4, or 5 hcp. I will use the following "estimates". A 15-17 1NT opening will hold 15 hcp 47% of the time, 16 hcp 32% of the time, and 17 hcp 21% of the time.

 

Calculating the odds, if partner has 3 hcp he can only hold a king: no Ace -- not enough points, and no Queen-JACK, because he can not hold a jack (we see all four. So his hand will have a king, and declarer will make anytime he holds 17 hcp. That will happen 21% of the time.

 

So we have to play partner for either four or five hcp, and declarer 15 or 16 hcp.

 

For partner to have 5 hcp, it has to be a king and a queen (not Ace-Jack, again because partner can not have a jack). We can see both major kings, so parnter would have minor suit king and one of three possible queens (♣, ♥, ♠). That gives him a 1/3 chance to hold the heart queen (if we ignore what we know from the opening lead and bidding.)

 

If partner has 4 hcp, it can be either two queens or an ACE. There are two aces partner can hold (♦A, or ♣A) so partner partner has a 50% chance to hold the ♣A if he holds an ace). If partner doesn't hold an ACE, then he hold two queens out of the ♥Q, ♦Q and ♠Q, giving him mathematically 66.6% of holding the heart queen.

 

So you could try to figure the frequency of the 1NT opener holding 15 hcp compared to 16 hcp (the a prior ratio is roughly 3:2 that declarer holds the 15 hcp as compared to 16). So you could do some math (chance of 15 hcp, times chance partner has the heart queen and not one of the other),

 

15HCP x chance partner has heart Queen + chances of 16 hcp x chances partner has club ace or heart queen

47% x 1/3 + 1/2 x (32% x (1/2)) + 1/2 x (32% x 2/3) = 0.34% you are going to set this.

 

Something some would consider is that if partner has "one queen and one king", if partner's king is the diamond king, you can beat it by cashing your two hearts and wait for your trump and diamond trick. But again, the defense is clear, partner has the ♥Queen, so lead "low-ish" heart back to get him to win and return a diamond to you.

[gnasher]

I don't think you've given us sufficient information to estimate the odds, because we don't know how often partner would lead a high one from 984, or what factors influence his decision about which card to lead.

 

My partners would always lead top from three small here, so I wouldn't have this problem.

[Flameous]

One thing to note is that if partner happens to hold heart Q and club K, leading club will also work cause declarer can't pitch dummys heart to anything. Not that it really matters, I'm playing a small heart anyways.

[Valardent]

Ptnr and I agreed on the attitude lead exception but I don't remember if we already "broke" the general rule once. So ♥4 could definitely come from 984.

 

Two reactions on ben's post :

 

- don't understand why p couldn't hv an ace

 

- his way of thinking what p could have is something I should have applied at the table.

 

The fact I could see all 4 jacks reduces the honnor combinations p might have.

 

Let's call line 1 (l1) ♥K play and line 2 (l2) ♥10 (or any small one) play.

 

If we focus only on the cases where l1 wins and l2 looses or the other way round, we get :

 

a) opener has 15 hcp, so p has 5

 

l1 w/l2 l if p has ♦K/♣Q

 

l2 w/l1 l if p has ♣K/♥Q

 

b ) opener has 16 hcp, so p has 4

 

l1 w/l2 l if p has ♦A

 

l2 w/l1 l if p has ♣Q/♥Q (p wouldn't hv bid 3♥ with Qx Qxx xxxx xxxx)

 

c) opener has 17 hcp, so p has a King

 

l1 w/l2 l if p has ♦K

 

Two more issues :

 

1) the lead suggests ♥Q and p's having 3♥ to declarer's 2, odds must favor p for ♥Q

 

2) declarer is marked with a 4234 distribution with at least 3 out of 4 from A&K♦,A&K♣. If p has one of those 4 honnors, chance he has a ♦ one is higher than a ♣ one.

 

So 1) & 2) are counterbalancing one and other (don't ask me in what range difference)

 

At the table, after 2 mins thinking, I came to the conclusion that it was a very close decision. What convinced me to play ♥10 was this thought : "ptnr doesn't hv much, so there are more chances he would bid 3♥ with ♥Q"

 

Wrong I was as his hand was xx 984 Kxxx QTxx.

 

I'm now convinced that without the lead (attitude or 3/5) issue, ♥K is a slightly better play.

 

Val

[Free]

If partner has an Ace, we'll always defeat the contract if we just cash in our tricks and lead a ♣ when we took ♠A. So you shouldn't consider the fact that partner has an Ace.

[Valardent]

If partner has an Ace, we'll always defeat the contract if we just cash in our tricks and lead a ♣ when we took ♠A. So you shouldn't consider the fact that partner has an Ace.

 

Not sure if get your point Fred.

 

My point is you must choose between 2 lines. If p has A♣ it will not matter but if p has A♦ and you choose to play 10♥, it gives away the contract.

[gwnn]

Ben when we know that RHO+us=20 hcp, LHO is much more likely than usual to hold a minimum and partner a maximum. I think your estimates are quite far from reality.