[mangurian]

I am in 4 spades playing match point duplicate.
I have a laydown 10 tricks.

The defenders have not bid and no reliable count has been revealed.
There are still hearts out.
The last 6 tricks come down to the following (I am in south).
All trump are out. Everyone figures to be in 4 spades.

----
----
Kx
AJ10x


xx
---
xx
xx

All I need are my two spade tricks and the club ace to make my contract.
What is the proper plan? At imps I would take my tricks.

[BunnyGo]

A lot of it depends on what the original hand was--so it's hard to say without seeing everything (including the opening lead). For example, if it's reasonable to think that most tables will try 3NT and make 10 tricks, then I better play for more than 10 tricks. If I think it's a game that most people won't bid (say only 21 pts and most will stop in a partscore) then I better cash out my 10 tricks.

[daveharty]

Unfortunately the director might have to get involved, since your hand and the dummy don't have the same number of cards.

Assuming that was not actually the case, then BunnyGo is correct: it depends on what you think is going on at other tables. If this is a completely normal contract reached by a simple standard auction (1S-3S-4S or whatever), then you should probably play for the most tricks you can, as long you are more likely than not to make it. If you eschew a 100% line for ten tricks in favor of a 75% line for 11, then even if you go down you should have some company.

[mangurian]

daveharty, on 2012-February-11, 16:18, said:

Unfortunately the director might have to get involved, since your hand and the dummy don't have the same number of cards.

Assuming that was not actually the case, then BunnyGo is correct: it depends on what you think is going on at other tables. If this is a completely normal contract reached by a simple standard auction (1S-3S-4S or whatever), then you should probably play for the most tricks you can, as long you are more likely than not to make it. If you eschew a 100% line for ten tricks in favor of a 75% line for 11, then even if you go down you should have some company.

When I played this hand, I estimated the probability of 11 tricks was very high.
It only fails if the diamond ace AND both club honors are with east.
I guess I am asking how much of an edge you need to take the risk.

[BunnyGo]

mangurian, on 2012-February-11, 17:06, said:

When I played this hand, I estimated the probability of 11 tricks was very high.
It only fails if the diamond ace AND both club honors are with east.
I guess I am asking how much of an edge you need to take the risk.

The point is, that it matters what's going to happen at the other tables, and judging this is a very difficult skill to master. For example, I once played a hand in 4♥ in a 4-3 fit when 3NT should be the normal (and better) spot. I noticed that in 3NT or 4♥ there were 10 easy tricks all day, so I took a roughly 15% line to make 11 tricks in 4♥ risking -1 85% of the time. Why? Because a 420 was going to be worth 0 matchpoints, just like a -50.

Imagine if your traveler (excluding your score) is:

170 7 times
420 2 times

Then 420 100% of the time gets you 8/9 matchpoints and 450 75% of the time gets 9/9 and -50 gets you 0. In this case, taking the 420 sounds pretty good.

If the traveler is

420 5 times
450 5 times

And there's a lead that would make 11 tricks easy (but your opponents weren't kind) then it's probably worth taking 50% or better odds for the overtrick.

The point is, the odds that matter are situational, and simply seeing the remaining 6 cards without seeing the whole hand doesn't give enough information to say whether 76% odds are good enough.

[daveharty]

You may want to check out Kit Woolsey's Matchpoints, which deals at length with such issues. It's a good read.

[CSGibson]

mangurian, on 2012-February-11, 17:06, said:

When I played this hand, I estimated the probability of 11 tricks was very high.
It only fails if the diamond ace AND both club honors are with east.
I guess I am asking how much of an edge you need to take the risk.

What everyone's telling you is that it's highly contextual. You have to take into account the possible position you are in, match point wise, before calculating what your expected risk/reward is for taking overtricks.

In helping evaluate, you should ask the following questions:

1) is this a normal contract?

If you've bid a minor suit slam or some tight major suit game which the field is not likely to be in, then you might have 9 of 10 match points just for being in the higher scoring contract. I would not risk my contract because taking risk for the overtrick has very little potential reward (1 mp) with regard to the risk (9 mp). On the other hand, if I am in an inferior part score contract from the normal, I would risk going down in my contract for any chance to get a higher score than those that would be in the better and more normal contract.

2) has the play so far been normal?

Has the defense already given you a trick or two? If so, you may be sitting on a mp score of 7 or 8 of 10 without additional risk. I would need a very high probability of an extra trick to risk what I've already gained. 75% looks about right (and on your scenario, I would place the percentage of all of the cards being wrong with no opposing bidding at being something like 5-10%, depending on the rest of the hand, of course). On the other hand, if the defense has been particularly sharp, or you've already dropped a trick in declarer play, then you might be sitting on a 1 or 2 match points out of 10, so I might take a lesser chance for an extra trick (even 30 or 40%, on some occasions) just to get back to par.

Ideally, you would like a formula, like this:

if expected matchpoints (safe play) < the multiple of the expected matchpoints (risky play succeeds) multiplied by the percentage of the risky play being successful, added to the expected matchpoints (risky play fails) multiplied by the percentage of the risky play failing, then you should make the risky play.

Of course, this all depends on you being able to tell what is the normal contract and the normal play, which is not necessarily easy for most players, since it is contextual on the field in which you play.

[BunnyGo]

daveharty, on 2012-February-11, 17:31, said:

You may want to check out Kit Woolsey's Matchpoints, which deals at length with such issues. It's a good read.

I second this, it's a good book for the advancing player and really helped my matchpoint bidding judgement and play a lot. If I had it available, I'd probably read it again.

[manudude03]

It's not really accurate, but a quick test I use is to estimate the score I am getting if I take my cold tricks, and then I will only take the risk if the probability of it working out exceeds that. On this particular board, instinctively, I am taking the risk very often, even if everything is wrong, you may just wind up with the 10th trick anyway (say East has 0 or 1 hearts left...)