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Why angels did not arise in bridge earlier? I do not know about chess. But they need angels exactly as we do. In many chess positions during - so called mittelspiel - it is impossible to prove that certain move is optimal. Paradoxically neither computers or any kind of robots or products of AI nor best players assisted by coaches do not solve the problem in general. Formulation of problem is very natural, while not easy. Assume we consider 2 chess moves of player P in a given position: A and B.

A is better if after a “long” sequence of optimal moves reaches better position for P than the “final” position after move B.

One may say that in bridge is differently. Say player is thinking what to do in the third trick. And also has 2 choices: A and B. There are 11 tricks to play and 40 decisions to make (in the last trick there is no decision).

In fact sequences after A and B can have different lenghts in both games. In chess the “long” sequence can consist of 36 pairs of moves for inicial móve A and 31 for B.

The same in bridge: We may have claiming in 6-th trick after A and in 8-th trick after B.

In both games all moves after A and B must be invented by angels. To be continued.

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Rosalind's comments are very accurate. In this quiz we will talk about declarer's play. But North has a big Chance to be a bidding angel i.e. 4♥ is a candidate to be an optimal bid within Polish Club!

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Dear Richard and Craig, I'm a mathematician, who elaborated a theory - especially - oriented for declarer's play and defense. Nothing can be understood if reader would not feel the notion od player's angel, who knows optimal moves (to be continued).

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Some inferences that should be done. They can make 2 ruffs. E showed the way how to do it playing ♣9. This says: you can reach me in higher between the reds. W made somewhat strange decisions taking that into account…

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Talking about IMPs scoring: IMHO 3♥ is obvious. The only value, I have, which is doubtful is ♠K. Lefty can have AQ e.g. Everything else is perfect. Pd knows that my possible spades values can be lost. So his decision about 4♥ should depend on his spades values.

At MPs 3♦ is bad because it does not confrm hearts fit. Pd may bid 3♠ or even 4♠.

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This would be absolutely obvious at IMPs. Here both options are risky. Pass has an additional possibility: N will go to 3♣. Who know if it is good for us or bad…

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Kit raised an important point, which I never considered. Double after Stayman makes other problem than after Texas. After Texas opener can pass the double with minumum HCPs, because he knows wether his side has fit (with tripleton, say) or not (with doubleton). After doubled Stayman pass makes troubles when opps will bid at level 3!

Andrzej Matuszewski

I do not know about chess. But they need angels exactly as we do.

In many chess positions during - so called mittelspiel - it is impossible to prove that certain move is optimal. Paradoxically neither computers or any kind of robots or products of AI nor best players assisted by coaches do not solve the problem in general.

Formulation of problem is very natural, while not easy.

Assume we consider 2 chess moves of player P in a given position: A and B.

A is better if after a “long” sequence of optimal moves reaches better position for P than the “final” position after move B.

One may say that in bridge is differently. Say player is thinking what to do in the third trick. And also has 2 choices: A and B. There are 11 tricks to play and 40 decisions to make (in the last trick there is no decision).

In fact sequences after A and B can have different lenghts in both games. In chess the “long” sequence can consist of 36 pairs of moves for inicial móve A and 31 for B.

The same in bridge: We may have claiming in 6-th trick after A and in 8-th trick after B.

In both games all moves after A and B must be invented by angels.

To be continued.

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

https://www.bridgebase.com/tools/handviewer.html?sn=mata2015&s=SQT976HAJD72CQT96&wn=bela&w=SA5H75DQJT983C432&nn=Mitko_Vn&n=S4H964DAK65CAK875&en=raj21&e=SKJ832HKQT832D4CJ&d=e&v=e&b=6&a=PP2D3C3H3SPPP&p=H7H4HQHAC6C3CKCJS4S2S9SAH5H6HKHJHTS6C2H9CQC4C5S3H8S7DQD5CTS5C7

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

They can make 2 ruffs. E showed the way how to do it playing ♣9. This says: you can reach me in higher between the reds.

W made somewhat strange decisions taking that into account…

Andrzej Matuszewski

Andrzej Matuszewski

The only value, I have, which is doubtful is ♠K. Lefty can have AQ e.g.

Everything else is perfect.

Pd knows that my possible spades values can be lost. So his decision about 4♥ should depend on his spades values.

At MPs 3♦ is bad because it does not confrm hearts fit. Pd may bid 3♠ or even 4♠.

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski

Andrzej Matuszewski