[FrancesHinden]

Play Swiss teams, 7-board matches, IMPs converted to VPs on a 20-0 scale.
Your two hands are

Scoring: IMP

---

At both tables the auction starts 1C from South, a 1S overcall from West, double from North and 2S from East. The auctions then diverge.

At one table, your team plays in 5C on a spade lead. The play is mildly interesting, but you emerge with 11 tricks for +600.

At the other table, the opposing team play in 3NT on a spade lead. They go off, because clubs are 4-0 onside. Declarer looks slightly embarrassed about going off in a makeable contract (B/I problem: what is the best technical line for 9 tricks?) but then defends himself by saying:

Yes, I could have won the spade lead, crossed to the ace of clubs and made 9 tricks by overtaking the queen of diamonds. This picks up the 4-0 club break. However, all the rest of the time I've given up an overtrick. If they are +600 at the other table, then I've cost myself 1 imp 93% of the time (given that spades are 5-3) but avoided losing 12-13 imps 7% of the time. So I took the right line.

You could argue that his odds are slightly out, because the opponents have bid to the 2-level, vulnerable, on a combined 13-count with an 8-card fit so are more likely to have some shape. But suppose he's right about the percentages.

Did he take the right line?

[OleBerg]

The most important thing is, how partner will feel about you going down in a cold contract.


Another, very less important, thing is the state of the match.
If you have a big lead, the IMP's you lose are more costly than the IMP's you gain (As the VP scale is not linear). Likewise, if you are trailing a lot, the IMP's you gain are more precious than those you loose.

So the percentages has to be adjusted, if there is a big difference in IMP's.

I have never had the patience to calculate such things, but I feel sure the difference has to big, to even warrant consideration.

[Winstonm]

A 7-board match that is then converted to VPs to me is more like matchpoints anyway - the idea is to get all the VPs as often as possible. Under this form of scoring I think he or she was right to play for the overtrick.

[orlam]

How certain is it that the other table is +600?

[mtvesuvius]

Looks to me like I want to take the sure thing. I will secure my plus.

[helene_t]

His calculations seem ok - I don't care how the IMPs are coverted to VPs, it doesn't matter much, especially when the state of the match is unknown.

He is making the assumption that the other table play 3NT as well, or 5♣. If something completely different happens at the other table, the overtrick may not result in one IMP, and making the contract may give more than 12-13 IMPs (or less, if the contract at the other table is 6♣ made).

So if he isn't confident that the other table is playing a game contract also, he should probably play safe.

[ArtK78]

Playing for overtricks at IMPs is sometimes undervalued. However, when the IMP score is converted to VPs, a one-IMP difference will mean absolutely nothing most of the time. But the difference between making and going down in a vul game is ALWAYS relevant (except when there is a blitz regardless of the result on this hand).

So, assuming that declarer's IMP odds calculation is accurate, and he will be plus IMPs (a very small amount) in the long run, he will still be minus VPs in the long run.

Aside from that, declarer's IMP odds calculation assumed that the opponents would make a vul game at the other table. Suppose that was not the case? Suppose the opps had some sort of accident - going down in slam, or failing to get to game. That changes the IMP odds significantly. Now the overtrick may not even be worth an IMP, but going down in game still costs a great deal.

[kfay]

OleBerg, on Jan 22 2009, 12:35 PM, said:

The most important thing is, how partner will feel about you going down in a cold contract.

I think this is basically what Kelsey says in Bridge Odds for Practical Players. This mental defeat can't really be calculated.

Having said that... 7 board match. Living in a vacuum I agree with him I guess. But if I were his partner I definitely would not.

[bid_em_up]

His problem is that the 1 imp difference on this one board is unlikely to change the overall VP result. He would need to accumulate several one imp advantanges in order for it to make any significant difference.

But going down one will be a huge difference in the VP score. Assume all other boards were pushes, he goes from winning 11-9 (by making the overtrick), to losing either 6-14 or 5-15.

Of course, its also dependent on whether this is an early match in the day, where your draw for opponents will be different (its better to have a small win than a big loss), or the last match of the day, where all that matters is that you win.

jmoo.

[Winstonm]

20 Point Victory Scale
IMP Difference
6-8 Boards Victory Points IMP Difference
0 10-10
1-2 11-9
8-10 14-6
11-13 15-5
A 1-imp overtrick changes the VP from a 10-10 tie to an 11-9 win. 10-imp loss loses 4 VP and a 12-imp loss converts to 5 VP. If the odds are 90%, then it looks to me like a clear 9/4 or 9/5 favorite to go for the overtrick.

[OleBerg]

bid_em_up, on Jan 22 2009, 10:08 PM, said:

His problem is that the 1 imp difference on this one board is unlikely to change the overall VP result.  He would need to accumulate several one imp advantages in order for it to make any significant difference.

It's not that unlikely, to be in a position where the gain of one IMP will win a VP, and the loss of a game will cost only a VP. (Well actually, if you are trailing big, you can be in a situation, where one IMP will give a VP, while the loss will cost you nothing.)

Of course it is more likely that the one IMP will not matter, but you cannot discard it as having no value, just because it is unlikely to make a difference.

All IMP's are basicly worth the same (roughly), when the match is equal.

If you know the state of the match (running scores on BBO ), that's a whole other ball-game. But as you are almost always guessing here, it is probably best to assume it is equal, unless something else is very obvious.

[OleBerg]

kfay, on Jan 22 2009, 09:06 PM, said:

OleBerg, on Jan 22 2009, 12:35 PM, said:

The most important thing is, how partner will feel about you going down in a cold contract.

I think this is basically what Kelsey says in Bridge Odds for Practical Players. This mental defeat can't really be calculated.

