[lamford]

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West leads a middle club to the Ace and East returns a club to your king, West following upwards, so he as at least three clubs. How would you play and for full marks indicate what you think the game-theory strategy is for the defenders for the various 4-1 trump breaks?

[mikeh]

One should always give the exact defensive cards and usually their lead conventions. Thus, at the table, I'd probably have more information (inferentially) than just that West probably had at least 3 clubs!

All too often posters don't think that this information is relevant and so don't provide it, but all too often it can be relevant, for reasons the OP didn't think about. Having said that, in fairness I doubt that inferring clubs to be 3=6 or 4=5, etc makes a lot of difference. Had we had the heart 8, it might. When in doubt, or even when not in doubt, what does it cost to provide the information that a real-world declarer would have?

Here, we can afford 2 trump losers, so the immediate thought process would be to play 2 rounds of trump, and then abandon the suit, ruffing spades, cashing diamonds etc. The hand is cold should trump be 3-2.

Since trump will usually be 3-2 (although the chances of that do depend on how we infer the clubs to behave....a 6-3 club break increases the likelihood of a bad trump break, and it can be helpful to know who to play for the long clubs...see above rant), it would be silly not to play trump now...we don't want someone ruffing/overruffing a pointed suit and still have to lose 2 trumps to AJ9, as one example.

Having got that far, working out that we are cold with 3-2 trump and that we can't afford not to play trump now, we move to consider the 4-1 issue.

Since I hold no spots in dummy, and the 9 may be useful, I start with low to the King. Note that were dummy to hold K8xx, we'd really want to know more about the clubs, at least inferentially: absent other considerations, we'd play the presumed longer club hand for the trump shortage.

If nothing exciting happens, I play low towards the Q9x. Since nothing exciting happened the previous trick, RHO will presumably play either the J or the 10...if he is void, we're down, and if he plays the Ace, he's an idiot for having ducked.

If he does play the 10 or the Jack, I may as well duck (see below for why this could fail). LHO may have Ax. And if RHO played the J, from an initial holding of Jx, I am fine with him holding the trick...he can't play another trump.

If the J or 10 appears on the first round, and the K holds, I duck the next trump to LHO.

If the J or 10 appears on the first round and RHO wins the Ace, we generate the interesting position. What does RHO return and what do we do next?

We'd like to get to dummy to lead low towards Q9x, to cater to the 4-1 onside. I think we need to do this even tho it can cause problems on some layouts.

Imagine a spade switch by RHO, or for that matter a diamond switch. In both instances we use a diamond to get to dummy to play a trump. Say the 9 holds, LHO showing out.

Now we play spades, ruffing....but RHO may overruff and return his last diamond and we can't squeeze LHO who was 4=1=4=4. Even worse, we've lost 3 tricks by now and RHO still has a trump out, and we're in dummy.

At the table I wouldn't think any deeper than this, unless playing a long match where one can take almost as long as one wants on tough hands. I'd conclude that there probably isn't any counter to this.

Note that LHO may have J10 tight or J10x. However, I'm okay in either event. I can afford two trump losers, and can draw the third round (and of course LHO might play a 3rd round if he had J10x), because I can establish diamonds if they are 4-2 or spades if they are 3=3 (and can test both).

So low to the King, and play low back to the 9.

As for how the opps should defend...if LHO has 4 trump, it is easy: he plays low on the first round. If RHO has 4, then he could screw me up, on some layouts, by ducking the K with AJ10x. I duck his Jack (or 10) on the next round, and he plays Ace and another, drawing all my trumps and now I need diamonds to break, since I don't have the count for a squeeze should LHO be 4=4 in the pointed suits. That defence doesn't work if LHO had a stiff honour: my 9 holds and I ignore trump thereafter.

[lamford]

Fair point about the club pips. The lead was the seven, and East returned the four and West played the eight on the second round. The clubs could be anything, with 87xx(x) with West the leader in the club house. When you lead a heart towards the king, how do you play
a) if West plays the four
b) if West plays the eight
c) if West plays the ten or jack?
I don't think East has any game theory to follow, and the only interesting position is ♥JT84 with West ... I think he has a Nash equilibrium, but I may be mistaken.

[mikeh]

 lamford, on 2018-September-14, 12:02, said:

Fair point about the club pips. The lead was the seven, and East returned the four and West played the eight on the second round. The clubs could be anything, with 87xx(x) with West the leader in the club house. When you lead a heart towards the king, how do you play
a) if West plays the four
b) if West plays the eight
c) if West plays the ten or jack?
I don't think East has any game theory to follow, and the only interesting position is ♥JT84 with West ... I think he has a Nash equilibrium, but I may be mistaken.

I explained how I would play were West to play the 10 or the Jack on the first lead of trump.

The rest of it is bordering on metaphysical, and to some degree depends on whether the defenders are giving off information by way of tells.

I am going to omit the detailed analysis, but it seems to me clear (having done the analysis) that, should LHO produce either the 4 or the 8, without any tempo issues, the percentage play is the King. I will add this: when the spot is the 4, the odds are equal as to stiff 4 in LHO's hand or stiff Ace in RHO's hand, and the deciding factor is that ducking costs an overtrick when LHO has A4.

Even tho the edge for the King is slight, no good player would throw that away unless playing for a swing or picking up on cues from the table action.

In reality, many opps will fail to play the 4 or the 8 smoothly when they hold 4 trump, and as soon as declarer gets that vibe, the odds change. But note that the odds are now dependent on reading the opps' tempo breaks and not the percentages in the suit itself.

[lamford]

I think the right strategy from JT84 is for West to play the 4 and 8 equally often, and NEVER to play the ten or jack, or declarer should duck and win against both a singleton honour and against JT8x. I agree that the king is the technically better card as it can make an overtrick, but I think in practice, almost all Wests will play the four much more often than the eight, and the right play is to duck if West plays the four, but to rise if he plays the eight. I think the potential overtrick is not as significant as the extra chance to make the contract.

[mikeh]

 lamford, on 2018-September-14, 18:20, said:

I think the right strategy from JT84 is for West to play the 4 and 8 equally often, and NEVER to play the ten or jack, or declarer should duck and win against both a singleton honour and against JT8x. I agree that the king is the technically better card as it can make an overtrick, but I think in practice, almost all Wests will play the four much more often than the eight, and the right play is to duck if West plays the four, but to rise if he plays the eight. I think the potential overtrick is not as significant as the extra chance to make the contract.

Personally, my thinking is that many west’s would think nothing of playing the 8 from J1084, in order to ‘force the Ace’. I guess we play different types of weak defenders, lol

[PhantomSac]

How are we cold on 3-2 trumps? Am I missing something?

Assuming I am not and we are not actually cold on 3-2 trumps I think a reasonable line if a trump to the king wins is just to play ace king and ruff a diamond. Assuming the HA is on my left and they aren't doing some shenanigans that seems to ensure me on 3-2 trumps, and it seems like I have no play on 4-1 trumps.

If I play play trump trump and they are able to pull 2 trumps and play a club it seems like I only have 2 trumps + 3 diamonds + 1 club + 2 spades + 1 ruff, and my entries will be severely messed up to even ruff out a suit whichever hand I take the ruff in (if I ruff in my hand I cannot ruff a diamond in my hand and also have no entry to ruff out spades and cash them, if I ruff in dummy I can no longer ruff a spade in dummy and I also can't ruff a diamond since I have no way to get back there).

Sorry if this is nonsense, posting late at night and I'm a novice poster now obv

[mikeh]

 PhantomSac, on 2018-September-15, 01:42, said:

How are we cold on 3-2 trumps? Am I missing something?

Assuming I am not and we are not actually cold on 3-2 trumps I think a reasonable line if a trump to the king wins is just to play ace king and ruff a diamond. Assuming the HA is on my left and they aren't doing some shenanigans that seems to ensure me on 3-2 trumps, and it seems like I have no play on 4-1 trumps.

If I play play trump trump and they are able to pull 2 trumps and play a club it seems like I only have 2 trumps + 3 diamonds + 1 club + 2 spades + 1 ruff, and my entries will be severely messed up to even ruff out a suit whichever hand I take the ruff in (if I ruff in my hand I cannot ruff a diamond in my hand and also have no entry to ruff out spades and cash them, if I ruff in dummy I can no longer ruff a spade in dummy and I also can't ruff a diamond since I have no way to get back there).

Sorry if this is nonsense, posting late at night and I'm a novice poster now obv

Ok, cold was an overbid

[PhantomSac]

 mikeh, on 2018-September-15, 01:46, said:

Ok, cold was an overbid

Ya I just mean even if they aren't going to unblock the jack from Jx (which I doubt people would), AJx on our left is fairly significant portion of the 3-2's with the ace on our left and then we will end up needing 3-3 diamonds, I think catering to that + 4-2 diamonds trumps other considerations, especially since I don't really see what else we can cater to. Lamfords line of leading a trump and ducking it just seems insane to me though, they just play a club and we are often wrecked. In a dream world it goes trump to the king and they win the ace and now we are basically cold on 3-2 trumps barring some disaster haha. I think we want to have the tempo here.

ETA: Nice posting with you again btw mike, hope all is well!