Yes, I knew I was stealing from somebody, couldn't remember who though.

(You know, with all the stealing I do...)

[hotShot]

How many chances to gain IMP's do you get in a 7 board match if your opps are of comparable strength?

93% seems to be a reasonable IMP to gain. And without deep thinking, you will expect that 5♣ will be in trouble too if the ♣ split 4-0.

[mikeh]

I think the arithmetical argument is inappropriate in this sort of case, and, in any event, cannot properly address all of the factors that should be considered.

I have never, ever been upset or had any teammate upset when in the comparison, we lost an imp on an overtrick where our declarer sacrificed the imp to ensure the contract, even when the overtrick was extremely odds-on.

But: go down in a cold vulnerable game, looking for the imp overtrick????? Do that very often, and you may have to find new teammates

The reality is that even against teams of fairly comparable strength, and even in a short 7 board match, there will usually be 2 or 3 swings of 5 - 12 imps. The results that usually determine who wins, at the end of the day, are the double-digit swings. I just don't feel, and it is a question of feel, not calculation, that risking an infrequent potentially event-deciding adverse swing to pick up an imp is justifiable.

Yes, I am sure most of us have had results in which a single imp has played a decisive role, but, realistically, they are infrequent. Very few events are decided by the winner having 1 vp more than the second place team. Far more events are decided by the 4 or 5 vps that a vul. game swing costs.

And we shouldn't worry about the board, or even (usually) about the match... in a vp event, we are really playing a 56 board or longer match, and we should worry about the event.

Now, if we were in the last round, playing for the event, with a very tight lead or lag over or to our opp... and this were board 1 or any later board with the match still apparently tight... now the overtrick is probably worth going for.

[helene_t]

Obviously the expected VP gain from a 1 IMP overtrick swing is less then that of a 10 IMP down-in-cold-game swing, but I see no reason to expect it to be, on average, less than a tenth of the VP loss from the 10 IMP swing. That is the relevant figure.

Of course if the teammates are known to have an irrational affinity with safety play and you want to win the post mortem, go for it.

[Echognome]

I think a correction to the probabilities is in order. The chance that 1 imp will give you an extra VP is less than 1. I don't know the exact probability, because there are scores for which the probability is zero (such as us already leading or behind by 60 imps), but let's say it's somewhere around 1/3, because of the IMP bands around the VP scale. Now the 12 imp loss will affect our VP score at a much higher percentage (not 1, because we might already be losing by 60 or winning by enough that a 12 imp loss still means no VP swing). So when we make the calculations not in terms of an expected IMP swing, but rather an expected VP swing, we see that the 1 imp gain is only worth say 0.3 VPs, whereas the expected VP loss is worth probably something around 5 VPs. So now you need to have odds of 5.0:0.3 or around 94%. These figures make it very close and since I have approximations above, could not be used to make the decision in this case. However, what I'm saying is that we should be doing VP expectations, not IMP expectations.

[mtvesuvius]

I think all this math is nice, but it's not really what matters here imo. Mike's post was the closest to reality, and I agree entirely with it. The psychological factor also plays a big role; if you go down in a cold contract, not only will you, your partner, and partners be mad, but they may not have been in game at the other table! Or bid game and gone down... Why risk this? In addition, 1 IMP will very rarely change your VP score, and even if it does it will almost never affect where you place in an event. Then there is the 10 IMP loss. This will be a loss of around 4 or 5 VPs, an event is often decided by 4 VPs. ofc there are other situations, like Mike said, if you are probably tied with the 1st place team, then maybe it's worth it. Otherwise, take the plus 600 and go home. I really disagree about 1 IMP mattering in any event, and if it does, there will always be another board with a bigger swing, and other opportunities.

[Echognome]

mtvesuvius, on Jan 22 2009, 03:46 PM, said:

I think all this math is nice, but it's not really what matters here imo. Mike's post was the closest to reality, and I agree entirely with it. The psychological factor also plays a big role; if you go down in a cold contract, not only will you, your partner, and partners be mad, but they may not have been in game at the other table! Or bid game and gone down... Why risk this? In addition, 1 IMP will very rarely change your VP score, and even if it does it will almost never affect where you place in an event. Then there is the 10 IMP loss. This will be a loss of around 4 or 5 VPs, an event is often decided by 4 VPs. ofc there are other situations, like Mike said, if you are probably tied with the 1st place team, then maybe it's worth it. Otherwise, take the plus 600 and go home. I really disagree about 1 IMP mattering in any event, and if it does, there will always be another board with a bigger swing, and other opportunities.

I agree with all this (and mikeh's post). I am only offering what I think is a correction that would be needed if one wanted to make a calculation. Using IMP odds does not work, because the scoring is in VPs converted from IMPs. The IMP odds quoted, ignore the VP conversion.

[mtvesuvius]

Echognome, on Jan 22 2009, 06:49 PM, said:

I am only offering what I think is a correction that would be needed if one wanted to make a calculation. Using IMP odds does not work, because the scoring is in VPs converted from IMPs. The IMP odds quoted, ignore the VP conversion.

I agree, and yours was certainly the closest to an accurate mathamatical estimation .

[Winstonm]

Truth be told, I don't ever remember purposely playing for an overtrick at imps if it risked my contract - in fact, I am certain I have never done so. I am also certain I do not know everything there is to know about the game and am willing to learn that the math might suggest - especially in a 7-board match - that playing for overtricks might be the best stategy.

The same principle can be applied to defense - if there is a play that will defeat the contract 10% of the time but give away an overtrick 90% of the time do you make the play?

I think the question cannot be answered properly without takiing into consideration the length of match. In my mind, 1-imp is worth much more in a 7-board match than over 28 or 32 boards.